BSSN formalism - code generation

${{{ \eta} _I} _J} = {\overset{I\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}}$
${{{ \eta} ^I} ^J} = {\overset{I\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}}$
${{{ \hat{\gamma}} _i} _j} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}}$
${\hat{\gamma}} = {1}$
${{{{ \hat{\Gamma}} _i} _j} _k} = {\overset{i\downarrow[{j\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{{{ \hat{\Gamma}} _I} _J} _K} = {\overset{I\downarrow[{J\downarrow K\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{{{ \hat{\Gamma}} ^I} _J} _K} = {\overset{I\downarrow[{J\downarrow K\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{ \hat{\Gamma}} ^I} = {\overset{I\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}}$
${{ \hat{\gamma}} _{,i}} = {\overset{i\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}}$
variable: $\alpha$
eqn:${{ \alpha} _{,t}} = {{{{{ \alpha} _{,i}}} {{{ \beta} ^I}} {{{{ e} ^i} _I}}} + {{{-1}} {{K}} {{f}} {{{\alpha}^{2}}}}}$
new eqn: ${{dt_alpha}} = {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _i}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}}} + {{{-1}} {{f}} {{{U->alpha}^{2}}} {{U->K}}}}$



double dt_alpha = -1. * U->K * f * U->alpha * U->alpha + U->beta_U.z * partial_alpha_l.z + U->beta_U.y * partial_alpha_l.y + U->beta_U.x * partial_alpha_l.x;

variable: $\beta$
eqn:${{{ \beta} ^I} _{,t}} = {{ B} ^I}$
new eqn: ${{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_beta_U.x} \\ {dt_beta_U.y} \\ {dt_beta_U.z}\end{matrix} \right]}} ^I} = {{ \overset{i\downarrow}{\left[ \begin{matrix} {U->B_U.x} \\ {U->B_U.y} \\ {U->B_U.z}\end{matrix} \right]}} ^I}$



double dt_beta_U.x = U->B_U.x;
double dt_beta_U.y = U->B_U.y;
double dt_beta_U.z = U->B_U.z;

variable: $B$
eqn:${{{ B} ^I} _{,t}} = {{{{-1}} {{\eta}} \cdot {{{ B} ^I}}} + {{{3}} \cdot {{\frac{1}{4}}} {{{{ \bar{\Lambda}} ^I} _{,t}}}}}$
new eqn: ${{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_B_U.x} \\ {dt_B_U.y} \\ {dt_B_U.z}\end{matrix} \right]}} ^I} = {{{{-1}} {{\eta}} \cdot {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->B_U.x} \\ {U->B_U.y} \\ {U->B_U.z}\end{matrix} \right]}} ^I}}} + {{{3}} \cdot {{\frac{1}{4}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_LambdaBar_U.x} \\ {dt_LambdaBar_U.y} \\ {dt_LambdaBar_U.z}\end{matrix} \right]}} ^I}}}}$



double tmp2 = 1. / 4.;
double dt_B_U.x = 3. * tmp2 * dt_LambdaBar_U.x + -1. * U->B_U.x * \eta;
double dt_B_U.y = 3. * dt_LambdaBar_U.y * tmp2 + -1. * U->B_U.y * \eta;
double dt_B_U.z = 3. * dt_LambdaBar_U.z * tmp2 + -1. * U->B_U.z * \eta;

variable: $W$
eqn:${{ W} _{,t}} = {{{{\frac{1}{3}}} {{K}} {{W}} {{\alpha}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{W}} {{{{ \beta} ^I} _{,i}}} {{{{ e} ^i} _I}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{W}} {{{ \beta} ^I}} {{{{{ e} ^i} _I} _{,i}}}} + {{{{ W} _{,i}}} {{{ \beta} ^I}} {{{{ e} ^i} _I}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{W}} {{{ \bar{\gamma}} _{,i}}} {{{ \beta} ^I}} {{{{ e} ^i} _I}} {{\frac{1}{\bar{\gamma}}}}}}$
new eqn: ${{dt_W}} = {{{{\frac{1}{3}}} {{W}} {{U->alpha}} \cdot {{U->K}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{W}} {{{{ \overset{I\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^I} _i}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{W}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{{{{ \overset{i\downarrow[{I\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _I} _i}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {partial_W_l.x} \\ {partial_W_l.y} \\ {partial_W_l.z}\end{matrix} \right]}} _i}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{W}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _i}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{\frac{1}{{det_gammaBar}}}}}}$



double tmp7 = 1. / 3.;
double dt_W = tmp7 * U->K * U->alpha * W + -1. * tmp7 * W * (partial_beta_Ul[0].x + partial_beta_Ul[1].y + partial_beta_Ul[2].z) + U->beta_U.z * partial_W_l.z + U->beta_U.y * partial_W_l.y + U->beta_U.x * partial_W_l.x;

variable: $K$
eqn:${{ K} _{,t}} = {{{{4}} {{S}} {{\alpha}} \cdot {{\pi}}} + {{{W}} {{{ W} _{,a}}} {{{ \alpha} _{,b}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}}} + {{{-1}} {{{{ \alpha} _{,a}} _{,b}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{W}^{2}}}} + {{{{ \alpha} _{,a}}} {{{ \bar{\Lambda}} ^A}} {{{{ e} ^a} _A}} {{{W}^{2}}}} + {{{-1}} {{{ \alpha} _{,a}}} {{{ \mathcal{C}} ^A}} {{{{ e} ^a} _A}} {{{W}^{2}}}} + {{{{ \alpha} _{,a}}} {{{ \hat{\Gamma}} ^A}} {{{{ e} ^a} _A}} {{{W}^{2}}}} + {{{{ K} _{,a}}} {{{ \beta} ^A}} {{{{ e} ^a} _A}}} + {{{-1}} {{{ \beta} ^F}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _F} _D} _{,e}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^e} _E}} {{{{{ e} _a} ^B} _{,e}}}} + {{{-1}} {{{ \beta} ^F}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _F} _G}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^G} _{,e}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^G}} {{{{ e} ^a} _A}} {{{{{ \bar{\gamma}} _D} _G} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^C} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{A}} _G} _C}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^e} _E}} {{{{{ e} _e} ^G} _{,a}}}} + {{{{ \beta} ^F}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _F} _E} _{,d}}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{ e} _a} ^C} _{,d}}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _A} _G}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _e} ^G} _{,d}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^D} ^C}} {{{{ e} ^a} _A}} {{{{{ \bar{A}} _D} _C} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _D} _C}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ e} _b} ^D} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _B} _E}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^E} _{,a}}}} + {{{\alpha}} \cdot {{{K}^{2}}}} + {{{-12}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}}} + {{{\alpha}} \cdot {{{{ R} _A} _B}} {{{{ \bar{\gamma}} ^A} ^B}} {{{W}^{2}}}}}$
new eqn: ${{dt_K}} = {{{{4}} {{S}} {{U->alpha}} \cdot {{{M_PI}}}} + {{{W}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_W_l.x} \\ {partial_W_l.y} \\ {partial_W_l.z}\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _b}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}}} + {{{-1}} {{{{ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_alpha_ll.xx} & {partial2_alpha_ll.xy} & {partial2_alpha_ll.xz} \\ {partial2_alpha_ll.xy} & {partial2_alpha_ll.yy} & {partial2_alpha_ll.yz} \\ {partial2_alpha_ll.xz} & {partial2_alpha_ll.yz} & {partial2_alpha_ll.zz}\end{matrix} \right]}} _a} _b}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{W}^{2}}}} + {{{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->LambdaBar_U.x} \\ {U->LambdaBar_U.y} \\ {U->LambdaBar_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}} + {{{-1}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {C_U.x} \\ {C_U.y} \\ {C_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}} + {{{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{A\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}} + {{{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_K_l.x} \\ {partial_K_l.y} \\ {partial_K_l.z}\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{F\downarrow[{D\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _F} _D} _e}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{a\downarrow[{B\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^B} _e}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _F} _G}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{G\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^G}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{D\downarrow[{G\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _D} _G} _a}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{C\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^C} _a}}} + {{{-1}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _G} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{e\downarrow[{G\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{F\downarrow[{E\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _F} _E} _d}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{a\downarrow[{C\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _d}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _A} _G}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{e\downarrow[{G\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{D\downarrow[{C\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xx} & {partial_ABar_LLl[1].xx} & {partial_ABar_LLl[2].xx} \\ {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz}\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].yy} & {partial_ABar_LLl[1].yy} & {partial_ABar_LLl[2].yy} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz}\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz} \\ {partial_ABar_LLl[0].zz} & {partial_ABar_LLl[1].zz} & {partial_ABar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _D} _C} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _D} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{b\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _a}}} + {{{{U->K}^{2}}} {{U->alpha}}} + {{{-12}} {{U->alpha}} \cdot {{U->rho}} \cdot {{{M_PI}}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {R_LL.xx} & {R_LL.xy} & {R_LL.xz} \\ {R_LL.xy} & {R_LL.yy} & {R_LL.yz} \\ {R_LL.xz} & {R_LL.yz} & {R_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{W}^{2}}} {{U->alpha}}}}$



double tmp36 = W * W;
double tmp52 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xx;
double tmp53 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xx;
double tmp54 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xx;
double tmp55 = tmp52 + tmp53;
double tmp56 = tmp54 + tmp55;
double tmp57 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xy;
double tmp58 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xy;
double tmp59 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xy;
double tmp60 = tmp57 + tmp58;
double tmp61 = tmp59 + tmp60;
double tmp62 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xz;
double tmp63 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xz;
double tmp64 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xz;
double tmp65 = tmp62 + tmp63;
double tmp66 = tmp64 + tmp65;
double tmp67 = gammaBar_UU.xy * tmp61;
double tmp68 = gammaBar_UU.xz * tmp66;
double tmp72 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xx;
double tmp73 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xx;
double tmp74 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xx;
double tmp75 = tmp72 + tmp73;
double tmp76 = tmp74 + tmp75;
double tmp77 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xy;
double tmp78 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xy;
double tmp79 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xy;
double tmp80 = tmp77 + tmp78;
double tmp81 = tmp79 + tmp80;
double tmp82 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xz;
double tmp83 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xz;
double tmp84 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xz;
double tmp85 = tmp82 + tmp83;
double tmp86 = tmp84 + tmp85;
double tmp87 = gammaBar_UU.xy * tmp81;
double tmp88 = gammaBar_UU.xz * tmp86;
double tmp92 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xx;
double tmp93 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xx;
double tmp94 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xx;
double tmp95 = tmp92 + tmp93;
double tmp96 = tmp94 + tmp95;
double tmp97 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xy;
double tmp98 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xy;
double tmp99 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xy;
double tmp100 = tmp97 + tmp98;
double tmp101 = tmp99 + tmp100;
double tmp102 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xz;
double tmp103 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xz;
double tmp104 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xz;
double tmp105 = tmp102 + tmp103;
double tmp106 = tmp104 + tmp105;
double tmp107 = gammaBar_UU.xy * tmp101;
double tmp108 = gammaBar_UU.xz * tmp106;
double tmp255 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yy;
double tmp256 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yy;
double tmp257 = gammaBar_UU.xx * partial_gammaBar_LLl[0].yy;
double tmp258 = tmp255 + tmp256;
double tmp259 = tmp257 + tmp258;
double tmp260 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yz;
double tmp261 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yz;
double tmp262 = gammaBar_UU.xx * partial_gammaBar_LLl[0].yz;
double tmp263 = tmp260 + tmp261;
double tmp264 = tmp262 + tmp263;
double tmp275 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yy;
double tmp276 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yy;
double tmp277 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yy;
double tmp278 = tmp275 + tmp276;
double tmp279 = tmp277 + tmp278;
double tmp280 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yz;
double tmp281 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yz;
double tmp282 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yz;
double tmp283 = tmp280 + tmp281;
double tmp284 = tmp282 + tmp283;
double tmp295 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yy;
double tmp296 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yy;
double tmp297 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yy;
double tmp298 = tmp295 + tmp296;
double tmp299 = tmp297 + tmp298;
double tmp300 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yz;
double tmp301 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yz;
double tmp302 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yz;
double tmp303 = tmp300 + tmp301;
double tmp304 = tmp302 + tmp303;
double tmp326 = gammaBar_UU.yz * tmp264;
double tmp346 = gammaBar_UU.yz * tmp284;
double tmp366 = gammaBar_UU.yz * tmp304;
double tmp458 = gammaBar_UU.xy * partial_gammaBar_LLl[1].zz;
double tmp459 = gammaBar_UU.xz * partial_gammaBar_LLl[2].zz;
double tmp460 = gammaBar_UU.xx * partial_gammaBar_LLl[0].zz;
double tmp461 = tmp458 + tmp459;
double tmp462 = tmp460 + tmp461;
double tmp478 = gammaBar_UU.yy * partial_gammaBar_LLl[1].zz;
double tmp479 = gammaBar_UU.yz * partial_gammaBar_LLl[2].zz;
double tmp480 = gammaBar_UU.xy * partial_gammaBar_LLl[0].zz;
double tmp481 = tmp478 + tmp479;
double tmp482 = tmp480 + tmp481;
double tmp498 = gammaBar_UU.yz * partial_gammaBar_LLl[1].zz;
double tmp499 = gammaBar_UU.zz * partial_gammaBar_LLl[2].zz;
double tmp500 = gammaBar_UU.xz * partial_gammaBar_LLl[0].zz;
double tmp501 = tmp498 + tmp499;
double tmp502 = tmp500 + tmp501;
double tmp649 = tmp79 + tmp104;
double tmp650 = tmp649 + tmp54;
double tmp654 = tmp277 + tmp302;
double tmp655 = tmp654 + tmp59;
double tmp659 = tmp282 + tmp500;
double tmp660 = tmp659 + tmp64;
double tmp661 = gammaBar_UU.xy * tmp655;
double tmp662 = gammaBar_UU.xz * tmp660;
double tmp663 = gammaBar_UU.xx * tmp650;
double tmp666 = gammaBar_UU.yy * partial_gammaBar_LLl[0].xy;
double tmp667 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xz;
double tmp669 = tmp666 + tmp667;
double tmp670 = tmp669 + tmp74;
double tmp671 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yy;
double tmp672 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yz;
double tmp674 = tmp671 + tmp672;
double tmp675 = tmp674 + tmp79;
double tmp676 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yz;
double tmp677 = gammaBar_UU.yz * partial_gammaBar_LLl[0].zz;
double tmp679 = tmp676 + tmp677;
double tmp680 = tmp679 + tmp84;
double tmp681 = gammaBar_UU.xy * tmp675;
double tmp682 = gammaBar_UU.xz * tmp680;
double tmp683 = gammaBar_UU.xx * tmp670;
double tmp686 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xy;
double tmp687 = gammaBar_UU.zz * partial_gammaBar_LLl[0].xz;
double tmp689 = tmp686 + tmp687;
double tmp690 = tmp689 + tmp94;
double tmp691 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yy;
double tmp692 = gammaBar_UU.zz * partial_gammaBar_LLl[0].yz;
double tmp694 = tmp691 + tmp692;
double tmp695 = tmp694 + tmp99;
double tmp697 = gammaBar_UU.zz * partial_gammaBar_LLl[0].zz;
double tmp699 = tmp697 + tmp672;
double tmp700 = tmp699 + tmp104;
double tmp701 = gammaBar_UU.xy * tmp695;
double tmp702 = gammaBar_UU.xz * tmp700;
double tmp703 = gammaBar_UU.xx * tmp690;
double tmp723 = gammaBar_UU.xy * tmp650;
double tmp743 = gammaBar_UU.xy * tmp670;
double tmp763 = gammaBar_UU.xy * tmp690;
double tmp783 = gammaBar_UU.xz * tmp650;
double tmp803 = gammaBar_UU.xz * tmp670;
double tmp823 = gammaBar_UU.xz * tmp690;
double tmp845 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xz;
double tmp846 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xx;
double tmp847 = tmp845 + tmp57;
double tmp848 = tmp846 + tmp847;
double tmp850 = gammaBar_UU.xz * partial_gammaBar_LLl[1].yz;
double tmp851 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xy;
double tmp852 = tmp850 + tmp255;
double tmp853 = tmp851 + tmp852;
double tmp855 = gammaBar_UU.xz * partial_gammaBar_LLl[1].zz;
double tmp856 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xz;
double tmp857 = tmp855 + tmp260;
double tmp858 = tmp856 + tmp857;
double tmp859 = gammaBar_UU.xy * tmp853;
double tmp867 = tmp77 + tmp102;
double tmp868 = tmp867 + tmp52;
double tmp872 = tmp275 + tmp300;
double tmp873 = tmp872 + tmp57;
double tmp877 = tmp280 + tmp498;
double tmp878 = tmp877 + tmp62;
double tmp879 = gammaBar_UU.xy * tmp873;
double tmp885 = gammaBar_UU.zz * partial_gammaBar_LLl[1].xz;
double tmp886 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xx;
double tmp887 = tmp885 + tmp97;
double tmp888 = tmp886 + tmp887;
double tmp890 = gammaBar_UU.zz * partial_gammaBar_LLl[1].yz;
double tmp891 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xy;
double tmp892 = tmp890 + tmp295;
double tmp893 = tmp891 + tmp892;
double tmp895 = gammaBar_UU.zz * partial_gammaBar_LLl[1].zz;
double tmp897 = tmp895 + tmp300;
double tmp898 = tmp897 + tmp845;
double tmp899 = gammaBar_UU.xy * tmp893;
double tmp919 = gammaBar_UU.yy * tmp853;
double tmp920 = gammaBar_UU.yz * tmp858;
double tmp921 = gammaBar_UU.xy * tmp848;
double tmp939 = gammaBar_UU.yy * tmp873;
double tmp940 = gammaBar_UU.yz * tmp878;
double tmp941 = gammaBar_UU.xy * tmp868;
double tmp959 = gammaBar_UU.yy * tmp893;
double tmp960 = gammaBar_UU.yz * tmp898;
double tmp961 = gammaBar_UU.xy * tmp888;
double tmp979 = gammaBar_UU.yz * tmp853;
double tmp999 = gammaBar_UU.yz * tmp873;
double tmp1019 = gammaBar_UU.yz * tmp893;
double tmp1042 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xy;
double tmp1044 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xx;
double tmp1045 = tmp1042 + tmp63;
double tmp1046 = tmp1044 + tmp1045;
double tmp1047 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yy;
double tmp1049 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xy;
double tmp1050 = tmp1047 + tmp261;
double tmp1051 = tmp1049 + tmp1050;
double tmp1052 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yz;
double tmp1054 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xz;
double tmp1055 = tmp1052 + tmp459;
double tmp1056 = tmp1054 + tmp1055;
double tmp1058 = gammaBar_UU.xz * tmp1056;
double tmp1062 = gammaBar_UU.yy * partial_gammaBar_LLl[2].xy;
double tmp1064 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xx;
double tmp1065 = tmp1062 + tmp83;
double tmp1066 = tmp1064 + tmp1065;
double tmp1067 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yy;
double tmp1070 = tmp1067 + tmp281;
double tmp1071 = tmp1070 + tmp1042;
double tmp1072 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yz;
double tmp1074 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xz;
double tmp1075 = tmp1072 + tmp479;
double tmp1076 = tmp1074 + tmp1075;
double tmp1078 = gammaBar_UU.xz * tmp1076;
double tmp1085 = tmp78 + tmp103;
double tmp1086 = tmp1085 + tmp53;
double tmp1090 = tmp276 + tmp301;
double tmp1091 = tmp1090 + tmp58;
double tmp1095 = tmp281 + tmp499;
double tmp1096 = tmp1095 + tmp63;
double tmp1098 = gammaBar_UU.xz * tmp1096;
double tmp1118 = gammaBar_UU.yz * tmp1056;
double tmp1138 = gammaBar_UU.yz * tmp1076;
double tmp1158 = gammaBar_UU.yz * tmp1096;
double tmp1177 = gammaBar_UU.yz * tmp1051;
double tmp1178 = gammaBar_UU.zz * tmp1056;
double tmp1179 = gammaBar_UU.xz * tmp1046;
double tmp1197 = gammaBar_UU.yz * tmp1071;
double tmp1198 = gammaBar_UU.zz * tmp1076;
double tmp1199 = gammaBar_UU.xz * tmp1066;
double tmp1217 = gammaBar_UU.yz * tmp1091;
double tmp1218 = gammaBar_UU.zz * tmp1096;
double tmp1219 = gammaBar_UU.xz * tmp1086;
double dt_K = U->alpha * tmp36 * (R_LL.zz * gammaBar_UU.zz + 2. * R_LL.yz * gammaBar_UU.yz + R_LL.yy * gammaBar_UU.yy + 2. * R_LL.xz * gammaBar_UU.xz + 2. * R_LL.xy * gammaBar_UU.xy + R_LL.xx * gammaBar_UU.xx) + -12. * M_PI * U->alpha * U->rho + U->alpha * U->K * U->K + U->beta_U.z * (gammaBar_UU.zz * partial_ABar_LLl[2].zz + 2. * gammaBar_UU.yz * partial_ABar_LLl[2].yz + gammaBar_UU.yy * partial_ABar_LLl[2].yy + 2. * gammaBar_UU.xz * partial_ABar_LLl[2].xz + 2. * gammaBar_UU.xy * partial_ABar_LLl[2].xy + gammaBar_UU.xx * partial_ABar_LLl[2].xx) + U->beta_U.y * (gammaBar_UU.zz * partial_ABar_LLl[1].zz + 2. * gammaBar_UU.yz * partial_ABar_LLl[1].yz + gammaBar_UU.yy * partial_ABar_LLl[1].yy + 2. * gammaBar_UU.xz * partial_ABar_LLl[1].xz + 2. * gammaBar_UU.xy * partial_ABar_LLl[1].xy + gammaBar_UU.xx * partial_ABar_LLl[1].xx) + U->beta_U.x * (gammaBar_UU.zz * partial_ABar_LLl[0].zz + 2. * gammaBar_UU.yz * partial_ABar_LLl[0].yz + gammaBar_UU.yy * partial_ABar_LLl[0].yy + 2. * gammaBar_UU.xz * partial_ABar_LLl[0].xz + 2. * gammaBar_UU.xy * partial_ABar_LLl[0].xy + gammaBar_UU.xx * partial_ABar_LLl[0].xx) + U->beta_U.z * (ABar_LL.zz * (tmp702 + tmp960 + tmp1218) + ABar_LL.yz * (tmp682 + tmp940 + tmp1198) + ABar_LL.xz * (tmp662 + tmp920 + tmp1178) + ABar_LL.yz * (tmp1158 + gammaBar_UU.yy * tmp898 + gammaBar_UU.xy * tmp700) + ABar_LL.yy * (tmp1138 + gammaBar_UU.yy * tmp878 + gammaBar_UU.xy * tmp680) + ABar_LL.xy * (tmp1118 + gammaBar_UU.yy * tmp858 + gammaBar_UU.xy * tmp660) + ABar_LL.xz * (tmp1098 + gammaBar_UU.xy * tmp898 + gammaBar_UU.xx * tmp700) + ABar_LL.xy * (tmp1078 + gammaBar_UU.xy * tmp878 + gammaBar_UU.xx * tmp680) + ABar_LL.xx * (tmp1058 + gammaBar_UU.xy * tmp858 + gammaBar_UU.xx * tmp660)) + U->beta_U.y * (ABar_LL.zz * (tmp1019 + gammaBar_UU.zz * tmp1091 + gammaBar_UU.xz * tmp695) + ABar_LL.yz * (tmp999 + gammaBar_UU.zz * tmp1071 + gammaBar_UU.xz * tmp675) + ABar_LL.xz * (tmp979 + gammaBar_UU.zz * tmp1051 + gammaBar_UU.xz * tmp655) + ABar_LL.yz * (tmp701 + tmp959 + tmp1217) + ABar_LL.yy * (tmp681 + tmp939 + tmp1197) + ABar_LL.xy * (tmp661 + tmp919 + tmp1177) + ABar_LL.xz * (tmp899 + gammaBar_UU.xz * tmp1091 + gammaBar_UU.xx * tmp695) + ABar_LL.xy * (tmp879 + gammaBar_UU.xz * tmp1071 + gammaBar_UU.xx * tmp675) + ABar_LL.xx * (tmp859 + gammaBar_UU.xz * tmp1051 + gammaBar_UU.xx * tmp655)) + U->beta_U.x * (ABar_LL.zz * (tmp823 + gammaBar_UU.zz * tmp1086 + gammaBar_UU.yz * tmp888) + ABar_LL.yz * (tmp803 + gammaBar_UU.zz * tmp1066 + gammaBar_UU.yz * tmp868) + ABar_LL.xz * (tmp783 + gammaBar_UU.zz * tmp1046 + gammaBar_UU.yz * tmp848) + ABar_LL.yz * (tmp763 + gammaBar_UU.yz * tmp1086 + gammaBar_UU.yy * tmp888) + ABar_LL.yy * (tmp743 + gammaBar_UU.yz * tmp1066 + gammaBar_UU.yy * tmp868) + ABar_LL.xy * (tmp723 + gammaBar_UU.yz * tmp1046 + gammaBar_UU.yy * tmp848) + ABar_LL.xz * (tmp703 + tmp961 + tmp1219) + ABar_LL.xy * (tmp683 + tmp941 + tmp1199) + ABar_LL.xx * (tmp663 + tmp921 + tmp1179)) + -1. * U->beta_U.z * (ABar_LL.zz * (tmp1219 + tmp1217 + tmp1218) + ABar_LL.yz * (tmp1199 + tmp1197 + tmp1198) + ABar_LL.xz * (tmp1179 + tmp1177 + tmp1178) + ABar_LL.yz * (tmp1158 + gammaBar_UU.yy * tmp1091 + gammaBar_UU.xy * tmp1086) + ABar_LL.yy * (tmp1138 + gammaBar_UU.yy * tmp1071 + gammaBar_UU.xy * tmp1066) + ABar_LL.xy * (tmp1118 + gammaBar_UU.yy * tmp1051 + gammaBar_UU.xy * tmp1046) + ABar_LL.xz * (tmp1098 + gammaBar_UU.xy * tmp1091 + gammaBar_UU.xx * tmp1086) + ABar_LL.xy * (tmp1078 + gammaBar_UU.xy * tmp1071 + gammaBar_UU.xx * tmp1066) + ABar_LL.xx * (tmp1058 + gammaBar_UU.xy * tmp1051 + gammaBar_UU.xx * tmp1046)) + -1. * U->beta_U.y * (ABar_LL.zz * (tmp1019 + gammaBar_UU.zz * tmp898 + gammaBar_UU.xz * tmp888) + ABar_LL.yz * (tmp999 + gammaBar_UU.zz * tmp878 + gammaBar_UU.xz * tmp868) + ABar_LL.xz * (tmp979 + gammaBar_UU.zz * tmp858 + gammaBar_UU.xz * tmp848) + ABar_LL.yz * (tmp961 + tmp959 + tmp960) + ABar_LL.yy * (tmp941 + tmp939 + tmp940) + ABar_LL.xy * (tmp921 + tmp919 + tmp920) + ABar_LL.xz * (tmp899 + gammaBar_UU.xz * tmp898 + gammaBar_UU.xx * tmp888) + ABar_LL.xy * (tmp879 + gammaBar_UU.xz * tmp878 + gammaBar_UU.xx * tmp868) + ABar_LL.xx * (tmp859 + gammaBar_UU.xz * tmp858 + gammaBar_UU.xx * tmp848)) + -1. * U->beta_U.x * (ABar_LL.zz * (tmp823 + gammaBar_UU.zz * tmp700 + gammaBar_UU.yz * tmp695) + ABar_LL.yz * (tmp803 + gammaBar_UU.zz * tmp680 + gammaBar_UU.yz * tmp675) + ABar_LL.xz * (tmp783 + gammaBar_UU.zz * tmp660 + gammaBar_UU.yz * tmp655) + ABar_LL.yz * (tmp763 + gammaBar_UU.yz * tmp700 + gammaBar_UU.yy * tmp695) + ABar_LL.yy * (tmp743 + gammaBar_UU.yz * tmp680 + gammaBar_UU.yy * tmp675) + ABar_LL.xy * (tmp723 + gammaBar_UU.yz * tmp660 + gammaBar_UU.yy * tmp655) + ABar_LL.xz * (tmp703 + tmp701 + tmp702) + ABar_LL.xy * (tmp683 + tmp681 + tmp682) + ABar_LL.xx * (tmp663 + tmp661 + tmp662)) + -1. * U->beta_U.z * (ABar_LL.zz * (tmp108 + tmp366 + gammaBar_UU.zz * tmp502) + ABar_LL.yz * (tmp88 + tmp346 + gammaBar_UU.zz * tmp482) + ABar_LL.xz * (tmp68 + tmp326 + gammaBar_UU.zz * tmp462) + ABar_LL.yz * (gammaBar_UU.yz * tmp502 + gammaBar_UU.yy * tmp304 + gammaBar_UU.xy * tmp106) + ABar_LL.yy * (gammaBar_UU.yz * tmp482 + gammaBar_UU.yy * tmp284 + gammaBar_UU.xy * tmp86) + ABar_LL.xy * (gammaBar_UU.yz * tmp462 + gammaBar_UU.yy * tmp264 + gammaBar_UU.xy * tmp66) + ABar_LL.xz * (gammaBar_UU.xz * tmp502 + gammaBar_UU.xy * tmp304 + gammaBar_UU.xx * tmp106) + ABar_LL.xy * (gammaBar_UU.xz * tmp482 + gammaBar_UU.xy * tmp284 + gammaBar_UU.xx * tmp86) + ABar_LL.xx * (gammaBar_UU.xz * tmp462 + gammaBar_UU.xy * tmp264 + gammaBar_UU.xx * tmp66)) + -1. * U->beta_U.y * (ABar_LL.zz * (gammaBar_UU.zz * tmp304 + gammaBar_UU.yz * tmp299 + gammaBar_UU.xz * tmp101) + ABar_LL.yz * (gammaBar_UU.zz * tmp284 + gammaBar_UU.yz * tmp279 + gammaBar_UU.xz * tmp81) + ABar_LL.xz * (gammaBar_UU.zz * tmp264 + gammaBar_UU.yz * tmp259 + gammaBar_UU.xz * tmp61) + ABar_LL.yz * (tmp107 + tmp366 + gammaBar_UU.yy * tmp299) + ABar_LL.yy * (tmp87 + tmp346 + gammaBar_UU.yy * tmp279) + ABar_LL.xy * (tmp67 + tmp326 + gammaBar_UU.yy * tmp259) + ABar_LL.xz * (gammaBar_UU.xz * tmp304 + gammaBar_UU.xy * tmp299 + gammaBar_UU.xx * tmp101) + ABar_LL.xy * (gammaBar_UU.xz * tmp284 + gammaBar_UU.xy * tmp279 + gammaBar_UU.xx * tmp81) + ABar_LL.xx * (gammaBar_UU.xz * tmp264 + gammaBar_UU.xy * tmp259 + gammaBar_UU.xx * tmp61)) + -1. * U->beta_U.x * (ABar_LL.zz * (gammaBar_UU.zz * tmp106 + gammaBar_UU.yz * tmp101 + gammaBar_UU.xz * tmp96) + ABar_LL.yz * (gammaBar_UU.zz * tmp86 + gammaBar_UU.yz * tmp81 + gammaBar_UU.xz * tmp76) + ABar_LL.xz * (gammaBar_UU.zz * tmp66 + gammaBar_UU.yz * tmp61 + gammaBar_UU.xz * tmp56) + ABar_LL.yz * (gammaBar_UU.yz * tmp106 + gammaBar_UU.yy * tmp101 + gammaBar_UU.xy * tmp96) + ABar_LL.yy * (gammaBar_UU.yz * tmp86 + gammaBar_UU.yy * tmp81 + gammaBar_UU.xy * tmp76) + ABar_LL.xy * (gammaBar_UU.yz * tmp66 + gammaBar_UU.yy * tmp61 + gammaBar_UU.xy * tmp56) + ABar_LL.xz * (tmp107 + tmp108 + gammaBar_UU.xx * tmp96) + ABar_LL.xy * (tmp87 + tmp88 + gammaBar_UU.xx * tmp76) + ABar_LL.xx * (tmp67 + tmp68 + gammaBar_UU.xx * tmp56)) + U->beta_U.z * partial_K_l.z + U->beta_U.y * partial_K_l.y + U->beta_U.x * partial_K_l.x + -1. * tmp36 * (C_U.z * partial_alpha_l.z + C_U.y * partial_alpha_l.y + C_U.x * partial_alpha_l.x) + tmp36 * (U->LambdaBar_U.z * partial_alpha_l.z + U->LambdaBar_U.y * partial_alpha_l.y + U->LambdaBar_U.x * partial_alpha_l.x) + -1. * tmp36 * (gammaBar_UU.zz * partial2_alpha_ll.zz + 2. * gammaBar_UU.yz * partial2_alpha_ll.yz + gammaBar_UU.yy * partial2_alpha_ll.yy + 2. * gammaBar_UU.xz * partial2_alpha_ll.xz + 2. * gammaBar_UU.xy * partial2_alpha_ll.xy + gammaBar_UU.xx * partial2_alpha_ll.xx) + W * (partial_W_l.z * (gammaBar_UU.zz * partial_alpha_l.z + gammaBar_UU.yz * partial_alpha_l.y + gammaBar_UU.xz * partial_alpha_l.x) + partial_W_l.y * (gammaBar_UU.yz * partial_alpha_l.z + gammaBar_UU.yy * partial_alpha_l.y + gammaBar_UU.xy * partial_alpha_l.x) + partial_W_l.x * (gammaBar_UU.xz * partial_alpha_l.z + gammaBar_UU.xy * partial_alpha_l.y + gammaBar_UU.xx * partial_alpha_l.x)) + 4. * M_PI * S * U->alpha;

variable: $\bar{\epsilon}$
eqn:${{{{ \bar{\epsilon}} _I} _J} _{,t}} = {{{{-2}} {{\alpha}} \cdot {{{{ \bar{A}} _I} _J}}} + {{{{{ \bar{\gamma}} _I} _K}} {{{{ \beta} ^K} _{,j}}} {{{{ e} ^j} _J}}} + {{{{{ \bar{\gamma}} _J} _K}} {{{{ \beta} ^K} _{,i}}} {{{{ e} ^i} _I}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} _I} _K}} {{{{ e} ^j} _J}} {{{{ e} _k} ^K}} {{{{{ e} ^k} _A} _{,j}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} _J} _K}} {{{{ e} ^i} _I}} {{{{ e} _k} ^K}} {{{{{ e} ^k} _A} _{,i}}}} + {{{{ \beta} ^K}} {{{{ \bar{\gamma}} _M} _J}} {{{{ e} ^i} _I}} {{{{ e} ^k} _K}} {{{{{ e} _i} ^M} _{,k}}}} + {{{{ \beta} ^K}} {{{{ \bar{\gamma}} _I} _N}} {{{{ e} ^j} _J}} {{{{ e} ^k} _K}} {{{{{ e} _j} ^N} _{,k}}}} + {{{{ \beta} ^K}} {{{{ e} ^k} _K}} {{{{{ \bar{\gamma}} _I} _J} _{,k}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^K}} {{{{ \bar{\gamma}} _I} _J}} {{{{{ e} ^k} _K} _{,k}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{{ \bar{\gamma}} _I} _J}} {{{{ \beta} ^K} _{,k}}} {{{{ e} ^k} _K}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \bar{\gamma}} _{,k}}} {{{ \beta} ^K}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^k} _K}} {{\frac{1}{\bar{\gamma}}}}}}$
new eqn: ${{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {dt_epsilonBar_LL.xx} & {dt_epsilonBar_LL.xy} & {dt_epsilonBar_LL.xz} \\ {dt_epsilonBar_LL.xy} & {dt_epsilonBar_LL.yy} & {dt_epsilonBar_LL.yz} \\ {dt_epsilonBar_LL.xz} & {dt_epsilonBar_LL.yz} & {dt_epsilonBar_LL.zz}\end{matrix} \right]}} _I} _J} = {{{{-2}} \cdot {{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^K}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{{ \overset{k\downarrow[{K\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^k} _K} _k}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{K\downarrow k\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^K} _k}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^k} _K}}} + {{{{-2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _I} _J}} {{U->alpha}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _K}} {{{{ \overset{K\downarrow j\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^K} _j}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _J} _K}} {{{{ \overset{K\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^K} _i}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _K}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _k} ^K}} {{{{{ \overset{k\downarrow[{A\downarrow j\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^k} _A} _j}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _J} _K}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _k} ^K}} {{{{{ \overset{k\downarrow[{A\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^k} _A} _i}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^K}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _M} _J}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^k} _K}} {{{{{ \overset{i\downarrow[{M\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{M\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _i} ^M} _k}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^K}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _N}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^k} _K}} {{{{{ \overset{j\downarrow[{N\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{N\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _j} ^N} _k}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^K}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^k} _K}} {{{{{ \overset{I\downarrow[{J\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow k\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{J\downarrow k\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{J\downarrow k\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _I} _J} _k}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{k\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _k}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^K}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^k} _K}} {{\frac{1}{{det_gammaBar}}}}}}$



double tmp17 = partial_beta_Ul[1].y + partial_beta_Ul[2].z;
double tmp18 = partial_beta_Ul[0].x + tmp17;
double tmp19 = 1. / 3.;
double tmp24 = ABar_LL.xy * U->alpha;
double tmp25 = U->beta_U.y * partial_gammaBar_LLl[1].xy;
double tmp26 = U->beta_U.z * partial_gammaBar_LLl[2].xy;
double tmp27 = U->beta_U.x * partial_gammaBar_LLl[0].xy;
double tmp28 = tmp25 + tmp26;
double tmp29 = gammaBar_LL.yz * partial_beta_Ul[0].z;
double tmp30 = tmp27 + tmp28;
double tmp31 = gammaBar_LL.yy * partial_beta_Ul[0].y;
double tmp33 = gammaBar_LL.xy * partial_beta_Ul[0].x;
double tmp35 = gammaBar_LL.xz * partial_beta_Ul[1].z;
double tmp37 = gammaBar_LL.xy * partial_beta_Ul[1].y;
double tmp39 = gammaBar_LL.xx * partial_beta_Ul[1].x;
double tmp41 = -2. * tmp24;
double tmp46 = gammaBar_LL.xy * tmp18;
double tmp47 = tmp46 * tmp19;
double tmp49 = -2. * tmp47;
double tmp50 = ABar_LL.xz * U->alpha;
double tmp51 = U->beta_U.y * partial_gammaBar_LLl[1].xz;
double tmp52 = U->beta_U.z * partial_gammaBar_LLl[2].xz;
double tmp53 = U->beta_U.x * partial_gammaBar_LLl[0].xz;
double tmp54 = tmp51 + tmp52;
double tmp55 = gammaBar_LL.zz * partial_beta_Ul[0].z;
double tmp56 = tmp53 + tmp54;
double tmp57 = gammaBar_LL.yz * partial_beta_Ul[0].y;
double tmp59 = gammaBar_LL.xz * partial_beta_Ul[0].x;
double tmp61 = gammaBar_LL.xz * partial_beta_Ul[2].z;
double tmp63 = gammaBar_LL.xy * partial_beta_Ul[2].y;
double tmp65 = gammaBar_LL.xx * partial_beta_Ul[2].x;
double tmp67 = -2. * tmp50;
double tmp72 = gammaBar_LL.xz * tmp18;
double tmp73 = tmp72 * tmp19;
double tmp75 = -2. * tmp73;
double tmp125 = ABar_LL.yz * U->alpha;
double tmp126 = U->beta_U.y * partial_gammaBar_LLl[1].yz;
double tmp127 = U->beta_U.z * partial_gammaBar_LLl[2].yz;
double tmp128 = U->beta_U.x * partial_gammaBar_LLl[0].yz;
double tmp129 = tmp126 + tmp127;
double tmp130 = gammaBar_LL.zz * partial_beta_Ul[1].z;
double tmp131 = tmp128 + tmp129;
double tmp132 = gammaBar_LL.yz * partial_beta_Ul[1].y;
double tmp134 = gammaBar_LL.xz * partial_beta_Ul[1].x;
double tmp136 = gammaBar_LL.yz * partial_beta_Ul[2].z;
double tmp138 = gammaBar_LL.yy * partial_beta_Ul[2].y;
double tmp140 = gammaBar_LL.xy * partial_beta_Ul[2].x;
double tmp142 = -2. * tmp125;
double tmp147 = gammaBar_LL.yz * tmp18;
double tmp148 = tmp147 * tmp19;
double tmp150 = -2. * tmp148;
double dt_epsilonBar_LL.xx = -2. * tmp19 * gammaBar_LL.xx * tmp18 + U->beta_U.z * partial_gammaBar_LLl[2].xx + U->beta_U.y * partial_gammaBar_LLl[1].xx + U->beta_U.x * partial_gammaBar_LLl[0].xx + 2. * gammaBar_LL.xz * partial_beta_Ul[0].z + 2. * gammaBar_LL.xy * partial_beta_Ul[0].y + 2. * gammaBar_LL.xx * partial_beta_Ul[0].x + -2. * ABar_LL.xx * U->alpha;
double dt_epsilonBar_LL.xy = tmp49 + tmp41 + tmp39 + tmp37 + tmp35 + tmp33 + tmp31 + tmp29 + tmp30;
double dt_epsilonBar_LL.xz = tmp75 + tmp67 + tmp65 + tmp63 + tmp61 + tmp59 + tmp57 + tmp55 + tmp56;
double dt_epsilonBar_LL.xy = tmp49 + tmp41 + tmp33 + tmp31 + tmp29 + tmp39 + tmp37 + tmp35 + tmp30;
double dt_epsilonBar_LL.yy = -2. * tmp19 * gammaBar_LL.yy * tmp18 + U->beta_U.z * partial_gammaBar_LLl[2].yy + U->beta_U.y * partial_gammaBar_LLl[1].yy + U->beta_U.x * partial_gammaBar_LLl[0].yy + 2. * gammaBar_LL.yz * partial_beta_Ul[1].z + 2. * gammaBar_LL.yy * partial_beta_Ul[1].y + 2. * gammaBar_LL.xy * partial_beta_Ul[1].x + -2. * ABar_LL.yy * U->alpha;
double dt_epsilonBar_LL.yz = tmp150 + tmp142 + tmp140 + tmp138 + tmp136 + tmp134 + tmp132 + tmp130 + tmp131;
double dt_epsilonBar_LL.xz = tmp75 + tmp67 + tmp59 + tmp57 + tmp55 + tmp65 + tmp63 + tmp61 + tmp56;
double dt_epsilonBar_LL.yz = tmp150 + tmp142 + tmp134 + tmp132 + tmp130 + tmp140 + tmp138 + tmp136 + tmp131;
double dt_epsilonBar_LL.zz = -2. * tmp19 * gammaBar_LL.zz * tmp18 + U->beta_U.z * partial_gammaBar_LLl[2].zz + U->beta_U.y * partial_gammaBar_LLl[1].zz + U->beta_U.x * partial_gammaBar_LLl[0].zz + 2. * gammaBar_LL.zz * partial_beta_Ul[2].z + 2. * gammaBar_LL.yz * partial_beta_Ul[2].y + 2. * gammaBar_LL.xz * partial_beta_Ul[2].x + -2. * ABar_LL.zz * U->alpha;

variable: $\bar{A}$
eqn:${{{{ \bar{A}} _I} _J} _{,t}} = {{{{8}} \cdot {{\frac{1}{3}}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \bar{\gamma}} _I} _J}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{A}} _I} _J}} {{{{ e} ^a} _A}} {{\frac{1}{\bar{\gamma}}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{W}} {{{ W} _{,a}}} {{{ \alpha} _{,b}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{\alpha}} \cdot {{{{ R} _A} _B}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _I} _J}} {{{W}^{2}}}} + {{{\frac{1}{3}}} {{{{ \alpha} _{,a}} _{,b}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{W}^{2}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \alpha} _{,a}}} {{{ \bar{\Lambda}} ^A}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _C} _I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^j} _J}} {{{{{ e} _b} ^C} _{,j}}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ e} ^a} _M}} {{{{ e} ^i} _I}} {{{{ e} ^j} _J}} {{{{{ e} _i} ^M} _{,j}}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _C} _J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^i} _I}} {{{{{ e} _b} ^C} _{,i}}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ e} ^a} _N}} {{{{ e} ^i} _I}} {{{{ e} ^j} _J}} {{{{{ e} _j} ^N} _{,i}}} {{{W}^{2}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _M} _J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^i} _I}} {{{{{ e} _i} ^M} _{,b}}} {{{W}^{2}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} _I} _N}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^j} _J}} {{{{{ e} _j} ^N} _{,b}}} {{{W}^{2}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _I} _J} _{,b}}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^i} _I}} {{{{{ \bar{\gamma}} _B} _J} _{,i}}} {{{W}^{2}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,a}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^j} _J}} {{{{{ \bar{\gamma}} _B} _I} _{,j}}} {{{W}^{2}}}} + {{{K}} {{\alpha}} \cdot {{{{ \bar{A}} _I} _J}}} + {{{-1}} {{W}} {{{ W} _{,i}}} {{{ \alpha} _{,j}}} {{{{ e} ^i} _I}} {{{{ e} ^j} _J}}} + {{{-1}} {{W}} {{{ W} _{,j}}} {{{ \alpha} _{,i}}} {{{{ e} ^i} _I}} {{{{ e} ^j} _J}}} + {{{\alpha}} \cdot {{{{ R} _I} _J}} {{{W}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _J}} {{{{ \bar{A}} _B} _I}} {{{{ \bar{\gamma}} ^A} ^B}}} + {{{-8}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _I} _J}} {{{W}^{2}}}} + {{{-1}} {{{{ \alpha} _{,i}} _{,j}}} {{{{ e} ^i} _I}} {{{{ e} ^j} _J}} {{{W}^{2}}}} + {{{{{ \bar{A}} _B} _I}} {{{{ \beta} ^B} _{,j}}} {{{{ e} ^j} _J}}} + {{{{{ \bar{A}} _B} _J}} {{{{ \beta} ^B} _{,i}}} {{{{ e} ^i} _I}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _M} _J}} {{{{ e} ^a} _A}} {{{{ e} ^i} _I}} {{{{{ e} _i} ^M} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{A}} _I} _N}} {{{{ e} ^a} _A}} {{{{ e} ^j} _J}} {{{{{ e} _j} ^N} _{,a}}}} + {{{{ \beta} ^A}} {{{{ e} ^a} _A}} {{{{{ \bar{A}} _I} _J} _{,a}}}} + {{{{ \beta} ^B}} {{{{ \bar{A}} _A} _I}} {{{{ e} _a} ^A}} {{{{ e} ^j} _J}} {{{{{ e} ^a} _B} _{,j}}}} + {{{{ \beta} ^B}} {{{{ \bar{A}} _A} _J}} {{{{ e} _a} ^A}} {{{{ e} ^i} _I}} {{{{{ e} ^a} _B} _{,i}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{{ \bar{A}} _B} _E} _{,a}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _I} _J}} {{{{{ e} ^a} _A} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _D} _E}} {{{{ \bar{\gamma}} ^D} ^C}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^E} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _D} _E}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ e} _b} ^D} _{,a}}}} + {{{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^F}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{{ \bar{\gamma}} _F} _E} _{,a}}}} + {{{\frac{1}{3}}} {{{ \beta} ^F}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _F} _D} _{,e}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^G}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _A} _G} _{,d}}}} + {{{\frac{1}{3}}} {{{ \beta} ^F}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _F} _G}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^G} _{,e}}}} + {{{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^e} _E}} {{{{{ e} _a} ^B} _{,e}}}} + {{{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _G} _C}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^e} _E}} {{{{{ e} _e} ^G} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} ^C} ^E}} {{{{ \bar{\gamma}} _A} _G}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _e} ^G} _{,d}}}} + {{{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^C} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \beta} ^A}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^B} ^D}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{ e} _a} ^C} _{,d}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{{ \bar{A}} _I} _J}} {{{{ \beta} ^A} _{,a}}} {{{{ e} ^a} _A}}} + {{{\frac{1}{3}}} {{{ \alpha} _{,a}}} {{{ \mathcal{C}} ^A}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{W}^{2}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \alpha} _{,a}}} {{{ \hat{\Gamma}} ^A}} {{{{ \bar{\gamma}} _I} _J}} {{{{ e} ^a} _A}} {{{W}^{2}}}}}$
new eqn: ${{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {dt_ABar_LL.xx} & {dt_ABar_LL.xy} & {dt_ABar_LL.xz} \\ {dt_ABar_LL.xy} & {dt_ABar_LL.yy} & {dt_ABar_LL.yz} \\ {dt_ABar_LL.xz} & {dt_ABar_LL.yz} & {dt_ABar_LL.zz}\end{matrix} \right]}} _I} _J} = {{{{8}} \cdot {{\frac{1}{3}}} {{S}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{U->alpha}} \cdot {{{M_PI}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{6}}} {{\left({{{{{4}} {{W}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_W_l.x} \\ {partial_W_l.y} \\ {partial_W_l.z}\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _b}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {R_LL.xx} & {R_LL.xy} & {R_LL.xz} \\ {R_LL.xy} & {R_LL.yy} & {R_LL.yz} \\ {R_LL.xz} & {R_LL.yz} & {R_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{W}^{2}}} {{U->alpha}}}} + {{{{2}} {{{{ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_alpha_ll.xx} & {partial2_alpha_ll.xy} & {partial2_alpha_ll.xz} \\ {partial2_alpha_ll.xy} & {partial2_alpha_ll.yy} & {partial2_alpha_ll.yz} \\ {partial2_alpha_ll.xz} & {partial2_alpha_ll.yz} & {partial2_alpha_ll.zz}\end{matrix} \right]}} _a} _b}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{W}^{2}}}} - {{{2}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->LambdaBar_U.x} \\ {U->LambdaBar_U.y} \\ {U->LambdaBar_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}}} + {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _C} _I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{b\downarrow[{C\downarrow j\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^C} _j}} {{{W}^{2}}}} + {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{a\downarrow M\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _M}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{i\downarrow[{M\downarrow j\rightarrow}]}{\left[ \begin{matrix} \overset{M\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _i} ^M} _j}} {{{W}^{2}}}} + {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _C} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{{ \overset{b\downarrow[{C\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^C} _i}} {{{W}^{2}}}} + {{{{{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{a\downarrow N\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _N}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{j\downarrow[{N\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{N\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _j} ^N} _i}} {{{W}^{2}}}} - {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _M} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{{ \overset{i\downarrow[{M\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{M\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _i} ^M} _b}} {{{W}^{2}}}}} - {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _N}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{j\downarrow[{N\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{N\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _j} ^N} _b}} {{{W}^{2}}}}} - {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{I\downarrow[{J\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _I} _J} _b}} {{{W}^{2}}}}} + {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{{ \overset{B\downarrow[{J\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{J\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{J\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _J} _i}} {{{W}^{2}}}} + {{{3}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{B\downarrow[{I\downarrow j\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow j\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{I\downarrow j\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{I\downarrow j\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _I} _j}} {{{W}^{2}}}} + {{{2}} {{\left({{{{{3}} {{\left({{{{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _I} _J}} {{U->alpha}} \cdot {{U->K}}} - {{{W}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {partial_W_l.x} \\ {partial_W_l.y} \\ {partial_W_l.z}\end{matrix} \right]}} _i}} {{{ \overset{j\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _j}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}}}} - {{{W}} {{{ \overset{j\downarrow}{\left[ \begin{matrix} {partial_W_l.x} \\ {partial_W_l.y} \\ {partial_W_l.z}\end{matrix} \right]}} _j}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _i}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}}}} + {{{{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {R_LL.xx} & {R_LL.xy} & {R_LL.xz} \\ {R_LL.xy} & {R_LL.yy} & {R_LL.yz} \\ {R_LL.xz} & {R_LL.yz} & {R_LL.zz}\end{matrix} \right]}} _I} _J}} {{{W}^{2}}} {{U->alpha}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{U->alpha}}}} - {{{8}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {S_LL.xx} & {S_LL.xy} & {S_LL.xz} \\ {S_LL.xy} & {S_LL.yy} & {S_LL.yz} \\ {S_LL.xz} & {S_LL.yz} & {S_LL.zz}\end{matrix} \right]}} _I} _J}} {{{W}^{2}}} {{U->alpha}} \cdot {{{M_PI}}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {partial2_alpha_ll.xx} & {partial2_alpha_ll.xy} & {partial2_alpha_ll.xz} \\ {partial2_alpha_ll.xy} & {partial2_alpha_ll.yy} & {partial2_alpha_ll.yz} \\ {partial2_alpha_ll.xz} & {partial2_alpha_ll.yz} & {partial2_alpha_ll.zz}\end{matrix} \right]}} _i} _j}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{W}^{2}}}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _I}} {{{{ \overset{B\downarrow j\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^B} _j}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _J}} {{{{ \overset{B\downarrow i\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^B} _i}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _M} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{{ \overset{i\downarrow[{M\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{M\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _i} ^M} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _I} _N}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{j\downarrow[{N\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{N\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _j} ^N} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{I\downarrow[{J\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xx} & {partial_ABar_LLl[1].xx} & {partial_ABar_LLl[2].xx} \\ {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz}\end{matrix} \right]} \\ \overset{J\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].yy} & {partial_ABar_LLl[1].yy} & {partial_ABar_LLl[2].yy} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz}\end{matrix} \right]} \\ \overset{J\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz} \\ {partial_ABar_LLl[0].zz} & {partial_ABar_LLl[1].zz} & {partial_ABar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _I} _J} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _a} ^A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^j} _J}} {{{{{ \overset{a\downarrow[{B\downarrow j\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _B} _j}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _a} ^A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^i} _I}} {{{{{ \overset{a\downarrow[{B\downarrow i\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _B} _i}}}}\right)}}} - {{{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{A\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}}} + {{{{{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {C_U.x} 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^A} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{a\downarrow[{C\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _d}}}} + {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{C\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^C} _a}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _A} _G}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{e\downarrow[{G\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _G} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{e\downarrow[{G\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{a\downarrow[{B\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^B} _e}}} + {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _F} _G}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{G\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^G}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{A\downarrow[{G\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _A} _G} _d}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{F\downarrow[{D\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _F} _D} _e}}} + {{{{{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{F\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _F} _E} _a}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _D} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{b\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _D} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _a}}}} - {{{2}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{{ \overset{a\downarrow[{A\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _A} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _I} _J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{B\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xx} & {partial_ABar_LLl[1].xx} & {partial_ABar_LLl[2].xx} \\ {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].yy} & {partial_ABar_LLl[1].yy} & {partial_ABar_LLl[2].yy} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz} \\ {partial_ABar_LLl[0].zz} & {partial_ABar_LLl[1].zz} & {partial_ABar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _E} _a}}}}}\right)}}}}\right)}}}}$



double tmp3 = 1. / 3.;
double tmp6 = gammaBar_UU.xy * partial_alpha_l.y;
double tmp7 = gammaBar_UU.xz * partial_alpha_l.z;
double tmp8 = gammaBar_UU.xx * partial_alpha_l.x;
double tmp9 = tmp6 + tmp7;
double tmp10 = tmp8 + tmp9;
double tmp11 = gammaBar_UU.yy * partial_alpha_l.y;
double tmp12 = gammaBar_UU.yz * partial_alpha_l.z;
double tmp13 = gammaBar_UU.xy * partial_alpha_l.x;
double tmp14 = tmp11 + tmp12;
double tmp15 = tmp13 + tmp14;
double tmp16 = gammaBar_UU.yz * partial_alpha_l.y;
double tmp17 = gammaBar_UU.zz * partial_alpha_l.z;
double tmp18 = gammaBar_UU.xz * partial_alpha_l.x;
double tmp19 = tmp16 + tmp17;
double tmp20 = tmp18 + tmp19;
double tmp21 = partial_W_l.y * tmp15;
double tmp22 = partial_W_l.z * tmp20;
double tmp23 = partial_W_l.x * tmp10;
double tmp24 = tmp21 + tmp22;
double tmp25 = tmp23 + tmp24;
double tmp30 = R_LL.xy * gammaBar_UU.xy;
double tmp31 = R_LL.xz * gammaBar_UU.xz;
double tmp32 = R_LL.yz * gammaBar_UU.yz;
double tmp33 = 2. * tmp32;
double tmp34 = R_LL.zz * gammaBar_UU.zz;
double tmp35 = R_LL.yy * gammaBar_UU.yy;
double tmp36 = tmp33 + tmp34;
double tmp37 = 2. * tmp31;
double tmp38 = tmp35 + tmp36;
double tmp39 = 2. * tmp30;
double tmp40 = tmp37 + tmp38;
double tmp41 = R_LL.xx * gammaBar_UU.xx;
double tmp42 = tmp39 + tmp40;
double tmp43 = W * W;
double tmp44 = tmp41 + tmp42;
double tmp45 = tmp43 * tmp44;
double tmp50 = gammaBar_UU.xy * partial2_alpha_ll.xy;
double tmp51 = gammaBar_UU.xz * partial2_alpha_ll.xz;
double tmp52 = gammaBar_UU.yz * partial2_alpha_ll.yz;
double tmp53 = 2. * tmp52;
double tmp54 = gammaBar_UU.zz * partial2_alpha_ll.zz;
double tmp55 = gammaBar_UU.yy * partial2_alpha_ll.yy;
double tmp56 = tmp53 + tmp54;
double tmp57 = 2. * tmp51;
double tmp58 = tmp55 + tmp56;
double tmp59 = 2. * tmp50;
double tmp60 = tmp57 + tmp58;
double tmp61 = gammaBar_UU.xx * partial2_alpha_ll.xx;
double tmp62 = tmp59 + tmp60;
double tmp64 = tmp61 + tmp62;
double tmp65 = tmp64 * tmp43;
double tmp68 = U->LambdaBar_U.y * partial_alpha_l.y;
double tmp69 = U->LambdaBar_U.z * partial_alpha_l.z;
double tmp70 = U->LambdaBar_U.x * partial_alpha_l.x;
double tmp71 = tmp68 + tmp69;
double tmp73 = tmp70 + tmp71;
double tmp74 = tmp73 * tmp43;
double tmp78 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xx;
double tmp79 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xx;
double tmp80 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xx;
double tmp81 = tmp78 + tmp79;
double tmp82 = tmp80 + tmp81;
double tmp83 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xx;
double tmp84 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xx;
double tmp85 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xx;
double tmp86 = tmp83 + tmp84;
double tmp87 = tmp85 + tmp86;
double tmp88 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xx;
double tmp89 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xx;
double tmp90 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xx;
double tmp91 = tmp88 + tmp89;
double tmp92 = tmp90 + tmp91;
double tmp99 = 1. / 2.;
double tmp102 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xy;
double tmp103 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xz;
double tmp105 = tmp102 + tmp103;
double tmp106 = tmp105 + tmp80;
double tmp107 = gammaBar_UU.yy * partial_gammaBar_LLl[0].xy;
double tmp108 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xz;
double tmp110 = tmp107 + tmp108;
double tmp111 = tmp110 + tmp85;
double tmp112 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xy;
double tmp113 = gammaBar_UU.zz * partial_gammaBar_LLl[0].xz;
double tmp115 = tmp112 + tmp113;
double tmp116 = tmp115 + tmp90;
double tmp123 = U->K * U->alpha;
double tmp129 = U->alpha * tmp43;
double tmp130 = ABar_LL.xy * gammaBar_UU.xy;
double tmp131 = ABar_LL.xz * gammaBar_UU.xz;
double tmp132 = ABar_LL.xx * gammaBar_UU.xx;
double tmp133 = tmp130 + tmp131;
double tmp134 = tmp132 + tmp133;
double tmp135 = ABar_LL.xy * gammaBar_UU.yy;
double tmp136 = ABar_LL.xz * gammaBar_UU.yz;
double tmp137 = ABar_LL.xx * gammaBar_UU.xy;
double tmp138 = tmp135 + tmp136;
double tmp139 = tmp137 + tmp138;
double tmp140 = ABar_LL.xy * gammaBar_UU.yz;
double tmp141 = ABar_LL.xz * gammaBar_UU.zz;
double tmp142 = ABar_LL.xx * gammaBar_UU.xz;
double tmp143 = tmp140 + tmp141;
double tmp144 = tmp142 + tmp143;
double tmp184 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yy;
double tmp185 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yz;
double tmp186 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xy;
double tmp187 = tmp184 + tmp185;
double tmp188 = tmp186 + tmp187;
double tmp189 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yz;
double tmp190 = gammaBar_UU.xz * partial_gammaBar_LLl[0].zz;
double tmp191 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xz;
double tmp192 = tmp189 + tmp190;
double tmp193 = tmp191 + tmp192;
double tmp194 = gammaBar_UU.xy * tmp188;
double tmp195 = gammaBar_UU.xz * tmp193;
double tmp196 = gammaBar_UU.xx * tmp106;
double tmp197 = tmp194 + tmp195;
double tmp198 = tmp196 + tmp197;
double tmp204 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yy;
double tmp205 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yz;
double tmp207 = tmp204 + tmp205;
double tmp208 = tmp207 + tmp102;
double tmp209 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yz;
double tmp210 = gammaBar_UU.yz * partial_gammaBar_LLl[0].zz;
double tmp211 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xz;
double tmp212 = tmp209 + tmp210;
double tmp213 = tmp211 + tmp212;
double tmp214 = gammaBar_UU.xy * tmp208;
double tmp215 = gammaBar_UU.xz * tmp213;
double tmp216 = gammaBar_UU.xx * tmp111;
double tmp217 = tmp214 + tmp215;
double tmp218 = tmp216 + tmp217;
double tmp234 = gammaBar_UU.yy * tmp188;
double tmp235 = gammaBar_UU.yz * tmp193;
double tmp236 = gammaBar_UU.xy * tmp106;
double tmp237 = tmp234 + tmp235;
double tmp238 = tmp236 + tmp237;
double tmp244 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yy;
double tmp245 = gammaBar_UU.zz * partial_gammaBar_LLl[0].yz;
double tmp246 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xy;
double tmp247 = tmp244 + tmp245;
double tmp248 = tmp246 + tmp247;
double tmp250 = gammaBar_UU.zz * partial_gammaBar_LLl[0].zz;
double tmp252 = tmp250 + tmp205;
double tmp253 = tmp252 + tmp103;
double tmp254 = gammaBar_UU.xy * tmp248;
double tmp255 = gammaBar_UU.xz * tmp253;
double tmp256 = gammaBar_UU.xx * tmp116;
double tmp257 = tmp254 + tmp255;
double tmp258 = tmp256 + tmp257;
double tmp274 = gammaBar_UU.yz * tmp188;
double tmp275 = gammaBar_UU.zz * tmp193;
double tmp276 = gammaBar_UU.xz * tmp106;
double tmp277 = tmp274 + tmp275;
double tmp278 = tmp276 + tmp277;
double tmp294 = gammaBar_UU.yy * tmp208;
double tmp295 = gammaBar_UU.yz * tmp213;
double tmp296 = gammaBar_UU.xy * tmp111;
double tmp297 = tmp294 + tmp295;
double tmp298 = tmp296 + tmp297;
double tmp314 = gammaBar_UU.yy * tmp248;
double tmp315 = gammaBar_UU.yz * tmp253;
double tmp316 = gammaBar_UU.xy * tmp116;
double tmp317 = tmp314 + tmp315;
double tmp318 = tmp316 + tmp317;
double tmp334 = gammaBar_UU.yz * tmp208;
double tmp335 = gammaBar_UU.zz * tmp213;
double tmp336 = gammaBar_UU.xz * tmp111;
double tmp337 = tmp334 + tmp335;
double tmp338 = tmp336 + tmp337;
double tmp354 = gammaBar_UU.yz * tmp248;
double tmp355 = gammaBar_UU.zz * tmp253;
double tmp356 = gammaBar_UU.xz * tmp116;
double tmp357 = tmp354 + tmp355;
double tmp358 = tmp356 + tmp357;
double tmp359 = ABar_LL.yz * tmp338;
double tmp360 = ABar_LL.zz * tmp358;
double tmp361 = ABar_LL.yz * tmp318;
double tmp362 = tmp359 + tmp360;
double tmp363 = ABar_LL.yy * tmp298;
double tmp364 = tmp361 + tmp362;
double tmp365 = ABar_LL.xz * tmp278;
double tmp366 = tmp363 + tmp364;
double tmp367 = ABar_LL.xz * tmp258;
double tmp368 = tmp365 + tmp366;
double tmp369 = ABar_LL.xy * tmp238;
double tmp370 = tmp367 + tmp368;
double tmp371 = ABar_LL.xy * tmp218;
double tmp372 = tmp369 + tmp370;
double tmp373 = ABar_LL.xx * tmp198;
double tmp374 = tmp371 + tmp372;
double tmp375 = tmp373 + tmp374;
double tmp376 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xy;
double tmp377 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xz;
double tmp378 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xx;
double tmp379 = tmp376 + tmp377;
double tmp380 = tmp378 + tmp379;
double tmp381 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yy;
double tmp382 = gammaBar_UU.xz * partial_gammaBar_LLl[1].yz;
double tmp383 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xy;
double tmp384 = tmp381 + tmp382;
double tmp385 = tmp383 + tmp384;
double tmp386 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yz;
double tmp387 = gammaBar_UU.xz * partial_gammaBar_LLl[1].zz;
double tmp388 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xz;
double tmp389 = tmp386 + tmp387;
double tmp390 = tmp388 + tmp389;
double tmp391 = gammaBar_UU.xy * tmp385;
double tmp392 = gammaBar_UU.xz * tmp390;
double tmp393 = gammaBar_UU.xx * tmp380;
double tmp394 = tmp391 + tmp392;
double tmp395 = tmp393 + tmp394;
double tmp396 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xy;
double tmp397 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xz;
double tmp399 = tmp396 + tmp397;
double tmp400 = tmp399 + tmp78;
double tmp401 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yy;
double tmp402 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yz;
double tmp404 = tmp401 + tmp402;
double tmp405 = tmp404 + tmp376;
double tmp406 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yz;
double tmp407 = gammaBar_UU.yz * partial_gammaBar_LLl[1].zz;
double tmp408 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xz;
double tmp409 = tmp406 + tmp407;
double tmp410 = tmp408 + tmp409;
double tmp411 = gammaBar_UU.xy * tmp405;
double tmp412 = gammaBar_UU.xz * tmp410;
double tmp413 = gammaBar_UU.xx * tmp400;
double tmp414 = tmp411 + tmp412;
double tmp415 = tmp413 + tmp414;
double tmp431 = gammaBar_UU.yy * tmp385;
double tmp432 = gammaBar_UU.yz * tmp390;
double tmp433 = gammaBar_UU.xy * tmp380;
double tmp434 = tmp431 + tmp432;
double tmp435 = tmp433 + tmp434;
double tmp436 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xy;
double tmp437 = gammaBar_UU.zz * partial_gammaBar_LLl[1].xz;
double tmp438 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xx;
double tmp439 = tmp436 + tmp437;
double tmp440 = tmp438 + tmp439;
double tmp441 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yy;
double tmp442 = gammaBar_UU.zz * partial_gammaBar_LLl[1].yz;
double tmp443 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xy;
double tmp444 = tmp441 + tmp442;
double tmp445 = tmp443 + tmp444;
double tmp447 = gammaBar_UU.zz * partial_gammaBar_LLl[1].zz;
double tmp449 = tmp447 + tmp402;
double tmp450 = tmp449 + tmp377;
double tmp451 = gammaBar_UU.xy * tmp445;
double tmp452 = gammaBar_UU.xz * tmp450;
double tmp453 = gammaBar_UU.xx * tmp440;
double tmp454 = tmp451 + tmp452;
double tmp455 = tmp453 + tmp454;
double tmp471 = gammaBar_UU.yz * tmp385;
double tmp472 = gammaBar_UU.zz * tmp390;
double tmp473 = gammaBar_UU.xz * tmp380;
double tmp474 = tmp471 + tmp472;
double tmp475 = tmp473 + tmp474;
double tmp491 = gammaBar_UU.yy * tmp405;
double tmp492 = gammaBar_UU.yz * tmp410;
double tmp493 = gammaBar_UU.xy * tmp400;
double tmp494 = tmp491 + tmp492;
double tmp495 = tmp493 + tmp494;
double tmp511 = gammaBar_UU.yy * tmp445;
double tmp512 = gammaBar_UU.yz * tmp450;
double tmp513 = gammaBar_UU.xy * tmp440;
double tmp514 = tmp511 + tmp512;
double tmp515 = tmp513 + tmp514;
double tmp531 = gammaBar_UU.yz * tmp405;
double tmp532 = gammaBar_UU.zz * tmp410;
double tmp533 = gammaBar_UU.xz * tmp400;
double tmp534 = tmp531 + tmp532;
double tmp535 = tmp533 + tmp534;
double tmp551 = gammaBar_UU.yz * tmp445;
double tmp552 = gammaBar_UU.zz * tmp450;
double tmp553 = gammaBar_UU.xz * tmp440;
double tmp554 = tmp551 + tmp552;
double tmp555 = tmp553 + tmp554;
double tmp556 = ABar_LL.yz * tmp535;
double tmp557 = ABar_LL.zz * tmp555;
double tmp558 = ABar_LL.yz * tmp515;
double tmp559 = tmp556 + tmp557;
double tmp560 = ABar_LL.yy * tmp495;
double tmp561 = tmp558 + tmp559;
double tmp562 = ABar_LL.xz * tmp475;
double tmp563 = tmp560 + tmp561;
double tmp564 = ABar_LL.xz * tmp455;
double tmp565 = tmp562 + tmp563;
double tmp566 = ABar_LL.xy * tmp435;
double tmp567 = tmp564 + tmp565;
double tmp568 = ABar_LL.xy * tmp415;
double tmp569 = tmp566 + tmp567;
double tmp570 = ABar_LL.xx * tmp395;
double tmp571 = tmp568 + tmp569;
double tmp572 = tmp570 + tmp571;
double tmp573 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xy;
double tmp574 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xz;
double tmp575 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xx;
double tmp576 = tmp573 + tmp574;
double tmp577 = tmp575 + tmp576;
double tmp578 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yy;
double tmp579 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yz;
double tmp580 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xy;
double tmp581 = tmp578 + tmp579;
double tmp582 = tmp580 + tmp581;
double tmp583 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yz;
double tmp584 = gammaBar_UU.xz * partial_gammaBar_LLl[2].zz;
double tmp585 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xz;
double tmp586 = tmp583 + tmp584;
double tmp587 = tmp585 + tmp586;
double tmp588 = gammaBar_UU.xy * tmp582;
double tmp589 = gammaBar_UU.xz * tmp587;
double tmp590 = gammaBar_UU.xx * tmp577;
double tmp591 = tmp588 + tmp589;
double tmp592 = tmp590 + tmp591;
double tmp593 = gammaBar_UU.yy * partial_gammaBar_LLl[2].xy;
double tmp594 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xz;
double tmp595 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xx;
double tmp596 = tmp593 + tmp594;
double tmp597 = tmp595 + tmp596;
double tmp598 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yy;
double tmp599 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yz;
double tmp601 = tmp598 + tmp599;
double tmp602 = tmp601 + tmp573;
double tmp603 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yz;
double tmp604 = gammaBar_UU.yz * partial_gammaBar_LLl[2].zz;
double tmp605 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xz;
double tmp606 = tmp603 + tmp604;
double tmp607 = tmp605 + tmp606;
double tmp608 = gammaBar_UU.xy * tmp602;
double tmp609 = gammaBar_UU.xz * tmp607;
double tmp610 = gammaBar_UU.xx * tmp597;
double tmp611 = tmp608 + tmp609;
double tmp612 = tmp610 + tmp611;
double tmp628 = gammaBar_UU.yy * tmp582;
double tmp629 = gammaBar_UU.yz * tmp587;
double tmp630 = gammaBar_UU.xy * tmp577;
double tmp631 = tmp628 + tmp629;
double tmp632 = tmp630 + tmp631;
double tmp633 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xy;
double tmp634 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xz;
double tmp636 = tmp633 + tmp634;
double tmp637 = tmp636 + tmp79;
double tmp638 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yy;
double tmp639 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yz;
double tmp640 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xy;
double tmp641 = tmp638 + tmp639;
double tmp642 = tmp640 + tmp641;
double tmp644 = gammaBar_UU.zz * partial_gammaBar_LLl[2].zz;
double tmp646 = tmp644 + tmp599;
double tmp647 = tmp646 + tmp574;
double tmp648 = gammaBar_UU.xy * tmp642;
double tmp649 = gammaBar_UU.xz * tmp647;
double tmp650 = gammaBar_UU.xx * tmp637;
double tmp651 = tmp648 + tmp649;
double tmp652 = tmp650 + tmp651;
double tmp668 = gammaBar_UU.yz * tmp582;
double tmp669 = gammaBar_UU.zz * tmp587;
double tmp670 = gammaBar_UU.xz * tmp577;
double tmp671 = tmp668 + tmp669;
double tmp672 = tmp670 + tmp671;
double tmp688 = gammaBar_UU.yy * tmp602;
double tmp689 = gammaBar_UU.yz * tmp607;
double tmp690 = gammaBar_UU.xy * tmp597;
double tmp691 = tmp688 + tmp689;
double tmp692 = tmp690 + tmp691;
double tmp708 = gammaBar_UU.yy * tmp642;
double tmp709 = gammaBar_UU.yz * tmp647;
double tmp710 = gammaBar_UU.xy * tmp637;
double tmp711 = tmp708 + tmp709;
double tmp712 = tmp710 + tmp711;
double tmp728 = gammaBar_UU.yz * tmp602;
double tmp729 = gammaBar_UU.zz * tmp607;
double tmp730 = gammaBar_UU.xz * tmp597;
double tmp731 = tmp728 + tmp729;
double tmp732 = tmp730 + tmp731;
double tmp748 = gammaBar_UU.yz * tmp642;
double tmp749 = gammaBar_UU.zz * tmp647;
double tmp750 = gammaBar_UU.xz * tmp637;
double tmp751 = tmp748 + tmp749;
double tmp752 = tmp750 + tmp751;
double tmp753 = ABar_LL.yz * tmp732;
double tmp754 = ABar_LL.zz * tmp752;
double tmp755 = ABar_LL.yz * tmp712;
double tmp756 = tmp753 + tmp754;
double tmp757 = ABar_LL.yy * tmp692;
double tmp758 = tmp755 + tmp756;
double tmp759 = ABar_LL.xz * tmp672;
double tmp760 = tmp757 + tmp758;
double tmp761 = ABar_LL.xz * tmp652;
double tmp762 = tmp759 + tmp760;
double tmp763 = ABar_LL.xy * tmp632;
double tmp764 = tmp761 + tmp762;
double tmp765 = ABar_LL.xy * tmp612;
double tmp766 = tmp763 + tmp764;
double tmp767 = ABar_LL.xx * tmp592;
double tmp768 = tmp765 + tmp766;
double tmp769 = tmp767 + tmp768;
double tmp770 = gammaBar_UU.xy * partial_ABar_LLl[0].xy;
double tmp771 = gammaBar_UU.xz * partial_ABar_LLl[0].xz;
double tmp772 = gammaBar_UU.yz * partial_ABar_LLl[0].yz;
double tmp773 = 2. * tmp772;
double tmp774 = gammaBar_UU.zz * partial_ABar_LLl[0].zz;
double tmp775 = gammaBar_UU.yy * partial_ABar_LLl[0].yy;
double tmp776 = tmp773 + tmp774;
double tmp777 = 2. * tmp771;
double tmp778 = tmp775 + tmp776;
double tmp779 = 2. * tmp770;
double tmp780 = tmp777 + tmp778;
double tmp781 = gammaBar_UU.xx * partial_ABar_LLl[0].xx;
double tmp782 = tmp779 + tmp780;
double tmp783 = tmp781 + tmp782;
double tmp784 = gammaBar_UU.xy * partial_ABar_LLl[1].xy;
double tmp785 = gammaBar_UU.xz * partial_ABar_LLl[1].xz;
double tmp786 = gammaBar_UU.yz * partial_ABar_LLl[1].yz;
double tmp787 = 2. * tmp786;
double tmp788 = gammaBar_UU.zz * partial_ABar_LLl[1].zz;
double tmp789 = gammaBar_UU.yy * partial_ABar_LLl[1].yy;
double tmp790 = tmp787 + tmp788;
double tmp791 = 2. * tmp785;
double tmp792 = tmp789 + tmp790;
double tmp793 = 2. * tmp784;
double tmp794 = tmp791 + tmp792;
double tmp795 = gammaBar_UU.xx * partial_ABar_LLl[1].xx;
double tmp796 = tmp793 + tmp794;
double tmp797 = tmp795 + tmp796;
double tmp798 = gammaBar_UU.xy * partial_ABar_LLl[2].xy;
double tmp799 = gammaBar_UU.xz * partial_ABar_LLl[2].xz;
double tmp800 = gammaBar_UU.yz * partial_ABar_LLl[2].yz;
double tmp801 = 2. * tmp800;
double tmp802 = gammaBar_UU.zz * partial_ABar_LLl[2].zz;
double tmp803 = gammaBar_UU.yy * partial_ABar_LLl[2].yy;
double tmp804 = tmp801 + tmp802;
double tmp805 = 2. * tmp799;
double tmp806 = tmp803 + tmp804;
double tmp807 = 2. * tmp798;
double tmp808 = tmp805 + tmp806;
double tmp809 = gammaBar_UU.xx * partial_ABar_LLl[2].xx;
double tmp810 = tmp807 + tmp808;
double tmp811 = tmp809 + tmp810;
double tmp812 = U->beta_U.y * tmp797;
double tmp813 = U->beta_U.z * tmp811;
double tmp814 = U->beta_U.x * tmp783;
double tmp815 = tmp812 + tmp813;
double tmp816 = U->beta_U.z * tmp769;
double tmp817 = tmp814 + tmp815;
double tmp818 = U->beta_U.y * tmp572;
double tmp819 = tmp816 - tmp817;
double tmp820 = U->beta_U.x * tmp375;
double tmp821 = tmp818 + tmp819;
double tmp822 = tmp820 + tmp821;
double tmp833 = tmp376 + tmp640;
double tmp834 = tmp833 + tmp186;
double tmp838 = tmp408 + tmp574;
double tmp839 = tmp838 + tmp191;
double tmp840 = gammaBar_UU.xy * tmp834;
double tmp841 = gammaBar_UU.xz * tmp839;
double tmp842 = gammaBar_UU.xx * tmp82;
double tmp843 = tmp840 + tmp841;
double tmp844 = tmp842 + tmp843;
double tmp853 = tmp396 + tmp633;
double tmp854 = tmp853 + tmp102;
double tmp855 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xz;
double tmp858 = tmp855 + tmp594;
double tmp859 = tmp858 + tmp211;
double tmp860 = gammaBar_UU.xy * tmp854;
double tmp861 = gammaBar_UU.xz * tmp859;
double tmp862 = gammaBar_UU.xx * tmp87;
double tmp863 = tmp860 + tmp861;
double tmp864 = tmp862 + tmp863;
double tmp880 = gammaBar_UU.yy * tmp834;
double tmp881 = gammaBar_UU.yz * tmp839;
double tmp882 = gammaBar_UU.xy * tmp82;
double tmp883 = tmp880 + tmp881;
double tmp884 = tmp882 + tmp883;
double tmp891 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xy;
double tmp893 = tmp891 + tmp436;
double tmp894 = tmp893 + tmp246;
double tmp898 = tmp397 + tmp634;
double tmp899 = tmp898 + tmp103;
double tmp900 = gammaBar_UU.xy * tmp894;
double tmp901 = gammaBar_UU.xz * tmp899;
double tmp902 = gammaBar_UU.xx * tmp92;
double tmp903 = tmp900 + tmp901;
double tmp904 = tmp902 + tmp903;
double tmp920 = gammaBar_UU.yz * tmp834;
double tmp921 = gammaBar_UU.zz * tmp839;
double tmp922 = gammaBar_UU.xz * tmp82;
double tmp923 = tmp920 + tmp921;
double tmp924 = tmp922 + tmp923;
double tmp940 = gammaBar_UU.yy * tmp854;
double tmp941 = gammaBar_UU.yz * tmp859;
double tmp942 = gammaBar_UU.xy * tmp87;
double tmp943 = tmp940 + tmp941;
double tmp944 = tmp942 + tmp943;
double tmp960 = gammaBar_UU.yy * tmp894;
double tmp961 = gammaBar_UU.yz * tmp899;
double tmp962 = gammaBar_UU.xy * tmp92;
double tmp963 = tmp960 + tmp961;
double tmp964 = tmp962 + tmp963;
double tmp980 = gammaBar_UU.yz * tmp854;
double tmp981 = gammaBar_UU.zz * tmp859;
double tmp982 = gammaBar_UU.xz * tmp87;
double tmp983 = tmp980 + tmp981;
double tmp984 = tmp982 + tmp983;
double tmp1000 = gammaBar_UU.yz * tmp894;
double tmp1001 = gammaBar_UU.zz * tmp899;
double tmp1002 = gammaBar_UU.xz * tmp92;
double tmp1003 = tmp1000 + tmp1001;
double tmp1004 = tmp1002 + tmp1003;
double tmp1005 = ABar_LL.yz * tmp984;
double tmp1006 = ABar_LL.zz * tmp1004;
double tmp1007 = ABar_LL.yz * tmp964;
double tmp1008 = tmp1005 + tmp1006;
double tmp1009 = ABar_LL.yy * tmp944;
double tmp1010 = tmp1007 + tmp1008;
double tmp1011 = ABar_LL.xz * tmp924;
double tmp1012 = tmp1009 + tmp1010;
double tmp1013 = ABar_LL.xz * tmp904;
double tmp1014 = tmp1011 + tmp1012;
double tmp1015 = ABar_LL.xy * tmp884;
double tmp1016 = tmp1013 + tmp1014;
double tmp1017 = ABar_LL.xy * tmp864;
double tmp1018 = tmp1015 + tmp1016;
double tmp1019 = ABar_LL.xx * tmp844;
double tmp1020 = tmp1017 + tmp1018;
double tmp1021 = tmp1019 + tmp1020;
double tmp1028 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yy;
double tmp1029 = gammaBar_UU.xx * partial_gammaBar_LLl[0].yy;
double tmp1030 = tmp1028 + tmp381;
double tmp1031 = tmp1029 + tmp1030;
double tmp1034 = gammaBar_UU.xx * partial_gammaBar_LLl[0].yz;
double tmp1035 = tmp386 + tmp579;
double tmp1036 = tmp1034 + tmp1035;
double tmp1037 = gammaBar_UU.xy * tmp1031;
double tmp1038 = gammaBar_UU.xz * tmp1036;
double tmp1039 = gammaBar_UU.xx * tmp834;
double tmp1040 = tmp1037 + tmp1038;
double tmp1041 = tmp1039 + tmp1040;
double tmp1050 = tmp401 + tmp638;
double tmp1051 = tmp1050 + tmp184;
double tmp1055 = tmp406 + tmp599;
double tmp1056 = tmp1055 + tmp189;
double tmp1057 = gammaBar_UU.xy * tmp1051;
double tmp1058 = gammaBar_UU.xz * tmp1056;
double tmp1059 = gammaBar_UU.xx * tmp854;
double tmp1060 = tmp1057 + tmp1058;
double tmp1061 = tmp1059 + tmp1060;
double tmp1077 = gammaBar_UU.yy * tmp1031;
double tmp1078 = gammaBar_UU.yz * tmp1036;
double tmp1080 = tmp1077 + tmp1078;
double tmp1081 = tmp1080 + tmp840;
double tmp1088 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yy;
double tmp1089 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yy;
double tmp1090 = tmp1088 + tmp441;
double tmp1091 = tmp1089 + tmp1090;
double tmp1095 = tmp402 + tmp639;
double tmp1096 = tmp1095 + tmp185;
double tmp1097 = gammaBar_UU.xy * tmp1091;
double tmp1098 = gammaBar_UU.xz * tmp1096;
double tmp1099 = gammaBar_UU.xx * tmp894;
double tmp1100 = tmp1097 + tmp1098;
double tmp1101 = tmp1099 + tmp1100;
double tmp1117 = gammaBar_UU.yz * tmp1031;
double tmp1118 = gammaBar_UU.zz * tmp1036;
double tmp1119 = gammaBar_UU.xz * tmp834;
double tmp1120 = tmp1117 + tmp1118;
double tmp1121 = tmp1119 + tmp1120;
double tmp1137 = gammaBar_UU.yy * tmp1051;
double tmp1138 = gammaBar_UU.yz * tmp1056;
double tmp1140 = tmp1137 + tmp1138;
double tmp1141 = tmp1140 + tmp860;
double tmp1157 = gammaBar_UU.yy * tmp1091;
double tmp1158 = gammaBar_UU.yz * tmp1096;
double tmp1160 = tmp1157 + tmp1158;
double tmp1161 = tmp1160 + tmp900;
double tmp1177 = gammaBar_UU.yz * tmp1051;
double tmp1178 = gammaBar_UU.zz * tmp1056;
double tmp1179 = gammaBar_UU.xz * tmp854;
double tmp1180 = tmp1177 + tmp1178;
double tmp1181 = tmp1179 + tmp1180;
double tmp1197 = gammaBar_UU.yz * tmp1091;
double tmp1198 = gammaBar_UU.zz * tmp1096;
double tmp1199 = gammaBar_UU.xz * tmp894;
double tmp1200 = tmp1197 + tmp1198;
double tmp1201 = tmp1199 + tmp1200;
double tmp1202 = ABar_LL.yz * tmp1181;
double tmp1203 = ABar_LL.zz * tmp1201;
double tmp1204 = ABar_LL.yz * tmp1161;
double tmp1205 = tmp1202 + tmp1203;
double tmp1206 = ABar_LL.yy * tmp1141;
double tmp1207 = tmp1204 + tmp1205;
double tmp1208 = ABar_LL.xz * tmp1121;
double tmp1209 = tmp1206 + tmp1207;
double tmp1210 = ABar_LL.xz * tmp1101;
double tmp1211 = tmp1208 + tmp1209;
double tmp1212 = ABar_LL.xy * tmp1081;
double tmp1213 = tmp1210 + tmp1211;
double tmp1214 = ABar_LL.xy * tmp1061;
double tmp1215 = tmp1212 + tmp1213;
double tmp1216 = ABar_LL.xx * tmp1041;
double tmp1217 = tmp1214 + tmp1215;
double tmp1218 = tmp1216 + tmp1217;
double tmp1229 = gammaBar_UU.xy * partial_gammaBar_LLl[1].zz;
double tmp1231 = gammaBar_UU.xx * partial_gammaBar_LLl[0].zz;
double tmp1232 = tmp1229 + tmp584;
double tmp1233 = tmp1231 + tmp1232;
double tmp1234 = gammaBar_UU.xy * tmp1036;
double tmp1235 = gammaBar_UU.xz * tmp1233;
double tmp1236 = gammaBar_UU.xx * tmp839;
double tmp1237 = tmp1234 + tmp1235;
double tmp1238 = tmp1236 + tmp1237;
double tmp1249 = gammaBar_UU.yy * partial_gammaBar_LLl[1].zz;
double tmp1251 = gammaBar_UU.xy * partial_gammaBar_LLl[0].zz;
double tmp1252 = tmp1249 + tmp604;
double tmp1253 = tmp1251 + tmp1252;
double tmp1254 = gammaBar_UU.xy * tmp1056;
double tmp1255 = gammaBar_UU.xz * tmp1253;
double tmp1256 = gammaBar_UU.xx * tmp859;
double tmp1257 = tmp1254 + tmp1255;
double tmp1258 = tmp1256 + tmp1257;
double tmp1274 = gammaBar_UU.yy * tmp1036;
double tmp1275 = gammaBar_UU.yz * tmp1233;
double tmp1276 = gammaBar_UU.xy * tmp839;
double tmp1277 = tmp1274 + tmp1275;
double tmp1278 = tmp1276 + tmp1277;
double tmp1292 = tmp407 + tmp644;
double tmp1293 = tmp1292 + tmp190;
double tmp1294 = gammaBar_UU.xy * tmp1096;
double tmp1295 = gammaBar_UU.xz * tmp1293;
double tmp1296 = gammaBar_UU.xx * tmp899;
double tmp1297 = tmp1294 + tmp1295;
double tmp1298 = tmp1296 + tmp1297;
double tmp1315 = gammaBar_UU.zz * tmp1233;
double tmp1317 = tmp1315 + tmp1078;
double tmp1318 = tmp1317 + tmp841;
double tmp1334 = gammaBar_UU.yy * tmp1056;
double tmp1335 = gammaBar_UU.yz * tmp1253;
double tmp1336 = gammaBar_UU.xy * tmp859;
double tmp1337 = tmp1334 + tmp1335;
double tmp1338 = tmp1336 + tmp1337;
double tmp1354 = gammaBar_UU.yy * tmp1096;
double tmp1355 = gammaBar_UU.yz * tmp1293;
double tmp1356 = gammaBar_UU.xy * tmp899;
double tmp1357 = tmp1354 + tmp1355;
double tmp1358 = tmp1356 + tmp1357;
double tmp1375 = gammaBar_UU.zz * tmp1253;
double tmp1377 = tmp1375 + tmp1138;
double tmp1378 = tmp1377 + tmp861;
double tmp1395 = gammaBar_UU.zz * tmp1293;
double tmp1397 = tmp1395 + tmp1158;
double tmp1398 = tmp1397 + tmp901;
double tmp1399 = ABar_LL.yz * tmp1378;
double tmp1400 = ABar_LL.zz * tmp1398;
double tmp1401 = ABar_LL.yz * tmp1358;
double tmp1402 = tmp1399 + tmp1400;
double tmp1403 = ABar_LL.yy * tmp1338;
double tmp1404 = tmp1401 + tmp1402;
double tmp1405 = ABar_LL.xz * tmp1318;
double tmp1406 = tmp1403 + tmp1404;
double tmp1407 = ABar_LL.xz * tmp1298;
double tmp1408 = tmp1405 + tmp1406;
double tmp1409 = ABar_LL.xy * tmp1278;
double tmp1410 = tmp1407 + tmp1408;
double tmp1411 = ABar_LL.xy * tmp1258;
double tmp1412 = tmp1409 + tmp1410;
double tmp1413 = ABar_LL.xx * tmp1238;
double tmp1414 = tmp1411 + tmp1412;
double tmp1415 = tmp1413 + tmp1414;
double tmp1416 = U->beta_U.y * tmp1218;
double tmp1417 = U->beta_U.z * tmp1415;
double tmp1418 = U->beta_U.x * tmp1021;
double tmp1419 = tmp1416 + tmp1417;
double tmp1420 = tmp1418 + tmp1419;
double tmp1441 = tmp433 + tmp670;
double tmp1442 = tmp1441 + tmp196;
double tmp1461 = tmp493 + tmp730;
double tmp1462 = tmp1461 + tmp216;
double tmp1478 = gammaBar_UU.yy * tmp380;
double tmp1479 = gammaBar_UU.yz * tmp577;
double tmp1481 = tmp1478 + tmp1479;
double tmp1482 = tmp1481 + tmp236;
double tmp1501 = tmp513 + tmp750;
double tmp1502 = tmp1501 + tmp256;
double tmp1518 = gammaBar_UU.yz * tmp380;
double tmp1519 = gammaBar_UU.zz * tmp577;
double tmp1521 = tmp1518 + tmp1519;
double tmp1522 = tmp1521 + tmp276;
double tmp1538 = gammaBar_UU.yy * tmp400;
double tmp1539 = gammaBar_UU.yz * tmp597;
double tmp1541 = tmp1538 + tmp1539;
double tmp1542 = tmp1541 + tmp296;
double tmp1558 = gammaBar_UU.yy * tmp440;
double tmp1559 = gammaBar_UU.yz * tmp637;
double tmp1561 = tmp1558 + tmp1559;
double tmp1562 = tmp1561 + tmp316;
double tmp1578 = gammaBar_UU.yz * tmp400;
double tmp1579 = gammaBar_UU.zz * tmp597;
double tmp1581 = tmp1578 + tmp1579;
double tmp1582 = tmp1581 + tmp336;
double tmp1598 = gammaBar_UU.yz * tmp440;
double tmp1599 = gammaBar_UU.zz * tmp637;
double tmp1601 = tmp1598 + tmp1599;
double tmp1602 = tmp1601 + tmp356;
double tmp1603 = ABar_LL.yz * tmp1582;
double tmp1604 = ABar_LL.zz * tmp1602;
double tmp1605 = ABar_LL.yz * tmp1562;
double tmp1606 = tmp1603 + tmp1604;
double tmp1607 = ABar_LL.yy * tmp1542;
double tmp1608 = tmp1605 + tmp1606;
double tmp1609 = ABar_LL.xz * tmp1522;
double tmp1610 = tmp1607 + tmp1608;
double tmp1611 = ABar_LL.xz * tmp1502;
double tmp1612 = tmp1609 + tmp1610;
double tmp1613 = ABar_LL.xy * tmp1482;
double tmp1614 = tmp1611 + tmp1612;
double tmp1615 = ABar_LL.xy * tmp1462;
double tmp1616 = tmp1613 + tmp1614;
double tmp1617 = ABar_LL.xx * tmp1442;
double tmp1618 = tmp1615 + tmp1616;
double tmp1619 = tmp1617 + tmp1618;
double tmp1636 = gammaBar_UU.xz * tmp582;
double tmp1637 = gammaBar_UU.xx * tmp188;
double tmp1638 = tmp1636 + tmp391;
double tmp1639 = tmp1637 + tmp1638;
double tmp1656 = gammaBar_UU.xz * tmp602;
double tmp1657 = gammaBar_UU.xx * tmp208;
double tmp1658 = tmp1656 + tmp411;
double tmp1659 = tmp1657 + tmp1658;
double tmp1678 = tmp431 + tmp668;
double tmp1679 = tmp1678 + tmp194;
double tmp1696 = gammaBar_UU.xz * tmp642;
double tmp1697 = gammaBar_UU.xx * tmp248;
double tmp1698 = tmp1696 + tmp451;
double tmp1699 = tmp1697 + tmp1698;
double tmp1716 = gammaBar_UU.zz * tmp582;
double tmp1717 = gammaBar_UU.xz * tmp188;
double tmp1718 = tmp1716 + tmp471;
double tmp1719 = tmp1717 + tmp1718;
double tmp1738 = tmp491 + tmp728;
double tmp1739 = tmp1738 + tmp214;
double tmp1758 = tmp511 + tmp748;
double tmp1759 = tmp1758 + tmp254;
double tmp1776 = gammaBar_UU.zz * tmp602;
double tmp1777 = gammaBar_UU.xz * tmp208;
double tmp1778 = tmp1776 + tmp531;
double tmp1779 = tmp1777 + tmp1778;
double tmp1796 = gammaBar_UU.zz * tmp642;
double tmp1797 = gammaBar_UU.xz * tmp248;
double tmp1798 = tmp1796 + tmp551;
double tmp1799 = tmp1797 + tmp1798;
double tmp1800 = ABar_LL.yz * tmp1779;
double tmp1801 = ABar_LL.zz * tmp1799;
double tmp1802 = ABar_LL.yz * tmp1759;
double tmp1803 = tmp1800 + tmp1801;
double tmp1804 = ABar_LL.yy * tmp1739;
double tmp1805 = tmp1802 + tmp1803;
double tmp1806 = ABar_LL.xz * tmp1719;
double tmp1807 = tmp1804 + tmp1805;
double tmp1808 = ABar_LL.xz * tmp1699;
double tmp1809 = tmp1806 + tmp1807;
double tmp1810 = ABar_LL.xy * tmp1679;
double tmp1811 = tmp1808 + tmp1809;
double tmp1812 = ABar_LL.xy * tmp1659;
double tmp1813 = tmp1810 + tmp1811;
double tmp1814 = ABar_LL.xx * tmp1639;
double tmp1815 = tmp1812 + tmp1813;
double tmp1816 = tmp1814 + tmp1815;
double tmp1832 = gammaBar_UU.xy * tmp390;
double tmp1834 = gammaBar_UU.xx * tmp193;
double tmp1835 = tmp1832 + tmp589;
double tmp1836 = tmp1834 + tmp1835;
double tmp1852 = gammaBar_UU.xy * tmp410;
double tmp1854 = gammaBar_UU.xx * tmp213;
double tmp1855 = tmp1852 + tmp609;
double tmp1856 = tmp1854 + tmp1855;
double tmp1872 = gammaBar_UU.yy * tmp390;
double tmp1874 = gammaBar_UU.xy * tmp193;
double tmp1875 = tmp1872 + tmp629;
double tmp1876 = tmp1874 + tmp1875;
double tmp1892 = gammaBar_UU.xy * tmp450;
double tmp1894 = gammaBar_UU.xx * tmp253;
double tmp1895 = tmp1892 + tmp649;
double tmp1896 = tmp1894 + tmp1895;
double tmp1915 = tmp432 + tmp669;
double tmp1916 = tmp1915 + tmp195;
double tmp1932 = gammaBar_UU.yy * tmp410;
double tmp1934 = gammaBar_UU.xy * tmp213;
double tmp1935 = tmp1932 + tmp689;
double tmp1936 = tmp1934 + tmp1935;
double tmp1952 = gammaBar_UU.yy * tmp450;
double tmp1954 = gammaBar_UU.xy * tmp253;
double tmp1955 = tmp1952 + tmp709;
double tmp1956 = tmp1954 + tmp1955;
double tmp1975 = tmp492 + tmp729;
double tmp1976 = tmp1975 + tmp215;
double tmp1995 = tmp512 + tmp749;
double tmp1996 = tmp1995 + tmp255;
double tmp1997 = ABar_LL.yz * tmp1976;
double tmp1998 = ABar_LL.zz * tmp1996;
double tmp1999 = ABar_LL.yz * tmp1956;
double tmp2000 = tmp1997 + tmp1998;
double tmp2001 = ABar_LL.yy * tmp1936;
double tmp2002 = tmp1999 + tmp2000;
double tmp2003 = ABar_LL.xz * tmp1916;
double tmp2004 = tmp2001 + tmp2002;
double tmp2005 = ABar_LL.xz * tmp1896;
double tmp2006 = tmp2003 + tmp2004;
double tmp2007 = ABar_LL.xy * tmp1876;
double tmp2008 = tmp2005 + tmp2006;
double tmp2009 = ABar_LL.xy * tmp1856;
double tmp2010 = tmp2007 + tmp2008;
double tmp2011 = ABar_LL.xx * tmp1836;
double tmp2012 = tmp2009 + tmp2010;
double tmp2013 = tmp2011 + tmp2012;
double tmp2014 = U->beta_U.y * tmp1816;
double tmp2015 = U->beta_U.z * tmp2013;
double tmp2016 = U->beta_U.x * tmp1619;
double tmp2017 = tmp2014 + tmp2015;
double tmp2018 = tmp2016 + tmp2017;
double tmp2022 = partial_beta_Ul[1].y + partial_beta_Ul[2].z;
double tmp2023 = partial_beta_Ul[0].x + tmp2022;
double tmp2027 = C_U.y * partial_alpha_l.y;
double tmp2028 = C_U.z * partial_alpha_l.z;
double tmp2029 = C_U.x * partial_alpha_l.x;
double tmp2030 = tmp2027 + tmp2028;
double tmp2032 = tmp2029 + tmp2030;
double tmp2033 = tmp2032 * tmp43;
double tmp2060 = U->alpha * gammaBar_LL.xy;
double tmp2061 = S * tmp2060;
double tmp2063 = M_PI * tmp2061;
double tmp2064 = tmp2063 * tmp3;
double tmp2085 = gammaBar_LL.xy * tmp25;
double tmp2087 = W * tmp2085;
double tmp2088 = tmp2087 * tmp3;
double tmp2105 = gammaBar_LL.xy * tmp45;
double tmp2107 = U->alpha * tmp2105;
double tmp2108 = tmp2107 * tmp3;
double tmp2126 = gammaBar_LL.xy * tmp65;
double tmp2135 = gammaBar_LL.xy * tmp74;
double tmp2136 = tmp2135 * tmp3;
double tmp2152 = partial_alpha_l.y * tmp854;
double tmp2153 = partial_alpha_l.z * tmp894;
double tmp2154 = partial_alpha_l.x * tmp834;
double tmp2155 = tmp2152 + tmp2153;
double tmp2157 = tmp2154 + tmp2155;
double tmp2159 = tmp2157 * tmp43;
double tmp2160 = tmp2159 * tmp99;
double tmp2176 = partial_alpha_l.y * tmp208;
double tmp2177 = partial_alpha_l.z * tmp248;
double tmp2178 = partial_alpha_l.x * tmp188;
double tmp2179 = tmp2176 + tmp2177;
double tmp2181 = tmp2178 + tmp2179;
double tmp2183 = tmp2181 * tmp43;
double tmp2199 = partial_alpha_l.y * tmp400;
double tmp2200 = partial_alpha_l.z * tmp440;
double tmp2201 = partial_alpha_l.x * tmp380;
double tmp2202 = tmp2199 + tmp2200;
double tmp2204 = tmp2201 + tmp2202;
double tmp2206 = tmp2204 * tmp43;
double tmp2208 = partial_W_l.x * partial_alpha_l.y;
double tmp2209 = ABar_LL.xy * tmp123;
double tmp2210 = W * tmp2208;
double tmp2211 = partial_W_l.y * partial_alpha_l.x;
double tmp2213 = W * tmp2211;
double tmp2237 = R_LL.xy * tmp129;
double tmp2241 = S_LL.xy * tmp129;
double tmp2242 = M_PI * tmp2241;
double tmp2244 = 8. * tmp2242;
double tmp2247 = partial2_alpha_ll.xy * tmp43;
double tmp2248 = U->beta_U.y * partial_ABar_LLl[1].xy;
double tmp2249 = U->beta_U.z * partial_ABar_LLl[2].xy;
double tmp2250 = U->beta_U.x * partial_ABar_LLl[0].xy;
double tmp2251 = tmp2248 + tmp2249;
double tmp2252 = ABar_LL.yz * partial_beta_Ul[0].z;
double tmp2253 = tmp2250 + tmp2251;
double tmp2254 = ABar_LL.yy * partial_beta_Ul[0].y;
double tmp2256 = ABar_LL.xy * partial_beta_Ul[0].x;
double tmp2258 = ABar_LL.xz * partial_beta_Ul[1].z;
double tmp2260 = ABar_LL.xy * partial_beta_Ul[1].y;
double tmp2262 = ABar_LL.xx * partial_beta_Ul[1].x;
double tmp2913 = gammaBar_LL.xy * tmp822;
double tmp3511 = gammaBar_LL.xy * tmp1420;
double tmp4109 = gammaBar_LL.xy * tmp2018;
double tmp4110 = tmp4109 * tmp3;
double tmp4114 = ABar_LL.xy * tmp2023;
double tmp4115 = tmp4114 * tmp3;
double tmp4124 = gammaBar_LL.xy * tmp2033;
double tmp4125 = -2. * tmp4115;
double tmp4126 = tmp4124 * tmp3;
double tmp4127 = -1. * tmp4110;
double tmp4128 = tmp4125 + tmp4126;
double tmp4129 = tmp3511 * tmp3;
double tmp4130 = tmp4127 + tmp4128;
double tmp4131 = tmp2913 * tmp3;
double tmp4132 = tmp4129 + tmp4130;
double tmp4134 = tmp4131 + tmp4132;
double tmp4135 = tmp2206 * tmp99;
double tmp4137 = tmp2183 * tmp99;
double tmp4139 = -1. * tmp2160;
double tmp4141 = -1. * tmp2136;
double tmp4143 = tmp2126 * tmp3;
double tmp4145 = -1. * tmp2108;
double tmp4147 = 2. * tmp2088;
double tmp4149 = 8. * tmp2064;
double tmp4151 = U->alpha * gammaBar_LL.xz;
double tmp4152 = S * tmp4151;
double tmp4154 = M_PI * tmp4152;
double tmp4155 = tmp4154 * tmp3;
double tmp4176 = gammaBar_LL.xz * tmp25;
double tmp4178 = W * tmp4176;
double tmp4179 = tmp4178 * tmp3;
double tmp4196 = gammaBar_LL.xz * tmp45;
double tmp4198 = U->alpha * tmp4196;
double tmp4199 = tmp4198 * tmp3;
double tmp4217 = gammaBar_LL.xz * tmp65;
double tmp4226 = gammaBar_LL.xz * tmp74;
double tmp4227 = tmp4226 * tmp3;
double tmp4243 = partial_alpha_l.y * tmp859;
double tmp4244 = partial_alpha_l.z * tmp899;
double tmp4245 = partial_alpha_l.x * tmp839;
double tmp4246 = tmp4243 + tmp4244;
double tmp4248 = tmp4245 + tmp4246;
double tmp4250 = tmp4248 * tmp43;
double tmp4251 = tmp4250 * tmp99;
double tmp4267 = partial_alpha_l.y * tmp213;
double tmp4268 = partial_alpha_l.z * tmp253;
double tmp4269 = partial_alpha_l.x * tmp193;
double tmp4270 = tmp4267 + tmp4268;
double tmp4272 = tmp4269 + tmp4270;
double tmp4274 = tmp4272 * tmp43;
double tmp4290 = partial_alpha_l.y * tmp597;
double tmp4291 = partial_alpha_l.z * tmp637;
double tmp4292 = partial_alpha_l.x * tmp577;
double tmp4293 = tmp4290 + tmp4291;
double tmp4295 = tmp4292 + tmp4293;
double tmp4297 = tmp4295 * tmp43;
double tmp4299 = partial_W_l.x * partial_alpha_l.z;
double tmp4300 = ABar_LL.xz * tmp123;
double tmp4301 = W * tmp4299;
double tmp4302 = partial_W_l.z * partial_alpha_l.x;
double tmp4304 = W * tmp4302;
double tmp4328 = R_LL.xz * tmp129;
double tmp4332 = S_LL.xz * tmp129;
double tmp4333 = M_PI * tmp4332;
double tmp4335 = 8. * tmp4333;
double tmp4338 = partial2_alpha_ll.xz * tmp43;
double tmp4339 = U->beta_U.y * partial_ABar_LLl[1].xz;
double tmp4340 = U->beta_U.z * partial_ABar_LLl[2].xz;
double tmp4341 = U->beta_U.x * partial_ABar_LLl[0].xz;
double tmp4342 = tmp4339 + tmp4340;
double tmp4343 = ABar_LL.zz * partial_beta_Ul[0].z;
double tmp4344 = tmp4341 + tmp4342;
double tmp4345 = ABar_LL.yz * partial_beta_Ul[0].y;
double tmp4347 = ABar_LL.xz * partial_beta_Ul[0].x;
double tmp4349 = ABar_LL.xz * partial_beta_Ul[2].z;
double tmp4351 = ABar_LL.xy * partial_beta_Ul[2].y;
double tmp4353 = ABar_LL.xx * partial_beta_Ul[2].x;
double tmp5004 = gammaBar_LL.xz * tmp822;
double tmp5602 = gammaBar_LL.xz * tmp1420;
double tmp6200 = gammaBar_LL.xz * tmp2018;
double tmp6201 = tmp6200 * tmp3;
double tmp6205 = ABar_LL.xz * tmp2023;
double tmp6206 = tmp6205 * tmp3;
double tmp6215 = gammaBar_LL.xz * tmp2033;
double tmp6216 = -2. * tmp6206;
double tmp6217 = tmp6215 * tmp3;
double tmp6218 = -1. * tmp6201;
double tmp6219 = tmp6216 + tmp6217;
double tmp6220 = tmp5602 * tmp3;
double tmp6221 = tmp6218 + tmp6219;
double tmp6222 = tmp5004 * tmp3;
double tmp6223 = tmp6220 + tmp6221;
double tmp6225 = tmp6222 + tmp6223;
double tmp6226 = tmp4297 * tmp99;
double tmp6228 = tmp4274 * tmp99;
double tmp6230 = -1. * tmp4251;
double tmp6232 = -1. * tmp4227;
double tmp6234 = tmp4217 * tmp3;
double tmp6236 = -1. * tmp4199;
double tmp6238 = 2. * tmp4179;
double tmp6240 = 8. * tmp4155;
double tmp6398 = ABar_LL.yy * gammaBar_UU.xy;
double tmp6399 = ABar_LL.yz * gammaBar_UU.xz;
double tmp6400 = ABar_LL.xy * gammaBar_UU.xx;
double tmp6401 = tmp6398 + tmp6399;
double tmp6402 = tmp6400 + tmp6401;
double tmp6403 = ABar_LL.yy * gammaBar_UU.yy;
double tmp6404 = ABar_LL.yz * gammaBar_UU.yz;
double tmp6406 = tmp6403 + tmp6404;
double tmp6407 = tmp6406 + tmp130;
double tmp6408 = ABar_LL.yy * gammaBar_UU.yz;
double tmp6409 = ABar_LL.yz * gammaBar_UU.zz;
double tmp6410 = ABar_LL.xy * gammaBar_UU.xz;
double tmp6411 = tmp6408 + tmp6409;
double tmp6412 = tmp6410 + tmp6411;
double tmp10392 = U->alpha * gammaBar_LL.yz;
double tmp10393 = S * tmp10392;
double tmp10395 = M_PI * tmp10393;
double tmp10396 = tmp10395 * tmp3;
double tmp10417 = gammaBar_LL.yz * tmp25;
double tmp10419 = W * tmp10417;
double tmp10420 = tmp10419 * tmp3;
double tmp10437 = gammaBar_LL.yz * tmp45;
double tmp10439 = U->alpha * tmp10437;
double tmp10440 = tmp10439 * tmp3;
double tmp10458 = gammaBar_LL.yz * tmp65;
double tmp10467 = gammaBar_LL.yz * tmp74;
double tmp10468 = tmp10467 * tmp3;
double tmp10484 = partial_alpha_l.y * tmp1056;
double tmp10485 = partial_alpha_l.z * tmp1096;
double tmp10486 = partial_alpha_l.x * tmp1036;
double tmp10487 = tmp10484 + tmp10485;
double tmp10489 = tmp10486 + tmp10487;
double tmp10491 = tmp10489 * tmp43;
double tmp10492 = tmp10491 * tmp99;
double tmp10508 = partial_alpha_l.y * tmp410;
double tmp10509 = partial_alpha_l.z * tmp450;
double tmp10510 = partial_alpha_l.x * tmp390;
double tmp10511 = tmp10508 + tmp10509;
double tmp10513 = tmp10510 + tmp10511;
double tmp10515 = tmp10513 * tmp43;
double tmp10531 = partial_alpha_l.y * tmp602;
double tmp10532 = partial_alpha_l.z * tmp642;
double tmp10533 = partial_alpha_l.x * tmp582;
double tmp10534 = tmp10531 + tmp10532;
double tmp10536 = tmp10533 + tmp10534;
double tmp10538 = tmp10536 * tmp43;
double tmp10540 = partial_W_l.y * partial_alpha_l.z;
double tmp10541 = ABar_LL.yz * tmp123;
double tmp10542 = W * tmp10540;
double tmp10543 = partial_W_l.z * partial_alpha_l.y;
double tmp10545 = W * tmp10543;
double tmp10569 = R_LL.yz * tmp129;
double tmp10573 = S_LL.yz * tmp129;
double tmp10574 = M_PI * tmp10573;
double tmp10576 = 8. * tmp10574;
double tmp10579 = partial2_alpha_ll.yz * tmp43;
double tmp10580 = U->beta_U.y * partial_ABar_LLl[1].yz;
double tmp10581 = U->beta_U.z * partial_ABar_LLl[2].yz;
double tmp10582 = U->beta_U.x * partial_ABar_LLl[0].yz;
double tmp10583 = tmp10580 + tmp10581;
double tmp10584 = ABar_LL.zz * partial_beta_Ul[1].z;
double tmp10585 = tmp10582 + tmp10583;
double tmp10586 = ABar_LL.yz * partial_beta_Ul[1].y;
double tmp10588 = ABar_LL.xz * partial_beta_Ul[1].x;
double tmp10590 = ABar_LL.yz * partial_beta_Ul[2].z;
double tmp10592 = ABar_LL.yy * partial_beta_Ul[2].y;
double tmp10594 = ABar_LL.xy * partial_beta_Ul[2].x;
double tmp11245 = gammaBar_LL.yz * tmp822;
double tmp11843 = gammaBar_LL.yz * tmp1420;
double tmp12441 = gammaBar_LL.yz * tmp2018;
double tmp12442 = tmp12441 * tmp3;
double tmp12446 = ABar_LL.yz * tmp2023;
double tmp12447 = tmp12446 * tmp3;
double tmp12456 = gammaBar_LL.yz * tmp2033;
double tmp12457 = -2. * tmp12447;
double tmp12458 = tmp12456 * tmp3;
double tmp12459 = -1. * tmp12442;
double tmp12460 = tmp12457 + tmp12458;
double tmp12461 = tmp11843 * tmp3;
double tmp12462 = tmp12459 + tmp12460;
double tmp12463 = tmp11245 * tmp3;
double tmp12464 = tmp12461 + tmp12462;
double tmp12466 = tmp12463 + tmp12464;
double tmp12467 = tmp10538 * tmp99;
double tmp12469 = tmp10515 * tmp99;
double tmp12471 = -1. * tmp10492;
double tmp12473 = -1. * tmp10468;
double tmp12475 = tmp10458 * tmp3;
double tmp12477 = -1. * tmp10440;
double tmp12479 = 2. * tmp10420;
double tmp12481 = 8. * tmp10396;
double tmp12639 = ABar_LL.yz * gammaBar_UU.xy;
double tmp12640 = ABar_LL.zz * gammaBar_UU.xz;
double tmp12641 = ABar_LL.xz * gammaBar_UU.xx;
double tmp12642 = tmp12639 + tmp12640;
double tmp12643 = tmp12641 + tmp12642;
double tmp12644 = ABar_LL.yz * gammaBar_UU.yy;
double tmp12645 = ABar_LL.zz * gammaBar_UU.yz;
double tmp12646 = ABar_LL.xz * gammaBar_UU.xy;
double tmp12647 = tmp12644 + tmp12645;
double tmp12648 = tmp12646 + tmp12647;
double tmp12650 = ABar_LL.zz * gammaBar_UU.zz;
double tmp12652 = tmp12650 + tmp6404;
double tmp12653 = tmp12652 + tmp131;
double dt_ABar_LL.xx = tmp3 * gammaBar_LL.xx * tmp2033 + -2. * tmp3 * ABar_LL.xx * tmp2023 + -1. * tmp3 * gammaBar_LL.xx * tmp2018 + tmp3 * gammaBar_LL.xx * tmp1420 + tmp3 * gammaBar_LL.xx * tmp822 + U->beta_U.z * partial_ABar_LLl[2].xx + U->beta_U.y * partial_ABar_LLl[1].xx + U->beta_U.x * partial_ABar_LLl[0].xx + 2. * ABar_LL.xz * partial_beta_Ul[0].z + 2. * ABar_LL.xy * partial_beta_Ul[0].y + 2. * ABar_LL.xx * partial_beta_Ul[0].x + R_LL.xx * tmp129 - 2. * U->alpha * (ABar_LL.xz * tmp144 + ABar_LL.xy * tmp139 + ABar_LL.xx * tmp134) - 8. * M_PI * S_LL.xx * tmp129 - partial2_alpha_ll.xx * tmp43 + ABar_LL.xx * tmp123 - 2. * W * partial_W_l.x * partial_alpha_l.x + tmp43 * (partial_alpha_l.z * tmp116 + partial_alpha_l.y * tmp111 + partial_alpha_l.x * tmp106) + -1. * tmp99 * tmp43 * (partial_alpha_l.z * tmp92 + partial_alpha_l.y * tmp87 + partial_alpha_l.x * tmp82) + -1. * tmp3 * gammaBar_LL.xx * tmp74 + tmp3 * gammaBar_LL.xx * tmp65 + -1. * tmp3 * U->alpha * gammaBar_LL.xx * tmp45 + 2. * tmp3 * W * gammaBar_LL.xx * tmp25 + 8. * tmp3 * M_PI * S * U->alpha * gammaBar_LL.xx;
double dt_ABar_LL.xy = tmp4149 + tmp4147 + tmp4145 + tmp4143 + tmp4141 + tmp4139 + tmp4137 + tmp4135 + tmp4134 + tmp2262 + tmp2260 + tmp2258 + tmp2256 + tmp2254 + tmp2252 + tmp2253 + tmp2237 - 2. * U->alpha * (ABar_LL.yz * tmp144 + ABar_LL.yy * tmp139 + ABar_LL.xy * tmp134) - tmp2244 - tmp2247 + tmp2209 - tmp2210 - tmp2213;
double dt_ABar_LL.xz = tmp6240 + tmp6238 + tmp6236 + tmp6234 + tmp6232 + tmp6230 + tmp6228 + tmp6226 + tmp6225 + tmp4353 + tmp4351 + tmp4349 + tmp4347 + tmp4345 + tmp4343 + tmp4344 + tmp4328 - 2. * U->alpha * (ABar_LL.zz * tmp144 + ABar_LL.yz * tmp139 + ABar_LL.xz * tmp134) - tmp4335 - tmp4338 + tmp4300 - tmp4301 - tmp4304;
double dt_ABar_LL.xy = tmp4149 + tmp4147 + tmp4145 + tmp4143 + tmp4141 + tmp4139 + tmp4135 + tmp4137 + tmp4134 + tmp2256 + tmp2254 + tmp2252 + tmp2262 + tmp2260 + tmp2258 + tmp2253 + tmp2237 - 2. * U->alpha * (ABar_LL.xz * tmp6412 + ABar_LL.xy * tmp6407 + ABar_LL.xx * tmp6402) - tmp2244 - tmp2247 + tmp2209 - tmp2213 - tmp2210;
double dt_ABar_LL.yy = tmp3 * gammaBar_LL.yy * tmp2033 + -2. * tmp3 * ABar_LL.yy * tmp2023 + -1. * tmp3 * gammaBar_LL.yy * tmp2018 + tmp3 * gammaBar_LL.yy * tmp1420 + tmp3 * gammaBar_LL.yy * tmp822 + U->beta_U.z * partial_ABar_LLl[2].yy + U->beta_U.y * partial_ABar_LLl[1].yy + U->beta_U.x * partial_ABar_LLl[0].yy + 2. * ABar_LL.yz * partial_beta_Ul[1].z + 2. * ABar_LL.yy * partial_beta_Ul[1].y + 2. * ABar_LL.xy * partial_beta_Ul[1].x + R_LL.yy * tmp129 - 2. * U->alpha * (ABar_LL.yz * tmp6412 + ABar_LL.yy * tmp6407 + ABar_LL.xy * tmp6402) - 8. * M_PI * S_LL.yy * tmp129 - partial2_alpha_ll.yy * tmp43 + ABar_LL.yy * tmp123 - 2. * W * partial_W_l.y * partial_alpha_l.y + tmp43 * (partial_alpha_l.z * tmp445 + partial_alpha_l.y * tmp405 + partial_alpha_l.x * tmp385) + -1. * tmp99 * tmp43 * (partial_alpha_l.z * tmp1091 + partial_alpha_l.y * tmp1051 + partial_alpha_l.x * tmp1031) + -1. * tmp3 * gammaBar_LL.yy * tmp74 + tmp3 * gammaBar_LL.yy * tmp65 + -1. * tmp3 * U->alpha * gammaBar_LL.yy * tmp45 + 2. * tmp3 * W * gammaBar_LL.yy * tmp25 + 8. * tmp3 * M_PI * S * U->alpha * gammaBar_LL.yy;
double dt_ABar_LL.yz = tmp12481 + tmp12479 + tmp12477 + tmp12475 + tmp12473 + tmp12471 + tmp12469 + tmp12467 + tmp12466 + tmp10594 + tmp10592 + tmp10590 + tmp10588 + tmp10586 + tmp10584 + tmp10585 + tmp10569 - 2. * U->alpha * (ABar_LL.zz * tmp6412 + ABar_LL.yz * tmp6407 + ABar_LL.xz * tmp6402) - tmp10576 - tmp10579 + tmp10541 - tmp10542 - tmp10545;
double dt_ABar_LL.xz = tmp6240 + tmp6238 + tmp6236 + tmp6234 + tmp6232 + tmp6230 + tmp6226 + tmp6228 + tmp6225 + tmp4347 + tmp4345 + tmp4343 + tmp4353 + tmp4351 + tmp4349 + tmp4344 + tmp4328 - 2. * U->alpha * (ABar_LL.xz * tmp12653 + ABar_LL.xy * tmp12648 + ABar_LL.xx * tmp12643) - tmp4335 - tmp4338 + tmp4300 - tmp4304 - tmp4301;
double dt_ABar_LL.yz = tmp12481 + tmp12479 + tmp12477 + tmp12475 + tmp12473 + tmp12471 + tmp12467 + tmp12469 + tmp12466 + tmp10588 + tmp10586 + tmp10584 + tmp10594 + tmp10592 + tmp10590 + tmp10585 + tmp10569 - 2. * U->alpha * (ABar_LL.yz * tmp12653 + ABar_LL.yy * tmp12648 + ABar_LL.xy * tmp12643) - tmp10576 - tmp10579 + tmp10541 - tmp10545 - tmp10542;
double dt_ABar_LL.zz = tmp3 * gammaBar_LL.zz * tmp2033 + -2. * tmp3 * ABar_LL.zz * tmp2023 + -1. * tmp3 * gammaBar_LL.zz * tmp2018 + tmp3 * gammaBar_LL.zz * tmp1420 + tmp3 * gammaBar_LL.zz * tmp822 + U->beta_U.z * partial_ABar_LLl[2].zz + U->beta_U.y * partial_ABar_LLl[1].zz + U->beta_U.x * partial_ABar_LLl[0].zz + 2. * ABar_LL.zz * partial_beta_Ul[2].z + 2. * ABar_LL.yz * partial_beta_Ul[2].y + 2. * ABar_LL.xz * partial_beta_Ul[2].x + R_LL.zz * tmp129 - 2. * U->alpha * (ABar_LL.zz * tmp12653 + ABar_LL.yz * tmp12648 + ABar_LL.xz * tmp12643) - 8. * M_PI * S_LL.zz * tmp129 - partial2_alpha_ll.zz * tmp43 + ABar_LL.zz * tmp123 - 2. * W * partial_W_l.z * partial_alpha_l.z + tmp43 * (partial_alpha_l.z * tmp647 + partial_alpha_l.y * tmp607 + partial_alpha_l.x * tmp587) + -1. * tmp99 * tmp43 * (partial_alpha_l.z * tmp1293 + partial_alpha_l.y * tmp1253 + partial_alpha_l.x * tmp1233) + -1. * tmp3 * gammaBar_LL.zz * tmp74 + tmp3 * gammaBar_LL.zz * tmp65 + -1. * tmp3 * U->alpha * gammaBar_LL.zz * tmp45 + 2. * tmp3 * W * gammaBar_LL.zz * tmp25 + 8. * tmp3 * M_PI * S * U->alpha * gammaBar_LL.zz;

variable: $\bar{\Lambda}$
eqn:${{{ \bar{\Lambda}} ^I} _{,t}} = {{{{2}} \cdot {{\frac{1}{3}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \beta} ^D} _{,d}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ e} _a} ^I} _{,b}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ \beta} ^D} _{,d}}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _c} ^F} _{,b}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ \beta} ^D} _{,d}}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _A} _F} _{,b}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \beta} ^C} _{,c}}} {{{{ e} ^c} _C}} {{{{{ \hat{\Gamma}} ^I} _A} _B}}} + {{{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _D}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^E} _{,a}}}} + {{{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _F}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _D}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _b} ^E} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^c} _F}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,a}}}} + {{{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _C} _D} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^E} ^C}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _E} _D} _{,a}}}} + {{{\frac{1}{3}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \beta} ^B} _{,a}} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _c} ^B} _{,a}}} {{{{{ e} _d} ^I} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _K}} {{{{ e} ^f} _F}} {{{{{ e} _c} ^F} _{,a}}} {{{{{ e} _f} ^K} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _H}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^I} _{,b}}} {{{{{ e} _e} ^H} _{,a}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^E} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _K}} {{{{ e} ^e} _E}} {{{{ e} ^f} _F}} {{{{{ e} _e} ^I} _{,a}}} {{{{{ e} _f} ^K} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _I} _K} _{,b}}} {{{{{ e} _c} ^K} _{,a}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ \bar{\gamma}} ^E} ^K}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _H} _K} _{,b}}} {{{{{ e} _e} ^H} _{,a}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ \bar{\gamma}} ^G} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _G} _E} _{,a}}} {{{{{ e} _d} ^I} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^G} ^I}} {{{{ \bar{\gamma}} ^H} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _K}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _G} _H} _{,a}}} {{{{{ e} _f} ^K} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ \bar{\gamma}} ^G} ^D}} {{{{ \bar{\gamma}} ^E} ^K}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _G} _E} _{,a}}} {{{{{ \bar{\gamma}} _D} _K} _{,b}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _F}} {{{{{{ e} _d} ^F} _{,a}} _{,b}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{{ e} _c} ^C} _{,a}} _{,b}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ \bar{\gamma}} ^E} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{{ \bar{\gamma}} _E} _D} _{,a}} _{,b}}}} + {{{\frac{1}{3}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{{{ e} ^b} _B} _{,a}} _{,b}}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^C}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{{ \hat{\Gamma}} ^I} _A} _B}} {{{{{ e} ^c} _C} _{,c}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ e} _a} ^I} _{,b}}} {{{{{ e} ^d} _D} _{,d}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^F} _{,b}}} {{{{{ e} ^d} _D} _{,d}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _A} _C} _{,b}}} {{{{{ e} ^d} _D} _{,d}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ e} _b} ^E} _{,a}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ e} _c} ^E} _{,a}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _F}} {{{{{ e} _d} ^F} _{,a}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _F}} {{{{{ e} ^d} _D} _{,c}}} {{{{{ e} _d} ^F} _{,a}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ \bar{\gamma}} _B} _F} _{,a}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{\frac{1}{2}}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} _d} ^F}} {{{{{ \bar{\gamma}} _C} _F} _{,a}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{-1}} {{\alpha}} \cdot {{{ \bar{\gamma}} _{,a}}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} ^I} ^C}} {{{{ e} ^a} _A}} {{\frac{1}{\bar{\gamma}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^B} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{2}}} {{{ \bar{\gamma}} _{,a}}} {{{{ \bar{\gamma}} ^B} ^A}} {{{{ \beta} ^I} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _b} ^I} _{,c}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^D} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _F}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,c}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _B} _F} _{,c}}} {{\frac{1}{\bar{\gamma}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{{ \hat{\Gamma}} ^I} _B} _C}} {{\frac{1}{\bar{\gamma}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{{ e} ^b} _B} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{2}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^I} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{2}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^D} ^I}} {{{{ e} ^a} _F}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{2}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _C} _F} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{2}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^J}} {{{{ \bar{\gamma}} ^B} ^A}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} _i} ^I}} {{{{{ e} ^i} _J} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{-2}} {{{ \alpha} _{,a}}} {{{{ \bar{A}} _B} _C}} {{{{ \bar{\gamma}} ^A} ^C}} {{{{ \bar{\gamma}} ^I} ^B}} {{{{ e} ^a} _A}}} + {{{-1}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \beta} ^I} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _a} ^C} _{,b}}}} + {{{-1}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ \beta} ^I} _{,c}}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,b}}}} + {{{-1}} {{{{ \bar{\gamma}} ^E} ^B}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ \beta} ^I} _{,c}}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _E} _D} _{,b}}}} + {{{-1}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ \bar{\gamma}} _E} _D}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _a} ^E} _{,b}}}} + {{{-1}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,b}}}} + {{{-1}} {{{{ \bar{\gamma}} ^E} ^B}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _E} _D} _{,b}}}} + {{{2}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \beta} ^D} _{,a}}} {{{{ e} ^a} _A}} {{{{{ \hat{\Gamma}} ^I} _B} _D}}} + {{{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \beta} ^I} _{,a}} _{,b}}}} + {{{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _D}} {{{{ \beta} ^D} _{,a}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _b} ^E} _{,c}}}} + {{{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^D} _{,a}}} {{{{ e} ^a} _A}} {{{{ e} ^c} _F}} {{{{ e} ^d} _D}} {{{{{ e} _d} ^F} _{,c}}}} + {{{-1}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ e} _a} ^B} _{,d}}}} + {{{-1}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _c} ^I} _{,d}}}} + {{{{{ \bar{\gamma}} ^A} ^I}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _a} ^C} _{,d}}}} + {{{{{ \bar{\gamma}} ^B} ^C}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _b} ^I} _{,d}}}} + {{{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^E} ^C}} {{{{ \beta} ^D} _{,a}}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _E} _D} _{,c}}}} + {{{-1}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ \bar{\gamma}} ^B} ^F}} {{{{ \beta} ^D} _{,b}}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _E} _F} _{,d}}}} + {{{{{ \bar{\gamma}} ^E} ^I}} {{{{ \bar{\gamma}} ^F} ^C}} {{{{ \beta} ^D} _{,c}}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _E} _F} _{,d}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \delta} ^K} _K}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _b} ^D} _{,c}}} {{{{{ e} _d} ^I} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ \bar{\gamma}} _G} _H}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^f} _F}} {{{{{ e} _b} ^G} _{,c}}} {{{{{ e} _f} ^H} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^D} ^E}} {{{{ \delta} ^K} _K}} {{{{ e} ^a} _A}} {{{{ e} ^c} _H}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^I} _{,a}}} {{{{{ e} _e} ^H} _{,c}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^I} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^c} _H}} {{{{ e} ^e} _E}} {{{{ e} ^f} _K}} {{{{{ e} _e} ^H} _{,c}}} {{{{{ e} _f} ^K} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} ^F} ^J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _J} _F} _{,a}}} {{{{{ e} _b} ^I} _{,c}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^D} ^E}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _H}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _D} _F} _{,a}}} {{{{{ e} _e} ^H} _{,c}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^G} ^C}} {{{{ \bar{\gamma}} ^D} ^H}} {{{{ \delta} ^K} _K}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _G} _H} _{,c}}} {{{{{ e} _d} ^I} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^G} ^C}} {{{{ \bar{\gamma}} ^F} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _G} _K} _{,c}}} {{{{{ e} _f} ^K} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} ^I} ^H}} {{{{ \bar{\gamma}} ^F} ^J}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _B} _H} _{,c}}} {{{{{ \bar{\gamma}} _J} _F} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ \hat{\Gamma}} ^I} _C} _E}} {{{{{ e} _b} ^E} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^D} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{ \hat{\Gamma}} ^I} _G} _E}} {{{{{ e} _d} ^G} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} ^G} ^E}} {{{{ e} ^a} _A}} {{{{{ \bar{\gamma}} _B} _G} _{,a}}} {{{{{ \hat{\Gamma}} ^I} _C} _E}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^J}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} ^f} _J}} {{{{{ e} _b} ^C} _{,f}}} {{{{{ e} _c} ^I} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{ e} ^f} _H}} {{{{{ e} _c} ^I} _{,a}}} {{{{{ e} _d} ^H} _{,f}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^E} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _K}} {{{{ e} ^e} _E}} {{{{ e} ^f} _F}} {{{{{ e} _b} ^I} _{,f}}} {{{{{ e} _e} ^K} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^E} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^d} _K}} {{{{ e} ^e} _E}} {{{{ e} ^f} _F}} {{{{{ e} _d} ^I} _{,f}}} {{{{{ e} _e} ^K} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^J}} {{{{ \bar{\gamma}} ^K} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _J} _K} _{,a}}} {{{{{ e} _b} ^I} _{,f}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ \bar{\gamma}} ^K} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _C} _K} _{,a}}} {{{{{ e} _d} ^I} _{,f}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^G} ^J}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^f} _J}} {{{{{ \bar{\gamma}} _G} _D} _{,f}}} {{{{{ e} _c} ^I} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^G} ^I}} {{{{ \bar{\gamma}} ^E} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^e} _E}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _G} _K} _{,f}}} {{{{{ e} _e} ^K} _{,a}}}} + {{{-1}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^J}} {{{{ \bar{\gamma}} ^I} ^D}} {{{{ \bar{\gamma}} ^K} ^F}} {{{{ e} ^a} _A}} {{{{ e} ^f} _F}} {{{{{ \bar{\gamma}} _B} _D} _{,f}}} {{{{{ \bar{\gamma}} _J} _K} _{,a}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^d} _D}} {{{{{{ e} _b} ^D} _{,a}} _{,d}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{{ e} _c} ^I} _{,a}} _{,d}}}} + {{{{ \beta} ^A}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^a} _A}} {{{{ e} ^d} _D}} {{{{{{ \bar{\gamma}} _E} _C} _{,a}} _{,d}}}} + {{{2}} {{{ \beta} ^C}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} _c} ^D}} {{{{{ \hat{\Gamma}} ^I} _B} _D}} {{{{{ e} ^c} _C} _{,a}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ \bar{\gamma}} _E} _F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ e} _a} ^E} _{,b}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{{ e} _d} ^F} _{,b}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^E} ^B}} {{{{ \bar{\gamma}} ^C} ^I}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ \bar{\gamma}} _E} _F} _{,b}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ \bar{\gamma}} _E} _F}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ e} _b} ^E} _{,c}}} {{{{{ e} ^d} _D} _{,a}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _F}} {{{{{ e} _d} ^F} _{,c}}} {{{{{ e} ^d} _D} _{,a}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ e} _a} ^B} _{,d}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ e} _a} ^C} _{,d}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _b} ^I} _{,d}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^I} _{,d}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{ e} _d} ^F}} {{{{{ \bar{\gamma}} _B} _F} _{,c}}} {{{{{ e} ^d} _D} _{,a}}}} + {{{{ \beta} ^D}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ \bar{\gamma}} ^F} ^C}} {{{{ e} ^c} _C}} {{{{{ \bar{\gamma}} _E} _F} _{,d}}} {{{{{ e} ^d} _D} _{,c}}}} + {{{-1}} {{{ \beta} ^D}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^b} _B}} {{{{{ \bar{\gamma}} _E} _C} _{,d}}} {{{{{ e} ^d} _D} _{,b}}}} + {{{-1}} {{{ \beta} ^J}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _i} ^I}} {{{{{ e} _a} ^C} _{,b}}} {{{{{ e} ^i} _J} _{,c}}}} + {{{-1}} {{{ \beta} ^J}} {{{{ \bar{\gamma}} ^C} ^D}} {{{{ e} ^b} _F}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{ e} _i} ^I}} {{{{{ e} _d} ^F} _{,b}}} {{{{{ e} ^i} _J} _{,c}}}} + {{{-1}} {{{ \beta} ^J}} {{{{ \bar{\gamma}} ^E} ^B}} {{{{ \bar{\gamma}} ^C} ^F}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{ e} _i} ^I}} {{{{{ \bar{\gamma}} _E} _F} _{,b}}} {{{{{ e} ^i} _J} _{,c}}}} + {{{{ \beta} ^J}} {{{{ \bar{\gamma}} ^A} ^B}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{ e} _i} ^I}} {{{{{{ e} ^i} _J} _{,a}} _{,b}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ e} ^c} _C}} {{{{ e} ^e} _E}} {{{{{ e} _c} ^B} _{,e}}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^D} ^B}} {{{{ e} ^c} _C}} {{{{ e} ^d} _D}} {{{{{ e} _c} ^I} _{,d}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \bar{A}} _G} _B}} {{{{ \bar{\gamma}} ^D} ^B}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^G} _{,e}}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _G} _B}} {{{{ \bar{\gamma}} ^D} ^B}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _e} ^G} _{,d}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^F} ^A}} {{{{ \bar{\gamma}} ^G} ^B}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _F} _G} _{,e}}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^D} ^B}} {{{{ \bar{\gamma}} ^E} ^I}} {{{{ e} ^d} _D}} {{{{{ \bar{\gamma}} _C} _E} _{,d}}}} + {{{-2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^D} ^B}} {{{{{ \hat{\Gamma}} ^I} _C} _D}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^D} ^E}} {{{{ \bar{\gamma}} ^I} ^B}} {{{{ e} ^e} _E}} {{{{{ \bar{\gamma}} _C} _D} _{,e}}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _B}} {{{{ \bar{\gamma}} ^C} ^A}} {{{{ \bar{\gamma}} ^I} ^B}} {{{{ e} ^c} _C}} {{{{ e} ^e} _E}} {{{{{ e} _c} ^E} _{,e}}}} + {{{2}} {{\alpha}} \cdot {{{{ \bar{A}} _G} _B}} {{{{ \bar{\gamma}} ^D} ^E}} {{{{ \bar{\gamma}} ^I} ^B}} {{{{ e} ^d} _D}} {{{{ e} ^e} _E}} {{{{{ e} _d} ^G} _{,e}}}} + {{{-2}} {{\alpha}} \cdot {{{{ \bar{A}} _D} _B}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ e} _a} ^D} _{,c}}}} + {{{\alpha}} \cdot {{{{ \bar{A}} _D} _E}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{{{{ e} _b} ^D} _{,a}}}} + {{{\alpha}} \cdot {{{{ \bar{A}} _B} _E}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^a} _A}} {{{{ e} ^c} _C}} {{{{{ e} _c} ^E} _{,a}}}} + {{{-2}} {{\alpha}} \cdot {{{{ \bar{A}} _A} _E}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^C}} {{{{ e} ^b} _B}} {{{{ e} ^c} _C}} {{{{{ e} _b} ^E} _{,c}}}} + {{{\alpha}} \cdot {{{{ \bar{\gamma}} ^A} ^I}} {{{{ \bar{\gamma}} ^B} ^E}} {{{{ e} ^a} _A}} {{{{{ \bar{A}} _B} _E} _{,a}}}} + {{{-2}} {{\alpha}} \cdot {{{{ \bar{\gamma}} ^D} ^I}} {{{{ \bar{\gamma}} ^E} ^C}} {{{{ e} ^c} _C}} {{{{{ \bar{A}} _D} _E} _{,c}}}} + {{{\frac{1}{6}}} {{{ \beta} ^I}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{6}}} {{{ \bar{\gamma}} _{,a}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^b} _B}} {{{{{ e} ^a} _A} _{,b}}} {{\frac{1}{\bar{\gamma}}}}} + {{{\frac{1}{6}}} {{{ \bar{\gamma}} _{,a}}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ \beta} ^A} _{,b}}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{\frac{1}{\bar{\gamma}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \bar{\gamma}} _{,a}}} {{{ \bar{\gamma}} _{,b}}} {{{ \beta} ^B}} {{{{ \bar{\gamma}} ^A} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{\frac{1}{{\bar{\gamma}}^{2}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \bar{\gamma}} _{,a}}} {{{ \bar{\gamma}} _{,b}}} {{{ \beta} ^A}} {{{{ \bar{\gamma}} ^B} ^I}} {{{{ e} ^a} _A}} {{{{ e} ^b} _B}} {{\frac{1}{{\bar{\gamma}}^{2}}}}}}$
new eqn: ${{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_LambdaBar_U.x} \\ {dt_LambdaBar_U.y} \\ {dt_LambdaBar_U.z}\end{matrix} \right]}} ^I} = {{{{2}} \cdot {{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _d}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{a\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^I} _b}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _d}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{c\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^F} _b}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _d}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{A\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _A} _F} _b}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{C\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^C} _c}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{I\downarrow[{A\downarrow B\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _A} _B}}} + {{{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _D}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _a}}} + {{{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _D}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{b\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a}}} + {{{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{C\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _D} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^C}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{E\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _D} _a}}} + {{{\frac{1}{3}}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{B\downarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].x} & {partial2_beta_Ull[0][1].x} & {partial2_beta_Ull[0][2].x} \\ {partial2_beta_Ull[1][0].x} & {partial2_beta_Ull[1][1].x} & {partial2_beta_Ull[1][2].x} \\ {partial2_beta_Ull[2][0].x} & {partial2_beta_Ull[2][1].x} & {partial2_beta_Ull[2][2].x}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].y} & {partial2_beta_Ull[0][1].y} & {partial2_beta_Ull[0][2].y} \\ {partial2_beta_Ull[1][0].y} & {partial2_beta_Ull[1][1].y} & {partial2_beta_Ull[1][2].y} \\ {partial2_beta_Ull[2][0].y} & {partial2_beta_Ull[2][1].y} & {partial2_beta_Ull[2][2].y}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].z} & {partial2_beta_Ull[0][1].z} & {partial2_beta_Ull[0][2].z} \\ {partial2_beta_Ull[1][0].z} & {partial2_beta_Ull[1][1].z} & {partial2_beta_Ull[1][2].z} \\ {partial2_beta_Ull[2][0].z} & {partial2_beta_Ull[2][1].z} & {partial2_beta_Ull[2][2].z}\end{matrix} \right]}\end{matrix} \right]}} ^B} _a} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{c\downarrow[{B\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^B} _a}} {{{{{ \overset{d\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _K}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{c\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^F} _a}} {{{{{ \overset{f\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _b}} {{{{{ \overset{e\downarrow[{H\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _a}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{e\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^I} _a}} {{{{{ \overset{f\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{I\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _I} _K} _b}} {{{{{ \overset{c\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^K} _a}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^K}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{H\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _H} _K} _b}} {{{{{ \overset{e\downarrow[{H\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _a}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{G\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _E} _a}} {{{{{ \overset{d\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^H} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _K}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{G\downarrow[{H\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _H} _a}} {{{{{ \overset{f\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^K}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{D\downarrow[{K\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _D} _K} _b}} {{{{{ \overset{G\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _E} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _F}} {{{{{{ \overset{d\downarrow F\rightarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a} _b}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{{ \overset{c\downarrow C\rightarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^C} _a} _b}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{{ \overset{E\downarrow D\rightarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xx} & {partial2_gammaBar_LLll[0][1].xx} & {partial2_gammaBar_LLll[0][2].xx} \\ {partial2_gammaBar_LLll[1][0].xx} & {partial2_gammaBar_LLll[1][1].xx} & {partial2_gammaBar_LLll[1][2].xx} \\ {partial2_gammaBar_LLll[2][0].xx} & {partial2_gammaBar_LLll[2][1].xx} & {partial2_gammaBar_LLll[2][2].xx}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xy} & {partial2_gammaBar_LLll[0][1].xy} & {partial2_gammaBar_LLll[0][2].xy} \\ {partial2_gammaBar_LLll[1][0].xy} & {partial2_gammaBar_LLll[1][1].xy} & {partial2_gammaBar_LLll[1][2].xy} \\ {partial2_gammaBar_LLll[2][0].xy} & {partial2_gammaBar_LLll[2][1].xy} & {partial2_gammaBar_LLll[2][2].xy}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xz} & {partial2_gammaBar_LLll[0][1].xz} & {partial2_gammaBar_LLll[0][2].xz} \\ {partial2_gammaBar_LLll[1][0].xz} & {partial2_gammaBar_LLll[1][1].xz} & {partial2_gammaBar_LLll[1][2].xz} \\ {partial2_gammaBar_LLll[2][0].xz} & {partial2_gammaBar_LLll[2][1].xz} & {partial2_gammaBar_LLll[2][2].xz}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xy} & {partial2_gammaBar_LLll[0][1].xy} & {partial2_gammaBar_LLll[0][2].xy} \\ {partial2_gammaBar_LLll[1][0].xy} & {partial2_gammaBar_LLll[1][1].xy} & {partial2_gammaBar_LLll[1][2].xy} \\ {partial2_gammaBar_LLll[2][0].xy} & {partial2_gammaBar_LLll[2][1].xy} & {partial2_gammaBar_LLll[2][2].xy}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yy} & {partial2_gammaBar_LLll[0][1].yy} & {partial2_gammaBar_LLll[0][2].yy} \\ {partial2_gammaBar_LLll[1][0].yy} & {partial2_gammaBar_LLll[1][1].yy} & {partial2_gammaBar_LLll[1][2].yy} \\ {partial2_gammaBar_LLll[2][0].yy} & {partial2_gammaBar_LLll[2][1].yy} & {partial2_gammaBar_LLll[2][2].yy}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yz} & {partial2_gammaBar_LLll[0][1].yz} & {partial2_gammaBar_LLll[0][2].yz} \\ {partial2_gammaBar_LLll[1][0].yz} & {partial2_gammaBar_LLll[1][1].yz} & {partial2_gammaBar_LLll[1][2].yz} \\ {partial2_gammaBar_LLll[2][0].yz} & {partial2_gammaBar_LLll[2][1].yz} & {partial2_gammaBar_LLll[2][2].yz}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xz} & {partial2_gammaBar_LLll[0][1].xz} & {partial2_gammaBar_LLll[0][2].xz} \\ {partial2_gammaBar_LLll[1][0].xz} & {partial2_gammaBar_LLll[1][1].xz} & {partial2_gammaBar_LLll[1][2].xz} \\ {partial2_gammaBar_LLll[2][0].xz} & {partial2_gammaBar_LLll[2][1].xz} & {partial2_gammaBar_LLll[2][2].xz}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yz} & {partial2_gammaBar_LLll[0][1].yz} & {partial2_gammaBar_LLll[0][2].yz} \\ {partial2_gammaBar_LLll[1][0].yz} & {partial2_gammaBar_LLll[1][1].yz} & {partial2_gammaBar_LLll[1][2].yz} \\ {partial2_gammaBar_LLll[2][0].yz} & {partial2_gammaBar_LLll[2][1].yz} & {partial2_gammaBar_LLll[2][2].yz}\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].zz} & {partial2_gammaBar_LLll[0][1].zz} & {partial2_gammaBar_LLll[0][2].zz} \\ {partial2_gammaBar_LLll[1][0].zz} & {partial2_gammaBar_LLll[1][1].zz} & {partial2_gammaBar_LLll[1][2].zz} \\ {partial2_gammaBar_LLll[2][0].zz} & {partial2_gammaBar_LLll[2][1].zz} & {partial2_gammaBar_LLll[2][2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _D} _a} _b}}} + {{{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{{ \overset{b\downarrow B\rightarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^b} _B} _a} _b}}} + {{{-2}} \cdot {{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{{ \overset{I\downarrow[{A\downarrow B\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _A} _B}} {{{{{ \overset{c\downarrow[{C\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^c} _C} _c}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{a\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^I} _b}} {{{{{ \overset{d\downarrow[{D\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _d}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^F} _b}} {{{{{ \overset{d\downarrow[{D\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _d}}} + {{{2}} \cdot {{\frac{1}{3}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{A\downarrow[{C\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _A} _C} _b}} {{{{{ \overset{d\downarrow[{D\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _d}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{b\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _a}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{c\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _a}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}} {{{{{ \overset{d\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _F}} {{{{{ \overset{d\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{B\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _F} _a}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{\frac{1}{2}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{C\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _F} _a}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}} + {{{-1}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{\frac{1}{{det_gammaBar}}}} {{U->alpha}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{B\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^B} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^A}} {{{{ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^I} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{b\downarrow[{I\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _c}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _c}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{B\downarrow[{F\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _F} _c}} {{\frac{1}{{det_gammaBar}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{I\downarrow[{B\downarrow C\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow C\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow C\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow C\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _B} _C}} {{\frac{1}{{det_gammaBar}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{b\downarrow[{B\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^b} _B} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{I\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^I}} {{{{ \overset{a\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _F}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{C\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _F} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _i} ^I}} {{{{{ \overset{i\downarrow[{J\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{6}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{a\downarrow[{A\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{A\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _A} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{A\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^A} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{{{{{{{{-2}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _a}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^I} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{a\downarrow[{C\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _b}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^I} _c}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^B}} {{{{ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^I} _c}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{E\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _D} _b}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _D}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{a\downarrow[{E\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^E} _b}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^B}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{E\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _D} _b}}}} + {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{I\downarrow[{B\downarrow D\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _B} _D}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{I\downarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].x} & {partial2_beta_Ull[0][1].x} & {partial2_beta_Ull[0][2].x} \\ {partial2_beta_Ull[1][0].x} & {partial2_beta_Ull[1][1].x} & {partial2_beta_Ull[1][2].x} \\ {partial2_beta_Ull[2][0].x} & {partial2_beta_Ull[2][1].x} & {partial2_beta_Ull[2][2].x}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].y} & {partial2_beta_Ull[0][1].y} & {partial2_beta_Ull[0][2].y} \\ {partial2_beta_Ull[1][0].y} & {partial2_beta_Ull[1][1].y} & {partial2_beta_Ull[1][2].y} \\ {partial2_beta_Ull[2][0].y} & {partial2_beta_Ull[2][1].y} & {partial2_beta_Ull[2][2].y}\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} {partial2_beta_Ull[0][0].z} & {partial2_beta_Ull[0][1].z} & {partial2_beta_Ull[0][2].z} \\ {partial2_beta_Ull[1][0].z} & {partial2_beta_Ull[1][1].z} & {partial2_beta_Ull[1][2].z} \\ {partial2_beta_Ull[2][0].z} & {partial2_beta_Ull[2][1].z} & {partial2_beta_Ull[2][2].z}\end{matrix} \right]}\end{matrix} \right]}} ^I} _a} _b}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _D}} {{{{ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{b\downarrow[{E\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _c}}} + {{{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{d\downarrow[{F\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _c}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{a\downarrow[{B\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^B} _d}}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{c\downarrow[{I\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _d}}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{a\downarrow[{C\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _d}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{b\downarrow[{I\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _d}}} + {{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^C}} {{{{ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{E\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _D} _c}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _b}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{E\downarrow[{F\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _F} _d}}}} + {{{{{{{{{{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^C}} {{{{ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_beta_Ul[0].x} & {partial_beta_Ul[1].x} & {partial_beta_Ul[2].x} \\ {partial_beta_Ul[0].y} & {partial_beta_Ul[1].y} & {partial_beta_Ul[2].y} \\ {partial_beta_Ul[0].z} & {partial_beta_Ul[1].z} & {partial_beta_Ul[2].z}\end{matrix} \right]}} ^D} _c}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{E\downarrow[{F\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _F} _d}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \delta} ^K} _K}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{b\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _c}} {{{{{ \overset{d\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _G} _H}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{b\downarrow[{G\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^G} _c}} {{{{{ \overset{f\downarrow[{H\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^H} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^E}} {{{{ \delta} ^K} _K}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _H}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _a}} {{{{{ \overset{e\downarrow[{H\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _K}} {{{{{ \overset{e\downarrow[{H\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _c}} {{{{{ \overset{f\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{J\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _J} _F} _a}} {{{{{ \overset{b\downarrow[{I\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{D\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _D} _F} _a}} {{{{{ \overset{e\downarrow[{H\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^H}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^C}} {{{{ \delta} ^K} _K}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{G\downarrow[{H\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _H} _c}} {{{{{ \overset{d\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{G\downarrow[{K\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _K} _c}} {{{{{ \overset{f\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^H}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{B\downarrow[{H\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _H} _c}} {{{{{ \overset{J\downarrow[{F\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _J} _F} _a}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{I\downarrow[{C\downarrow E\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _C} _E}} {{{{{ \overset{b\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _a}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{I\downarrow[{G\downarrow E\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _G} _E}} {{{{{ \overset{d\downarrow[{G\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _a}}} + {{{{{{{{{{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{B\downarrow[{G\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _G} _a}} {{{{{ \overset{I\downarrow[{C\downarrow E\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _C} _E}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _J}} {{{{{ \overset{b\downarrow[{C\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^C} _f}} {{{{{ \overset{c\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{f\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _H}} {{{{{ \overset{c\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _a}} {{{{{ \overset{d\downarrow[{H\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{H\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^H} _f}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{b\downarrow[{I\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _f}} {{{{{ \overset{e\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{d\downarrow[{I\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _f}} {{{{{ \overset{e\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^K} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{J\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _J} _K} _a}} {{{{{ \overset{b\downarrow[{I\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _f}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^K} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{C\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _K} _a}} {{{{{ \overset{d\downarrow[{I\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _f}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^J}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _J}} {{{{{ \overset{G\downarrow[{D\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _D} _f}} {{{{{ \overset{c\downarrow[{I\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{G\downarrow[{K\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _G} _K} _f}} {{{{{ \overset{e\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _a}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^K} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^f} _F}} {{{{{ \overset{B\downarrow[{D\downarrow f\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow f\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _D} _f}} {{{{{ \overset{J\downarrow[{K\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _J} _K} _a}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{{ \overset{b\downarrow D\rightarrow[{a\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _a} _d}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{{ \overset{c\downarrow I\rightarrow[{a\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _a} _d}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{{ \overset{E\downarrow C\rightarrow[{a\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xx} & {partial2_gammaBar_LLll[0][1].xx} & {partial2_gammaBar_LLll[0][2].xx} \\ {partial2_gammaBar_LLll[1][0].xx} & {partial2_gammaBar_LLll[1][1].xx} & {partial2_gammaBar_LLll[1][2].xx} \\ {partial2_gammaBar_LLll[2][0].xx} & {partial2_gammaBar_LLll[2][1].xx} & {partial2_gammaBar_LLll[2][2].xx}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xy} & {partial2_gammaBar_LLll[0][1].xy} & {partial2_gammaBar_LLll[0][2].xy} \\ {partial2_gammaBar_LLll[1][0].xy} & {partial2_gammaBar_LLll[1][1].xy} & {partial2_gammaBar_LLll[1][2].xy} \\ {partial2_gammaBar_LLll[2][0].xy} & {partial2_gammaBar_LLll[2][1].xy} & {partial2_gammaBar_LLll[2][2].xy}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xz} & {partial2_gammaBar_LLll[0][1].xz} & {partial2_gammaBar_LLll[0][2].xz} \\ {partial2_gammaBar_LLll[1][0].xz} & {partial2_gammaBar_LLll[1][1].xz} & {partial2_gammaBar_LLll[1][2].xz} \\ {partial2_gammaBar_LLll[2][0].xz} & {partial2_gammaBar_LLll[2][1].xz} & {partial2_gammaBar_LLll[2][2].xz}\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xy} & {partial2_gammaBar_LLll[0][1].xy} & {partial2_gammaBar_LLll[0][2].xy} \\ {partial2_gammaBar_LLll[1][0].xy} & {partial2_gammaBar_LLll[1][1].xy} & {partial2_gammaBar_LLll[1][2].xy} \\ {partial2_gammaBar_LLll[2][0].xy} & {partial2_gammaBar_LLll[2][1].xy} & {partial2_gammaBar_LLll[2][2].xy}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yy} & {partial2_gammaBar_LLll[0][1].yy} & {partial2_gammaBar_LLll[0][2].yy} \\ {partial2_gammaBar_LLll[1][0].yy} & {partial2_gammaBar_LLll[1][1].yy} & {partial2_gammaBar_LLll[1][2].yy} \\ {partial2_gammaBar_LLll[2][0].yy} & {partial2_gammaBar_LLll[2][1].yy} & {partial2_gammaBar_LLll[2][2].yy}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yz} & {partial2_gammaBar_LLll[0][1].yz} & {partial2_gammaBar_LLll[0][2].yz} \\ {partial2_gammaBar_LLll[1][0].yz} & {partial2_gammaBar_LLll[1][1].yz} & {partial2_gammaBar_LLll[1][2].yz} \\ {partial2_gammaBar_LLll[2][0].yz} & {partial2_gammaBar_LLll[2][1].yz} & {partial2_gammaBar_LLll[2][2].yz}\end{matrix} \right]} \\ \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].xz} & {partial2_gammaBar_LLll[0][1].xz} & {partial2_gammaBar_LLll[0][2].xz} \\ {partial2_gammaBar_LLll[1][0].xz} & {partial2_gammaBar_LLll[1][1].xz} & {partial2_gammaBar_LLll[1][2].xz} \\ {partial2_gammaBar_LLll[2][0].xz} & {partial2_gammaBar_LLll[2][1].xz} & {partial2_gammaBar_LLll[2][2].xz}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].yz} & {partial2_gammaBar_LLll[0][1].yz} & {partial2_gammaBar_LLll[0][2].yz} \\ {partial2_gammaBar_LLll[1][0].yz} & {partial2_gammaBar_LLll[1][1].yz} & {partial2_gammaBar_LLll[1][2].yz} \\ {partial2_gammaBar_LLll[2][0].yz} & {partial2_gammaBar_LLll[2][1].yz} & {partial2_gammaBar_LLll[2][2].yz}\end{matrix} \right]} & \overset{a\downarrow d\rightarrow}{\left[ \begin{matrix} {partial2_gammaBar_LLll[0][0].zz} & {partial2_gammaBar_LLll[0][1].zz} & {partial2_gammaBar_LLll[0][2].zz} \\ {partial2_gammaBar_LLll[1][0].zz} & {partial2_gammaBar_LLll[1][1].zz} & {partial2_gammaBar_LLll[1][2].zz} \\ {partial2_gammaBar_LLll[2][0].zz} & {partial2_gammaBar_LLll[2][1].zz} & {partial2_gammaBar_LLll[2][2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _C} _a} _d}}} + {{{{{{2}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _c} ^D}} {{{{{ \overset{I\downarrow[{B\downarrow D\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _B} _D}} {{{{{ \overset{c\downarrow[{C\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^c} _C} _a}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{a\downarrow[{E\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^E} _b}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}} {{{{{ \overset{d\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^B}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{E\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _F} _b}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_LL.xx} & {gammaBar_LL.xy} & {gammaBar_LL.xz} \\ {gammaBar_LL.xy} & {gammaBar_LL.yy} & {gammaBar_LL.yz} \\ {gammaBar_LL.xz} & {gammaBar_LL.yz} & {gammaBar_LL.zz}\end{matrix} \right]}} _E} _F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{b\downarrow[{E\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _c}} {{{{{ \overset{d\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _a}}} + {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _F}} {{{{{ \overset{d\downarrow[{F\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _c}} {{{{{ \overset{d\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _a}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{a\downarrow[{B\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^B} _d}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{a\downarrow[{C\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _d}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{b\downarrow[{I\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _d}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{I\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _d}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _d} ^F}} {{{{{ \overset{B\downarrow[{F\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _F} _c}} {{{{{ \overset{d\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _a}}} + {{{{{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^C}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{E\downarrow[{F\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _F} _d}} {{{{{ \overset{d\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^D}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{E\downarrow[{C\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _C} _d}} {{{{{ \overset{d\downarrow[{D\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _i} ^I}} {{{{{ \overset{a\downarrow[{C\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _b}} {{{{{ \overset{i\downarrow[{J\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^D}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _i} ^I}} {{{{{ \overset{d\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}} {{{{{ \overset{i\downarrow[{J\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}}} - {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^F}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^B}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _i} ^I}} {{{{{ \overset{E\downarrow[{F\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _E} _F} _b}} {{{{{ \overset{i\downarrow[{J\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}}} + {{{{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^J}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^B}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} _i} ^I}} {{{{{{ \overset{i\downarrow J\rightarrow[{a\downarrow b\rightarrow}]}{\left[ \begin{matrix} \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} & \overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _a} _b}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{c\downarrow[{B\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^B} _e}} {{U->alpha}}}} + {{{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{c\downarrow[{I\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _d}} {{U->alpha}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _G} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{G\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}} {{U->alpha}}}} + {{{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _G} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{e\downarrow[{G\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}} {{U->alpha}}} - {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^F} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^G} ^B}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{F\downarrow[{G\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _F} _G} _e}} {{U->alpha}}}} + {{{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^I}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{{ \overset{C\downarrow[{E\downarrow d\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow d\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _E} _d}} {{U->alpha}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^B}} {{{{{ \overset{I\downarrow[{C\downarrow D\rightarrow}]}{\left[ \begin{matrix} \overset{C\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _C} _D}} {{U->alpha}}}} + {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^B}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{C\downarrow[{D\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xx} & {partial_gammaBar_LLl[1].xx} & {partial_gammaBar_LLl[2].xx} \\ {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xy} & {partial_gammaBar_LLl[1].xy} & {partial_gammaBar_LLl[2].xy} \\ {partial_gammaBar_LLl[0].yy} & {partial_gammaBar_LLl[1].yy} & {partial_gammaBar_LLl[2].yy} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz}\end{matrix} \right]} \\ \overset{D\downarrow e\rightarrow}{\left[ \begin{matrix} {partial_gammaBar_LLl[0].xz} & {partial_gammaBar_LLl[1].xz} & {partial_gammaBar_LLl[2].xz} \\ {partial_gammaBar_LLl[0].yz} & {partial_gammaBar_LLl[1].yz} & {partial_gammaBar_LLl[2].yz} \\ {partial_gammaBar_LLl[0].zz} & {partial_gammaBar_LLl[1].zz} & {partial_gammaBar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _C} _D} _e}} {{U->alpha}}} + {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^C} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{c\downarrow[{E\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _e}} {{U->alpha}}} + {{{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _G} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^I} ^B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^e} _E}} {{{{{ \overset{d\downarrow[{G\downarrow e\rightarrow}]}{\left[ \begin{matrix} \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}} {{U->alpha}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _D} _B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{a\downarrow[{D\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^D} _c}} {{U->alpha}}}} + {{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _D} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{{ \overset{b\downarrow[{D\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _a}} {{U->alpha}}} + {{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _B} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{c\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _a}} {{U->alpha}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {ABar_LL.xx} & {ABar_LL.xy} & {ABar_LL.xz} \\ {ABar_LL.xy} & {ABar_LL.yy} & {ABar_LL.yz} \\ {ABar_LL.xz} & {ABar_LL.yz} & {ABar_LL.zz}\end{matrix} \right]}} _A} _E}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^C}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{b\downarrow[{E\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _c}} {{U->alpha}}}} + {{{{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{{ \overset{B\downarrow[{E\downarrow a\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xx} & {partial_ABar_LLl[1].xx} & {partial_ABar_LLl[2].xx} \\ {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].yy} & {partial_ABar_LLl[1].yy} & {partial_ABar_LLl[2].yy} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz} \\ {partial_ABar_LLl[0].zz} & {partial_ABar_LLl[1].zz} & {partial_ABar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _B} _E} _a}} {{U->alpha}}} - {{{2}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^D} ^I}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^E} ^C}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^c} _C}} {{{{{ \overset{D\downarrow[{E\downarrow c\rightarrow}]}{\left[ \begin{matrix} \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xx} & {partial_ABar_LLl[1].xx} & {partial_ABar_LLl[2].xx} \\ {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz}\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xy} & {partial_ABar_LLl[1].xy} & {partial_ABar_LLl[2].xy} \\ {partial_ABar_LLl[0].yy} & {partial_ABar_LLl[1].yy} & {partial_ABar_LLl[2].yy} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz}\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} {partial_ABar_LLl[0].xz} & {partial_ABar_LLl[1].xz} & {partial_ABar_LLl[2].xz} \\ {partial_ABar_LLl[0].yz} & {partial_ABar_LLl[1].yz} & {partial_ABar_LLl[2].yz} \\ {partial_ABar_LLl[0].zz} & {partial_ABar_LLl[1].zz} & {partial_ABar_LLl[2].zz}\end{matrix} \right]}\end{matrix} \right]}} _D} _E} _c}} {{U->alpha}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _b}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^A}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^B} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{{det_gammaBar}}^{2}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} 0 \\ 0 \\ 0\end{matrix} \right]}} _b}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^B}} {{{{ \overset{i\downarrow j\rightarrow}{\left[ \begin{matrix} {gammaBar_UU.xx} & {gammaBar_UU.xy} & {gammaBar_UU.xz} \\ {gammaBar_UU.xy} & {gammaBar_UU.yy} & {gammaBar_UU.yz} \\ {gammaBar_UU.xz} & {gammaBar_UU.yz} & {gammaBar_UU.zz}\end{matrix} \right]}} ^A} ^I}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{{det_gammaBar}}^{2}}}}}}$



double tmp1 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xy;
double tmp2 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xz;
double tmp3 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xx;
double tmp4 = tmp1 + tmp2;
double tmp5 = tmp3 + tmp4;
double tmp6 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yy;
double tmp7 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yz;
double tmp8 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xy;
double tmp9 = tmp6 + tmp7;
double tmp10 = tmp8 + tmp9;
double tmp11 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xy;
double tmp12 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xz;
double tmp13 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xx;
double tmp14 = tmp11 + tmp12;
double tmp15 = tmp13 + tmp14;
double tmp16 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yz;
double tmp17 = gammaBar_UU.xz * partial_gammaBar_LLl[0].zz;
double tmp18 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xz;
double tmp19 = tmp16 + tmp17;
double tmp20 = tmp18 + tmp19;
double tmp21 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xy;
double tmp22 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xz;
double tmp23 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xx;
double tmp24 = tmp21 + tmp22;
double tmp25 = tmp23 + tmp24;
double tmp26 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yy;
double tmp27 = gammaBar_UU.xz * partial_gammaBar_LLl[1].yz;
double tmp28 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xy;
double tmp29 = tmp26 + tmp27;
double tmp30 = tmp28 + tmp29;
double tmp31 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yz;
double tmp32 = gammaBar_UU.xz * partial_gammaBar_LLl[1].zz;
double tmp33 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xz;
double tmp34 = tmp31 + tmp32;
double tmp35 = tmp33 + tmp34;
double tmp36 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yy;
double tmp37 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yz;
double tmp38 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xy;
double tmp39 = tmp36 + tmp37;
double tmp40 = tmp38 + tmp39;
double tmp41 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yz;
double tmp42 = gammaBar_UU.xz * partial_gammaBar_LLl[2].zz;
double tmp43 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xz;
double tmp44 = tmp41 + tmp42;
double tmp45 = tmp43 + tmp44;
double tmp46 = gammaBar_UU.yz * tmp40;
double tmp47 = gammaBar_UU.zz * tmp45;
double tmp48 = gammaBar_UU.yz * tmp35;
double tmp49 = tmp46 + tmp47;
double tmp50 = gammaBar_UU.yy * tmp30;
double tmp51 = tmp48 + tmp49;
double tmp52 = gammaBar_UU.xz * tmp25;
double tmp53 = tmp50 + tmp51;
double tmp54 = gammaBar_UU.xz * tmp20;
double tmp55 = tmp52 + tmp53;
double tmp56 = gammaBar_UU.xy * tmp15;
double tmp57 = tmp54 + tmp55;
double tmp58 = gammaBar_UU.xy * tmp10;
double tmp59 = tmp56 + tmp57;
double tmp60 = gammaBar_UU.xx * tmp5;
double tmp61 = tmp58 + tmp59;
double tmp62 = partial_beta_Ul[1].y + partial_beta_Ul[2].z;
double tmp63 = tmp60 + tmp61;
double tmp64 = partial_beta_Ul[0].x + tmp62;
double tmp65 = 1. / 3.;
double tmp68 = partial2_beta_Ull[2][1].y + partial2_beta_Ull[2][2].z;
double tmp69 = partial2_beta_Ull[2][0].x + tmp68;
double tmp72 = partial2_beta_Ull[1][1].y + partial2_beta_Ull[1][2].z;
double tmp73 = partial2_beta_Ull[1][0].x + tmp72;
double tmp76 = partial2_beta_Ull[0][1].y + partial2_beta_Ull[0][2].z;
double tmp77 = partial2_beta_Ull[0][0].x + tmp76;
double tmp84 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].xx;
double tmp85 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].xx;
double tmp86 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].xx;
double tmp87 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].xy;
double tmp88 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].xy;
double tmp89 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].xy;
double tmp90 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].xz;
double tmp91 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].xz;
double tmp92 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].xz;
double tmp93 = gammaBar_UU.yz * tmp91;
double tmp94 = gammaBar_UU.zz * tmp92;
double tmp95 = gammaBar_UU.xz * tmp90;
double tmp96 = tmp93 + tmp94;
double tmp97 = gammaBar_UU.yz * tmp89;
double tmp98 = tmp95 + tmp96;
double tmp99 = gammaBar_UU.yy * tmp88;
double tmp100 = tmp97 + tmp98;
double tmp101 = gammaBar_UU.xy * tmp87;
double tmp102 = tmp99 + tmp100;
double tmp103 = gammaBar_UU.xz * tmp86;
double tmp104 = tmp101 + tmp102;
double tmp105 = gammaBar_UU.xy * tmp85;
double tmp106 = tmp103 + tmp104;
double tmp107 = gammaBar_UU.xx * tmp84;
double tmp108 = tmp105 + tmp106;
double tmp109 = tmp107 + tmp108;
double tmp111 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].xx;
double tmp112 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].xx;
double tmp114 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].xy;
double tmp115 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].xy;
double tmp117 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].xz;
double tmp118 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].xz;
double tmp119 = gammaBar_UU.yz * tmp117;
double tmp120 = gammaBar_UU.zz * tmp118;
double tmp121 = gammaBar_UU.xz * tmp91;
double tmp122 = tmp119 + tmp120;
double tmp123 = gammaBar_UU.yz * tmp115;
double tmp124 = tmp121 + tmp122;
double tmp125 = gammaBar_UU.yy * tmp114;
double tmp126 = tmp123 + tmp124;
double tmp127 = gammaBar_UU.xy * tmp88;
double tmp128 = tmp125 + tmp126;
double tmp129 = gammaBar_UU.xz * tmp112;
double tmp130 = tmp127 + tmp128;
double tmp131 = gammaBar_UU.xy * tmp111;
double tmp132 = tmp129 + tmp130;
double tmp133 = gammaBar_UU.xx * tmp85;
double tmp134 = tmp131 + tmp132;
double tmp135 = tmp133 + tmp134;
double tmp138 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].xx;
double tmp141 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].xy;
double tmp144 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].xz;
double tmp145 = gammaBar_UU.yz * tmp118;
double tmp146 = gammaBar_UU.zz * tmp144;
double tmp147 = gammaBar_UU.xz * tmp92;
double tmp148 = tmp145 + tmp146;
double tmp149 = gammaBar_UU.yz * tmp141;
double tmp150 = tmp147 + tmp148;
double tmp151 = gammaBar_UU.yy * tmp115;
double tmp152 = tmp149 + tmp150;
double tmp153 = gammaBar_UU.xy * tmp89;
double tmp154 = tmp151 + tmp152;
double tmp155 = gammaBar_UU.xz * tmp138;
double tmp156 = tmp153 + tmp154;
double tmp157 = gammaBar_UU.xy * tmp112;
double tmp158 = tmp155 + tmp156;
double tmp159 = gammaBar_UU.xx * tmp86;
double tmp160 = tmp157 + tmp158;
double tmp161 = tmp159 + tmp160;
double tmp165 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].yy;
double tmp166 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].yy;
double tmp167 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].yy;
double tmp168 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].yz;
double tmp169 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].yz;
double tmp170 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].yz;
double tmp171 = gammaBar_UU.yz * tmp169;
double tmp172 = gammaBar_UU.zz * tmp170;
double tmp173 = gammaBar_UU.xz * tmp168;
double tmp174 = tmp171 + tmp172;
double tmp175 = gammaBar_UU.yz * tmp167;
double tmp176 = tmp173 + tmp174;
double tmp177 = gammaBar_UU.yy * tmp166;
double tmp178 = tmp175 + tmp176;
double tmp179 = gammaBar_UU.xy * tmp165;
double tmp180 = tmp177 + tmp178;
double tmp181 = gammaBar_UU.xz * tmp89;
double tmp182 = tmp179 + tmp180;
double tmp184 = tmp181 + tmp182;
double tmp185 = gammaBar_UU.xx * tmp87;
double tmp186 = tmp184 + tmp127;
double tmp187 = tmp185 + tmp186;
double tmp192 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].yy;
double tmp193 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].yy;
double tmp195 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].yz;
double tmp196 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].yz;
double tmp197 = gammaBar_UU.yz * tmp195;
double tmp198 = gammaBar_UU.zz * tmp196;
double tmp199 = gammaBar_UU.xz * tmp169;
double tmp200 = tmp197 + tmp198;
double tmp201 = gammaBar_UU.yz * tmp193;
double tmp202 = tmp199 + tmp200;
double tmp203 = gammaBar_UU.yy * tmp192;
double tmp204 = tmp201 + tmp202;
double tmp205 = gammaBar_UU.xy * tmp166;
double tmp206 = tmp203 + tmp204;
double tmp207 = gammaBar_UU.xz * tmp115;
double tmp208 = tmp205 + tmp206;
double tmp209 = gammaBar_UU.xy * tmp114;
double tmp210 = tmp207 + tmp208;
double tmp211 = gammaBar_UU.xx * tmp88;
double tmp212 = tmp209 + tmp210;
double tmp213 = tmp211 + tmp212;
double tmp219 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].yy;
double tmp222 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].yz;
double tmp223 = gammaBar_UU.yz * tmp196;
double tmp224 = gammaBar_UU.zz * tmp222;
double tmp225 = gammaBar_UU.xz * tmp170;
double tmp226 = tmp223 + tmp224;
double tmp227 = gammaBar_UU.yz * tmp219;
double tmp228 = tmp225 + tmp226;
double tmp229 = gammaBar_UU.yy * tmp193;
double tmp230 = tmp227 + tmp228;
double tmp231 = gammaBar_UU.xy * tmp167;
double tmp232 = tmp229 + tmp230;
double tmp233 = gammaBar_UU.xz * tmp141;
double tmp234 = tmp231 + tmp232;
double tmp235 = gammaBar_UU.xy * tmp115;
double tmp236 = tmp233 + tmp234;
double tmp237 = gammaBar_UU.xx * tmp89;
double tmp238 = tmp235 + tmp236;
double tmp239 = tmp237 + tmp238;
double tmp246 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[2].zz;
double tmp247 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[2].zz;
double tmp248 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[2].zz;
double tmp249 = gammaBar_UU.yz * tmp247;
double tmp250 = gammaBar_UU.zz * tmp248;
double tmp251 = gammaBar_UU.xz * tmp246;
double tmp252 = tmp249 + tmp250;
double tmp253 = gammaBar_UU.yz * tmp170;
double tmp254 = tmp251 + tmp252;
double tmp255 = gammaBar_UU.yy * tmp169;
double tmp256 = tmp253 + tmp254;
double tmp257 = gammaBar_UU.xy * tmp168;
double tmp258 = tmp255 + tmp256;
double tmp260 = tmp257 + tmp258;
double tmp261 = gammaBar_UU.xy * tmp91;
double tmp262 = tmp260 + tmp147;
double tmp263 = gammaBar_UU.xx * tmp90;
double tmp264 = tmp261 + tmp262;
double tmp265 = tmp263 + tmp264;
double tmp273 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[2].zz;
double tmp274 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[2].zz;
double tmp275 = gammaBar_UU.yz * tmp273;
double tmp276 = gammaBar_UU.zz * tmp274;
double tmp277 = gammaBar_UU.xz * tmp247;
double tmp278 = tmp275 + tmp276;
double tmp280 = tmp277 + tmp278;
double tmp281 = gammaBar_UU.yy * tmp195;
double tmp282 = tmp280 + tmp223;
double tmp283 = gammaBar_UU.xy * tmp169;
double tmp284 = tmp281 + tmp282;
double tmp285 = gammaBar_UU.xz * tmp118;
double tmp286 = tmp283 + tmp284;
double tmp287 = gammaBar_UU.xy * tmp117;
double tmp288 = tmp285 + tmp286;
double tmp289 = gammaBar_UU.xx * tmp91;
double tmp290 = tmp287 + tmp288;
double tmp291 = tmp289 + tmp290;
double tmp300 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[2].zz;
double tmp301 = gammaBar_UU.yz * tmp274;
double tmp302 = gammaBar_UU.zz * tmp300;
double tmp303 = gammaBar_UU.xz * tmp248;
double tmp304 = tmp301 + tmp302;
double tmp305 = gammaBar_UU.yz * tmp222;
double tmp306 = tmp303 + tmp304;
double tmp307 = gammaBar_UU.yy * tmp196;
double tmp308 = tmp305 + tmp306;
double tmp309 = gammaBar_UU.xy * tmp170;
double tmp310 = tmp307 + tmp308;
double tmp311 = gammaBar_UU.xz * tmp144;
double tmp312 = tmp309 + tmp310;
double tmp313 = gammaBar_UU.xy * tmp118;
double tmp314 = tmp311 + tmp312;
double tmp315 = gammaBar_UU.xx * tmp92;
double tmp316 = tmp313 + tmp314;
double tmp317 = tmp315 + tmp316;
double tmp318 = gammaBar_UU.yz * tmp291;
double tmp319 = gammaBar_UU.zz * tmp317;
double tmp320 = gammaBar_UU.xz * tmp265;
double tmp321 = tmp318 + tmp319;
double tmp322 = gammaBar_UU.yz * tmp239;
double tmp323 = tmp320 + tmp321;
double tmp324 = gammaBar_UU.yy * tmp213;
double tmp325 = tmp322 + tmp323;
double tmp326 = gammaBar_UU.xy * tmp187;
double tmp327 = tmp324 + tmp325;
double tmp328 = gammaBar_UU.xz * tmp161;
double tmp329 = tmp326 + tmp327;
double tmp330 = gammaBar_UU.xy * tmp135;
double tmp331 = tmp328 + tmp329;
double tmp332 = gammaBar_UU.xx * tmp109;
double tmp333 = tmp330 + tmp331;
double tmp334 = tmp332 + tmp333;
double tmp335 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].xx;
double tmp336 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].xx;
double tmp337 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].xx;
double tmp338 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].xy;
double tmp339 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].xy;
double tmp340 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].xy;
double tmp341 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].xz;
double tmp342 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].xz;
double tmp343 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].xz;
double tmp344 = gammaBar_UU.yz * tmp342;
double tmp345 = gammaBar_UU.zz * tmp343;
double tmp346 = gammaBar_UU.xz * tmp341;
double tmp347 = tmp344 + tmp345;
double tmp348 = gammaBar_UU.yz * tmp340;
double tmp349 = tmp346 + tmp347;
double tmp350 = gammaBar_UU.yy * tmp339;
double tmp351 = tmp348 + tmp349;
double tmp352 = gammaBar_UU.xy * tmp338;
double tmp353 = tmp350 + tmp351;
double tmp354 = gammaBar_UU.xz * tmp337;
double tmp355 = tmp352 + tmp353;
double tmp356 = gammaBar_UU.xy * tmp336;
double tmp357 = tmp354 + tmp355;
double tmp358 = gammaBar_UU.xx * tmp335;
double tmp359 = tmp356 + tmp357;
double tmp360 = tmp358 + tmp359;
double tmp362 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].xx;
double tmp363 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].xx;
double tmp365 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].xy;
double tmp366 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].xy;
double tmp368 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].xz;
double tmp369 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].xz;
double tmp370 = gammaBar_UU.yz * tmp368;
double tmp371 = gammaBar_UU.zz * tmp369;
double tmp372 = gammaBar_UU.xz * tmp342;
double tmp373 = tmp370 + tmp371;
double tmp374 = gammaBar_UU.yz * tmp366;
double tmp375 = tmp372 + tmp373;
double tmp376 = gammaBar_UU.yy * tmp365;
double tmp377 = tmp374 + tmp375;
double tmp378 = gammaBar_UU.xy * tmp339;
double tmp379 = tmp376 + tmp377;
double tmp380 = gammaBar_UU.xz * tmp363;
double tmp381 = tmp378 + tmp379;
double tmp382 = gammaBar_UU.xy * tmp362;
double tmp383 = tmp380 + tmp381;
double tmp384 = gammaBar_UU.xx * tmp336;
double tmp385 = tmp382 + tmp383;
double tmp386 = tmp384 + tmp385;
double tmp389 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].xx;
double tmp392 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].xy;
double tmp395 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].xz;
double tmp396 = gammaBar_UU.yz * tmp369;
double tmp397 = gammaBar_UU.zz * tmp395;
double tmp398 = gammaBar_UU.xz * tmp343;
double tmp399 = tmp396 + tmp397;
double tmp400 = gammaBar_UU.yz * tmp392;
double tmp401 = tmp398 + tmp399;
double tmp402 = gammaBar_UU.yy * tmp366;
double tmp403 = tmp400 + tmp401;
double tmp404 = gammaBar_UU.xy * tmp340;
double tmp405 = tmp402 + tmp403;
double tmp406 = gammaBar_UU.xz * tmp389;
double tmp407 = tmp404 + tmp405;
double tmp408 = gammaBar_UU.xy * tmp363;
double tmp409 = tmp406 + tmp407;
double tmp410 = gammaBar_UU.xx * tmp337;
double tmp411 = tmp408 + tmp409;
double tmp412 = tmp410 + tmp411;
double tmp416 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].yy;
double tmp417 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].yy;
double tmp418 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].yy;
double tmp419 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].yz;
double tmp420 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].yz;
double tmp421 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].yz;
double tmp422 = gammaBar_UU.yz * tmp420;
double tmp423 = gammaBar_UU.zz * tmp421;
double tmp424 = gammaBar_UU.xz * tmp419;
double tmp425 = tmp422 + tmp423;
double tmp426 = gammaBar_UU.yz * tmp418;
double tmp427 = tmp424 + tmp425;
double tmp428 = gammaBar_UU.yy * tmp417;
double tmp429 = tmp426 + tmp427;
double tmp430 = gammaBar_UU.xy * tmp416;
double tmp431 = tmp428 + tmp429;
double tmp432 = gammaBar_UU.xz * tmp340;
double tmp433 = tmp430 + tmp431;
double tmp435 = tmp432 + tmp433;
double tmp436 = gammaBar_UU.xx * tmp338;
double tmp437 = tmp435 + tmp378;
double tmp438 = tmp436 + tmp437;
double tmp443 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].yy;
double tmp444 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].yy;
double tmp446 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].yz;
double tmp447 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].yz;
double tmp448 = gammaBar_UU.yz * tmp446;
double tmp449 = gammaBar_UU.zz * tmp447;
double tmp450 = gammaBar_UU.xz * tmp420;
double tmp451 = tmp448 + tmp449;
double tmp452 = gammaBar_UU.yz * tmp444;
double tmp453 = tmp450 + tmp451;
double tmp454 = gammaBar_UU.yy * tmp443;
double tmp455 = tmp452 + tmp453;
double tmp456 = gammaBar_UU.xy * tmp417;
double tmp457 = tmp454 + tmp455;
double tmp458 = gammaBar_UU.xz * tmp366;
double tmp459 = tmp456 + tmp457;
double tmp460 = gammaBar_UU.xy * tmp365;
double tmp461 = tmp458 + tmp459;
double tmp462 = gammaBar_UU.xx * tmp339;
double tmp463 = tmp460 + tmp461;
double tmp464 = tmp462 + tmp463;
double tmp470 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].yy;
double tmp473 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].yz;
double tmp474 = gammaBar_UU.yz * tmp447;
double tmp475 = gammaBar_UU.zz * tmp473;
double tmp476 = gammaBar_UU.xz * tmp421;
double tmp477 = tmp474 + tmp475;
double tmp478 = gammaBar_UU.yz * tmp470;
double tmp479 = tmp476 + tmp477;
double tmp480 = gammaBar_UU.yy * tmp444;
double tmp481 = tmp478 + tmp479;
double tmp482 = gammaBar_UU.xy * tmp418;
double tmp483 = tmp480 + tmp481;
double tmp484 = gammaBar_UU.xz * tmp392;
double tmp485 = tmp482 + tmp483;
double tmp486 = gammaBar_UU.xy * tmp366;
double tmp487 = tmp484 + tmp485;
double tmp488 = gammaBar_UU.xx * tmp340;
double tmp489 = tmp486 + tmp487;
double tmp490 = tmp488 + tmp489;
double tmp497 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[2].zz;
double tmp498 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[2].zz;
double tmp499 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[2].zz;
double tmp500 = gammaBar_UU.yz * tmp498;
double tmp501 = gammaBar_UU.zz * tmp499;
double tmp502 = gammaBar_UU.xz * tmp497;
double tmp503 = tmp500 + tmp501;
double tmp504 = gammaBar_UU.yz * tmp421;
double tmp505 = tmp502 + tmp503;
double tmp506 = gammaBar_UU.yy * tmp420;
double tmp507 = tmp504 + tmp505;
double tmp508 = gammaBar_UU.xy * tmp419;
double tmp509 = tmp506 + tmp507;
double tmp511 = tmp508 + tmp509;
double tmp512 = gammaBar_UU.xy * tmp342;
double tmp513 = tmp511 + tmp398;
double tmp514 = gammaBar_UU.xx * tmp341;
double tmp515 = tmp512 + tmp513;
double tmp516 = tmp514 + tmp515;
double tmp524 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[2].zz;
double tmp525 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[2].zz;
double tmp526 = gammaBar_UU.yz * tmp524;
double tmp527 = gammaBar_UU.zz * tmp525;
double tmp528 = gammaBar_UU.xz * tmp498;
double tmp529 = tmp526 + tmp527;
double tmp531 = tmp528 + tmp529;
double tmp532 = gammaBar_UU.yy * tmp446;
double tmp533 = tmp531 + tmp474;
double tmp534 = gammaBar_UU.xy * tmp420;
double tmp535 = tmp532 + tmp533;
double tmp536 = gammaBar_UU.xz * tmp369;
double tmp537 = tmp534 + tmp535;
double tmp538 = gammaBar_UU.xy * tmp368;
double tmp539 = tmp536 + tmp537;
double tmp540 = gammaBar_UU.xx * tmp342;
double tmp541 = tmp538 + tmp539;
double tmp542 = tmp540 + tmp541;
double tmp551 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[2].zz;
double tmp552 = gammaBar_UU.yz * tmp525;
double tmp553 = gammaBar_UU.zz * tmp551;
double tmp554 = gammaBar_UU.xz * tmp499;
double tmp555 = tmp552 + tmp553;
double tmp556 = gammaBar_UU.yz * tmp473;
double tmp557 = tmp554 + tmp555;
double tmp558 = gammaBar_UU.yy * tmp447;
double tmp559 = tmp556 + tmp557;
double tmp560 = gammaBar_UU.xy * tmp421;
double tmp561 = tmp558 + tmp559;
double tmp562 = gammaBar_UU.xz * tmp395;
double tmp563 = tmp560 + tmp561;
double tmp564 = gammaBar_UU.xy * tmp369;
double tmp565 = tmp562 + tmp563;
double tmp566 = gammaBar_UU.xx * tmp343;
double tmp567 = tmp564 + tmp565;
double tmp568 = tmp566 + tmp567;
double tmp569 = gammaBar_UU.yz * tmp542;
double tmp570 = gammaBar_UU.zz * tmp568;
double tmp571 = gammaBar_UU.xz * tmp516;
double tmp572 = tmp569 + tmp570;
double tmp573 = gammaBar_UU.yz * tmp490;
double tmp574 = tmp571 + tmp572;
double tmp575 = gammaBar_UU.yy * tmp464;
double tmp576 = tmp573 + tmp574;
double tmp577 = gammaBar_UU.xy * tmp438;
double tmp578 = tmp575 + tmp576;
double tmp579 = gammaBar_UU.xz * tmp412;
double tmp580 = tmp577 + tmp578;
double tmp581 = gammaBar_UU.xy * tmp386;
double tmp582 = tmp579 + tmp580;
double tmp583 = gammaBar_UU.xx * tmp360;
double tmp584 = tmp581 + tmp582;
double tmp585 = tmp583 + tmp584;
double tmp586 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].xx;
double tmp587 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].xy;
double tmp588 = gammaBar_UU.xy * tmp587;
double tmp589 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].xz;
double tmp590 = gammaBar_UU.xz * tmp589;
double tmp591 = partial_gammaBar_LLl[2].xy * partial_gammaBar_LLl[2].xy;
double tmp592 = partial_gammaBar_LLl[2].xy * partial_gammaBar_LLl[2].xz;
double tmp593 = gammaBar_UU.yz * tmp592;
double tmp594 = partial_gammaBar_LLl[2].xz * partial_gammaBar_LLl[2].xz;
double tmp595 = 2. * tmp593;
double tmp596 = gammaBar_UU.zz * tmp594;
double tmp597 = gammaBar_UU.yy * tmp591;
double tmp598 = tmp595 + tmp596;
double tmp599 = 2. * tmp590;
double tmp600 = tmp597 + tmp598;
double tmp601 = 2. * tmp588;
double tmp602 = tmp599 + tmp600;
double tmp603 = gammaBar_UU.xx * tmp586;
double tmp604 = tmp601 + tmp602;
double tmp605 = tmp603 + tmp604;
double tmp607 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].yy;
double tmp608 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].yz;
double tmp610 = partial_gammaBar_LLl[2].xy * partial_gammaBar_LLl[2].yy;
double tmp611 = partial_gammaBar_LLl[2].xy * partial_gammaBar_LLl[2].yz;
double tmp613 = partial_gammaBar_LLl[2].xz * partial_gammaBar_LLl[2].yy;
double tmp614 = partial_gammaBar_LLl[2].xz * partial_gammaBar_LLl[2].yz;
double tmp615 = gammaBar_UU.yz * tmp613;
double tmp616 = gammaBar_UU.zz * tmp614;
double tmp617 = gammaBar_UU.xz * tmp592;
double tmp618 = tmp615 + tmp616;
double tmp619 = gammaBar_UU.yz * tmp611;
double tmp620 = tmp617 + tmp618;
double tmp621 = gammaBar_UU.yy * tmp610;
double tmp622 = tmp619 + tmp620;
double tmp623 = gammaBar_UU.xy * tmp591;
double tmp624 = tmp621 + tmp622;
double tmp625 = gammaBar_UU.xz * tmp608;
double tmp626 = tmp623 + tmp624;
double tmp627 = gammaBar_UU.xy * tmp607;
double tmp628 = tmp625 + tmp626;
double tmp629 = gammaBar_UU.xx * tmp587;
double tmp630 = tmp627 + tmp628;
double tmp631 = tmp629 + tmp630;
double tmp632 = gammaBar_UU.xy * tmp631;
double tmp635 = partial_gammaBar_LLl[2].xx * partial_gammaBar_LLl[2].zz;
double tmp638 = partial_gammaBar_LLl[2].xy * partial_gammaBar_LLl[2].zz;
double tmp641 = partial_gammaBar_LLl[2].xz * partial_gammaBar_LLl[2].zz;
double tmp642 = gammaBar_UU.yz * tmp614;
double tmp643 = gammaBar_UU.zz * tmp641;
double tmp644 = gammaBar_UU.xz * tmp594;
double tmp645 = tmp642 + tmp643;
double tmp646 = gammaBar_UU.yz * tmp638;
double tmp647 = tmp644 + tmp645;
double tmp648 = gammaBar_UU.yy * tmp611;
double tmp649 = tmp646 + tmp647;
double tmp650 = gammaBar_UU.xy * tmp592;
double tmp651 = tmp648 + tmp649;
double tmp652 = gammaBar_UU.xz * tmp635;
double tmp653 = tmp650 + tmp651;
double tmp654 = gammaBar_UU.xy * tmp608;
double tmp655 = tmp652 + tmp653;
double tmp656 = gammaBar_UU.xx * tmp589;
double tmp657 = tmp654 + tmp655;
double tmp658 = tmp656 + tmp657;
double tmp659 = gammaBar_UU.xz * tmp658;
double tmp662 = gammaBar_UU.xy * tmp610;
double tmp664 = gammaBar_UU.xz * tmp611;
double tmp665 = partial_gammaBar_LLl[2].yy * partial_gammaBar_LLl[2].yy;
double tmp666 = partial_gammaBar_LLl[2].yy * partial_gammaBar_LLl[2].yz;
double tmp667 = gammaBar_UU.yz * tmp666;
double tmp668 = partial_gammaBar_LLl[2].yz * partial_gammaBar_LLl[2].yz;
double tmp669 = 2. * tmp667;
double tmp670 = gammaBar_UU.zz * tmp668;
double tmp671 = gammaBar_UU.yy * tmp665;
double tmp672 = tmp669 + tmp670;
double tmp673 = 2. * tmp664;
double tmp674 = tmp671 + tmp672;
double tmp675 = 2. * tmp662;
double tmp676 = tmp673 + tmp674;
double tmp677 = gammaBar_UU.xx * tmp591;
double tmp678 = tmp675 + tmp676;
double tmp679 = tmp677 + tmp678;
double tmp685 = partial_gammaBar_LLl[2].yy * partial_gammaBar_LLl[2].zz;
double tmp688 = partial_gammaBar_LLl[2].yz * partial_gammaBar_LLl[2].zz;
double tmp689 = gammaBar_UU.yz * tmp668;
double tmp690 = gammaBar_UU.zz * tmp688;
double tmp691 = gammaBar_UU.xz * tmp614;
double tmp692 = tmp689 + tmp690;
double tmp693 = gammaBar_UU.yz * tmp685;
double tmp694 = tmp691 + tmp692;
double tmp695 = gammaBar_UU.yy * tmp666;
double tmp696 = tmp693 + tmp694;
double tmp697 = gammaBar_UU.xy * tmp613;
double tmp698 = tmp695 + tmp696;
double tmp699 = gammaBar_UU.xz * tmp638;
double tmp700 = tmp697 + tmp698;
double tmp701 = gammaBar_UU.xy * tmp611;
double tmp702 = tmp699 + tmp700;
double tmp703 = gammaBar_UU.xx * tmp592;
double tmp704 = tmp701 + tmp702;
double tmp705 = tmp703 + tmp704;
double tmp706 = gammaBar_UU.yz * tmp705;
double tmp709 = gammaBar_UU.xy * tmp614;
double tmp711 = gammaBar_UU.xz * tmp641;
double tmp714 = gammaBar_UU.yz * tmp688;
double tmp715 = partial_gammaBar_LLl[2].zz * partial_gammaBar_LLl[2].zz;
double tmp716 = 2. * tmp714;
double tmp717 = gammaBar_UU.zz * tmp715;
double tmp718 = gammaBar_UU.yy * tmp668;
double tmp719 = tmp716 + tmp717;
double tmp720 = 2. * tmp711;
double tmp721 = tmp718 + tmp719;
double tmp722 = 2. * tmp709;
double tmp723 = tmp720 + tmp721;
double tmp724 = gammaBar_UU.xx * tmp594;
double tmp725 = tmp722 + tmp723;
double tmp726 = tmp724 + tmp725;
double tmp727 = 2. * tmp706;
double tmp728 = gammaBar_UU.zz * tmp726;
double tmp729 = gammaBar_UU.yy * tmp679;
double tmp730 = tmp727 + tmp728;
double tmp731 = 2. * tmp659;
double tmp732 = tmp729 + tmp730;
double tmp733 = 2. * tmp632;
double tmp734 = tmp731 + tmp732;
double tmp735 = gammaBar_UU.xx * tmp605;
double tmp736 = tmp733 + tmp734;
double tmp737 = tmp735 + tmp736;
double tmp743 = 1. / 2.;
double tmp745 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].xx;
double tmp746 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].xx;
double tmp747 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].xx;
double tmp748 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].xy;
double tmp749 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].xy;
double tmp750 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].xy;
double tmp751 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].xz;
double tmp752 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].xz;
double tmp753 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].xz;
double tmp754 = gammaBar_UU.yz * tmp752;
double tmp755 = gammaBar_UU.zz * tmp753;
double tmp756 = gammaBar_UU.xz * tmp751;
double tmp757 = tmp754 + tmp755;
double tmp758 = gammaBar_UU.yz * tmp750;
double tmp759 = tmp756 + tmp757;
double tmp760 = gammaBar_UU.yy * tmp749;
double tmp761 = tmp758 + tmp759;
double tmp762 = gammaBar_UU.xy * tmp748;
double tmp763 = tmp760 + tmp761;
double tmp764 = gammaBar_UU.xz * tmp747;
double tmp765 = tmp762 + tmp763;
double tmp766 = gammaBar_UU.xy * tmp746;
double tmp767 = tmp764 + tmp765;
double tmp768 = gammaBar_UU.xx * tmp745;
double tmp769 = tmp766 + tmp767;
double tmp770 = tmp768 + tmp769;
double tmp772 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].xx;
double tmp773 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].xx;
double tmp775 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].xy;
double tmp776 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].xy;
double tmp778 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].xz;
double tmp779 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].xz;
double tmp780 = gammaBar_UU.yz * tmp778;
double tmp781 = gammaBar_UU.zz * tmp779;
double tmp782 = gammaBar_UU.xz * tmp752;
double tmp783 = tmp780 + tmp781;
double tmp784 = gammaBar_UU.yz * tmp776;
double tmp785 = tmp782 + tmp783;
double tmp786 = gammaBar_UU.yy * tmp775;
double tmp787 = tmp784 + tmp785;
double tmp788 = gammaBar_UU.xy * tmp749;
double tmp789 = tmp786 + tmp787;
double tmp790 = gammaBar_UU.xz * tmp773;
double tmp791 = tmp788 + tmp789;
double tmp792 = gammaBar_UU.xy * tmp772;
double tmp793 = tmp790 + tmp791;
double tmp794 = gammaBar_UU.xx * tmp746;
double tmp795 = tmp792 + tmp793;
double tmp796 = tmp794 + tmp795;
double tmp799 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].xx;
double tmp802 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].xy;
double tmp805 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].xz;
double tmp806 = gammaBar_UU.yz * tmp779;
double tmp807 = gammaBar_UU.zz * tmp805;
double tmp808 = gammaBar_UU.xz * tmp753;
double tmp809 = tmp806 + tmp807;
double tmp810 = gammaBar_UU.yz * tmp802;
double tmp811 = tmp808 + tmp809;
double tmp812 = gammaBar_UU.yy * tmp776;
double tmp813 = tmp810 + tmp811;
double tmp814 = gammaBar_UU.xy * tmp750;
double tmp815 = tmp812 + tmp813;
double tmp816 = gammaBar_UU.xz * tmp799;
double tmp817 = tmp814 + tmp815;
double tmp818 = gammaBar_UU.xy * tmp773;
double tmp819 = tmp816 + tmp817;
double tmp820 = gammaBar_UU.xx * tmp747;
double tmp821 = tmp818 + tmp819;
double tmp822 = tmp820 + tmp821;
double tmp826 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].yy;
double tmp827 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].yy;
double tmp828 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].yy;
double tmp829 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].yz;
double tmp830 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].yz;
double tmp831 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].yz;
double tmp832 = gammaBar_UU.yz * tmp830;
double tmp833 = gammaBar_UU.zz * tmp831;
double tmp834 = gammaBar_UU.xz * tmp829;
double tmp835 = tmp832 + tmp833;
double tmp836 = gammaBar_UU.yz * tmp828;
double tmp837 = tmp834 + tmp835;
double tmp838 = gammaBar_UU.yy * tmp827;
double tmp839 = tmp836 + tmp837;
double tmp840 = gammaBar_UU.xy * tmp826;
double tmp841 = tmp838 + tmp839;
double tmp842 = gammaBar_UU.xz * tmp750;
double tmp843 = tmp840 + tmp841;
double tmp845 = tmp842 + tmp843;
double tmp846 = gammaBar_UU.xx * tmp748;
double tmp847 = tmp845 + tmp788;
double tmp848 = tmp846 + tmp847;
double tmp853 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].yy;
double tmp854 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].yy;
double tmp856 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].yz;
double tmp857 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].yz;
double tmp858 = gammaBar_UU.yz * tmp856;
double tmp859 = gammaBar_UU.zz * tmp857;
double tmp860 = gammaBar_UU.xz * tmp830;
double tmp861 = tmp858 + tmp859;
double tmp862 = gammaBar_UU.yz * tmp854;
double tmp863 = tmp860 + tmp861;
double tmp864 = gammaBar_UU.yy * tmp853;
double tmp865 = tmp862 + tmp863;
double tmp866 = gammaBar_UU.xy * tmp827;
double tmp867 = tmp864 + tmp865;
double tmp868 = gammaBar_UU.xz * tmp776;
double tmp869 = tmp866 + tmp867;
double tmp870 = gammaBar_UU.xy * tmp775;
double tmp871 = tmp868 + tmp869;
double tmp872 = gammaBar_UU.xx * tmp749;
double tmp873 = tmp870 + tmp871;
double tmp874 = tmp872 + tmp873;
double tmp880 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].yy;
double tmp883 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].yz;
double tmp884 = gammaBar_UU.yz * tmp857;
double tmp885 = gammaBar_UU.zz * tmp883;
double tmp886 = gammaBar_UU.xz * tmp831;
double tmp887 = tmp884 + tmp885;
double tmp888 = gammaBar_UU.yz * tmp880;
double tmp889 = tmp886 + tmp887;
double tmp890 = gammaBar_UU.yy * tmp854;
double tmp891 = tmp888 + tmp889;
double tmp892 = gammaBar_UU.xy * tmp828;
double tmp893 = tmp890 + tmp891;
double tmp894 = gammaBar_UU.xz * tmp802;
double tmp895 = tmp892 + tmp893;
double tmp896 = gammaBar_UU.xy * tmp776;
double tmp897 = tmp894 + tmp895;
double tmp898 = gammaBar_UU.xx * tmp750;
double tmp899 = tmp896 + tmp897;
double tmp900 = tmp898 + tmp899;
double tmp907 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[1].zz;
double tmp908 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[1].zz;
double tmp909 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[1].zz;
double tmp910 = gammaBar_UU.yz * tmp908;
double tmp911 = gammaBar_UU.zz * tmp909;
double tmp912 = gammaBar_UU.xz * tmp907;
double tmp913 = tmp910 + tmp911;
double tmp914 = gammaBar_UU.yz * tmp831;
double tmp915 = tmp912 + tmp913;
double tmp916 = gammaBar_UU.yy * tmp830;
double tmp917 = tmp914 + tmp915;
double tmp918 = gammaBar_UU.xy * tmp829;
double tmp919 = tmp916 + tmp917;
double tmp921 = tmp918 + tmp919;
double tmp922 = gammaBar_UU.xy * tmp752;
double tmp923 = tmp921 + tmp808;
double tmp924 = gammaBar_UU.xx * tmp751;
double tmp925 = tmp922 + tmp923;
double tmp926 = tmp924 + tmp925;
double tmp934 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[1].zz;
double tmp935 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[1].zz;
double tmp936 = gammaBar_UU.yz * tmp934;
double tmp937 = gammaBar_UU.zz * tmp935;
double tmp938 = gammaBar_UU.xz * tmp908;
double tmp939 = tmp936 + tmp937;
double tmp941 = tmp938 + tmp939;
double tmp942 = gammaBar_UU.yy * tmp856;
double tmp943 = tmp941 + tmp884;
double tmp944 = gammaBar_UU.xy * tmp830;
double tmp945 = tmp942 + tmp943;
double tmp946 = gammaBar_UU.xz * tmp779;
double tmp947 = tmp944 + tmp945;
double tmp948 = gammaBar_UU.xy * tmp778;
double tmp949 = tmp946 + tmp947;
double tmp950 = gammaBar_UU.xx * tmp752;
double tmp951 = tmp948 + tmp949;
double tmp952 = tmp950 + tmp951;
double tmp961 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[1].zz;
double tmp962 = gammaBar_UU.yz * tmp935;
double tmp963 = gammaBar_UU.zz * tmp961;
double tmp964 = gammaBar_UU.xz * tmp909;
double tmp965 = tmp962 + tmp963;
double tmp966 = gammaBar_UU.yz * tmp883;
double tmp967 = tmp964 + tmp965;
double tmp968 = gammaBar_UU.yy * tmp857;
double tmp969 = tmp966 + tmp967;
double tmp970 = gammaBar_UU.xy * tmp831;
double tmp971 = tmp968 + tmp969;
double tmp972 = gammaBar_UU.xz * tmp805;
double tmp973 = tmp970 + tmp971;
double tmp974 = gammaBar_UU.xy * tmp779;
double tmp975 = tmp972 + tmp973;
double tmp976 = gammaBar_UU.xx * tmp753;
double tmp977 = tmp974 + tmp975;
double tmp978 = tmp976 + tmp977;
double tmp979 = gammaBar_UU.yz * tmp952;
double tmp980 = gammaBar_UU.zz * tmp978;
double tmp981 = gammaBar_UU.xz * tmp926;
double tmp982 = tmp979 + tmp980;
double tmp983 = gammaBar_UU.yz * tmp900;
double tmp984 = tmp981 + tmp982;
double tmp985 = gammaBar_UU.yy * tmp874;
double tmp986 = tmp983 + tmp984;
double tmp987 = gammaBar_UU.xy * tmp848;
double tmp988 = tmp985 + tmp986;
double tmp989 = gammaBar_UU.xz * tmp822;
double tmp990 = tmp987 + tmp988;
double tmp991 = gammaBar_UU.xy * tmp796;
double tmp992 = tmp989 + tmp990;
double tmp993 = gammaBar_UU.xx * tmp770;
double tmp994 = tmp991 + tmp992;
double tmp995 = tmp993 + tmp994;
double tmp996 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].xx;
double tmp997 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].xy;
double tmp998 = gammaBar_UU.xy * tmp997;
double tmp999 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].xz;
double tmp1000 = gammaBar_UU.xz * tmp999;
double tmp1001 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[1].xy;
double tmp1002 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[1].xz;
double tmp1003 = gammaBar_UU.yz * tmp1002;
double tmp1004 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[1].xz;
double tmp1005 = 2. * tmp1003;
double tmp1006 = gammaBar_UU.zz * tmp1004;
double tmp1007 = gammaBar_UU.yy * tmp1001;
double tmp1008 = tmp1005 + tmp1006;
double tmp1009 = 2. * tmp1000;
double tmp1010 = tmp1007 + tmp1008;
double tmp1011 = 2. * tmp998;
double tmp1012 = tmp1009 + tmp1010;
double tmp1013 = gammaBar_UU.xx * tmp996;
double tmp1014 = tmp1011 + tmp1012;
double tmp1015 = tmp1013 + tmp1014;
double tmp1017 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].yy;
double tmp1018 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].yz;
double tmp1020 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[1].yy;
double tmp1021 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[1].yz;
double tmp1023 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[1].yy;
double tmp1024 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[1].yz;
double tmp1025 = gammaBar_UU.yz * tmp1023;
double tmp1026 = gammaBar_UU.zz * tmp1024;
double tmp1027 = gammaBar_UU.xz * tmp1002;
double tmp1028 = tmp1025 + tmp1026;
double tmp1029 = gammaBar_UU.yz * tmp1021;
double tmp1030 = tmp1027 + tmp1028;
double tmp1031 = gammaBar_UU.yy * tmp1020;
double tmp1032 = tmp1029 + tmp1030;
double tmp1033 = gammaBar_UU.xy * tmp1001;
double tmp1034 = tmp1031 + tmp1032;
double tmp1035 = gammaBar_UU.xz * tmp1018;
double tmp1036 = tmp1033 + tmp1034;
double tmp1037 = gammaBar_UU.xy * tmp1017;
double tmp1038 = tmp1035 + tmp1036;
double tmp1039 = gammaBar_UU.xx * tmp997;
double tmp1040 = tmp1037 + tmp1038;
double tmp1041 = tmp1039 + tmp1040;
double tmp1042 = gammaBar_UU.xy * tmp1041;
double tmp1045 = partial_gammaBar_LLl[1].xx * partial_gammaBar_LLl[1].zz;
double tmp1048 = partial_gammaBar_LLl[1].xy * partial_gammaBar_LLl[1].zz;
double tmp1051 = partial_gammaBar_LLl[1].xz * partial_gammaBar_LLl[1].zz;
double tmp1052 = gammaBar_UU.yz * tmp1024;
double tmp1053 = gammaBar_UU.zz * tmp1051;
double tmp1054 = gammaBar_UU.xz * tmp1004;
double tmp1055 = tmp1052 + tmp1053;
double tmp1056 = gammaBar_UU.yz * tmp1048;
double tmp1057 = tmp1054 + tmp1055;
double tmp1058 = gammaBar_UU.yy * tmp1021;
double tmp1059 = tmp1056 + tmp1057;
double tmp1060 = gammaBar_UU.xy * tmp1002;
double tmp1061 = tmp1058 + tmp1059;
double tmp1062 = gammaBar_UU.xz * tmp1045;
double tmp1063 = tmp1060 + tmp1061;
double tmp1064 = gammaBar_UU.xy * tmp1018;
double tmp1065 = tmp1062 + tmp1063;
double tmp1066 = gammaBar_UU.xx * tmp999;
double tmp1067 = tmp1064 + tmp1065;
double tmp1068 = tmp1066 + tmp1067;
double tmp1069 = gammaBar_UU.xz * tmp1068;
double tmp1072 = gammaBar_UU.xy * tmp1020;
double tmp1074 = gammaBar_UU.xz * tmp1021;
double tmp1075 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[1].yy;
double tmp1076 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[1].yz;
double tmp1077 = gammaBar_UU.yz * tmp1076;
double tmp1078 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[1].yz;
double tmp1079 = 2. * tmp1077;
double tmp1080 = gammaBar_UU.zz * tmp1078;
double tmp1081 = gammaBar_UU.yy * tmp1075;
double tmp1082 = tmp1079 + tmp1080;
double tmp1083 = 2. * tmp1074;
double tmp1084 = tmp1081 + tmp1082;
double tmp1085 = 2. * tmp1072;
double tmp1086 = tmp1083 + tmp1084;
double tmp1087 = gammaBar_UU.xx * tmp1001;
double tmp1088 = tmp1085 + tmp1086;
double tmp1089 = tmp1087 + tmp1088;
double tmp1095 = partial_gammaBar_LLl[1].yy * partial_gammaBar_LLl[1].zz;
double tmp1098 = partial_gammaBar_LLl[1].yz * partial_gammaBar_LLl[1].zz;
double tmp1099 = gammaBar_UU.yz * tmp1078;
double tmp1100 = gammaBar_UU.zz * tmp1098;
double tmp1101 = gammaBar_UU.xz * tmp1024;
double tmp1102 = tmp1099 + tmp1100;
double tmp1103 = gammaBar_UU.yz * tmp1095;
double tmp1104 = tmp1101 + tmp1102;
double tmp1105 = gammaBar_UU.yy * tmp1076;
double tmp1106 = tmp1103 + tmp1104;
double tmp1107 = gammaBar_UU.xy * tmp1023;
double tmp1108 = tmp1105 + tmp1106;
double tmp1109 = gammaBar_UU.xz * tmp1048;
double tmp1110 = tmp1107 + tmp1108;
double tmp1111 = gammaBar_UU.xy * tmp1021;
double tmp1112 = tmp1109 + tmp1110;
double tmp1113 = gammaBar_UU.xx * tmp1002;
double tmp1114 = tmp1111 + tmp1112;
double tmp1115 = tmp1113 + tmp1114;
double tmp1116 = gammaBar_UU.yz * tmp1115;
double tmp1119 = gammaBar_UU.xy * tmp1024;
double tmp1121 = gammaBar_UU.xz * tmp1051;
double tmp1124 = gammaBar_UU.yz * tmp1098;
double tmp1125 = partial_gammaBar_LLl[1].zz * partial_gammaBar_LLl[1].zz;
double tmp1126 = 2. * tmp1124;
double tmp1127 = gammaBar_UU.zz * tmp1125;
double tmp1128 = gammaBar_UU.yy * tmp1078;
double tmp1129 = tmp1126 + tmp1127;
double tmp1130 = 2. * tmp1121;
double tmp1131 = tmp1128 + tmp1129;
double tmp1132 = 2. * tmp1119;
double tmp1133 = tmp1130 + tmp1131;
double tmp1134 = gammaBar_UU.xx * tmp1004;
double tmp1135 = tmp1132 + tmp1133;
double tmp1136 = tmp1134 + tmp1135;
double tmp1137 = 2. * tmp1116;
double tmp1138 = gammaBar_UU.zz * tmp1136;
double tmp1139 = gammaBar_UU.yy * tmp1089;
double tmp1140 = tmp1137 + tmp1138;
double tmp1141 = 2. * tmp1069;
double tmp1142 = tmp1139 + tmp1140;
double tmp1143 = 2. * tmp1042;
double tmp1144 = tmp1141 + tmp1142;
double tmp1145 = gammaBar_UU.xx * tmp1015;
double tmp1146 = tmp1143 + tmp1144;
double tmp1147 = tmp1145 + tmp1146;
double tmp1160 = tmp348 + tmp345;
double tmp1162 = tmp1160 + tmp354;
double tmp1164 = tmp1162 + tmp344;
double tmp1166 = tmp1164 + tmp350;
double tmp1168 = tmp1166 + tmp356;
double tmp1170 = tmp1168 + tmp346;
double tmp1172 = tmp1170 + tmp352;
double tmp1173 = tmp1172 + tmp358;
double tmp1186 = tmp426 + tmp423;
double tmp1188 = tmp1186 + tmp432;
double tmp1190 = tmp1188 + tmp422;
double tmp1192 = tmp1190 + tmp428;
double tmp1194 = tmp1192 + tmp378;
double tmp1196 = tmp1194 + tmp424;
double tmp1198 = tmp1196 + tmp430;
double tmp1199 = tmp1198 + tmp436;
double tmp1212 = tmp504 + tmp501;
double tmp1214 = tmp1212 + tmp398;
double tmp1216 = tmp1214 + tmp500;
double tmp1218 = tmp1216 + tmp506;
double tmp1220 = tmp1218 + tmp512;
double tmp1222 = tmp1220 + tmp502;
double tmp1224 = tmp1222 + tmp508;
double tmp1225 = tmp1224 + tmp514;
double tmp1238 = tmp374 + tmp371;
double tmp1240 = tmp1238 + tmp380;
double tmp1242 = tmp1240 + tmp370;
double tmp1244 = tmp1242 + tmp376;
double tmp1246 = tmp1244 + tmp382;
double tmp1248 = tmp1246 + tmp372;
double tmp1250 = tmp1248 + tmp378;
double tmp1251 = tmp1250 + tmp384;
double tmp1264 = tmp452 + tmp449;
double tmp1266 = tmp1264 + tmp458;
double tmp1268 = tmp1266 + tmp448;
double tmp1270 = tmp1268 + tmp454;
double tmp1272 = tmp1270 + tmp460;
double tmp1274 = tmp1272 + tmp450;
double tmp1276 = tmp1274 + tmp456;
double tmp1277 = tmp1276 + tmp462;
double tmp1290 = tmp474 + tmp527;
double tmp1292 = tmp1290 + tmp536;
double tmp1294 = tmp1292 + tmp526;
double tmp1296 = tmp1294 + tmp532;
double tmp1298 = tmp1296 + tmp538;
double tmp1300 = tmp1298 + tmp528;
double tmp1302 = tmp1300 + tmp534;
double tmp1303 = tmp1302 + tmp540;
double tmp1316 = tmp400 + tmp397;
double tmp1318 = tmp1316 + tmp406;
double tmp1320 = tmp1318 + tmp396;
double tmp1322 = tmp1320 + tmp402;
double tmp1324 = tmp1322 + tmp408;
double tmp1326 = tmp1324 + tmp398;
double tmp1328 = tmp1326 + tmp404;
double tmp1329 = tmp1328 + tmp410;
double tmp1342 = tmp478 + tmp475;
double tmp1344 = tmp1342 + tmp484;
double tmp1346 = tmp1344 + tmp474;
double tmp1348 = tmp1346 + tmp480;
double tmp1350 = tmp1348 + tmp486;
double tmp1352 = tmp1350 + tmp476;
double tmp1354 = tmp1352 + tmp482;
double tmp1355 = tmp1354 + tmp488;
double tmp1368 = tmp556 + tmp553;
double tmp1370 = tmp1368 + tmp562;
double tmp1372 = tmp1370 + tmp552;
double tmp1374 = tmp1372 + tmp558;
double tmp1376 = tmp1374 + tmp564;
double tmp1378 = tmp1376 + tmp554;
double tmp1380 = tmp1378 + tmp560;
double tmp1381 = tmp1380 + tmp566;
double tmp1382 = gammaBar_UU.yz * tmp1355;
double tmp1383 = gammaBar_UU.zz * tmp1381;
double tmp1384 = gammaBar_UU.xz * tmp1329;
double tmp1385 = tmp1382 + tmp1383;
double tmp1386 = gammaBar_UU.yz * tmp1303;
double tmp1387 = tmp1384 + tmp1385;
double tmp1388 = gammaBar_UU.yy * tmp1277;
double tmp1389 = tmp1386 + tmp1387;
double tmp1390 = gammaBar_UU.xy * tmp1251;
double tmp1391 = tmp1388 + tmp1389;
double tmp1392 = gammaBar_UU.xz * tmp1225;
double tmp1393 = tmp1390 + tmp1391;
double tmp1394 = gammaBar_UU.xy * tmp1199;
double tmp1395 = tmp1392 + tmp1393;
double tmp1396 = gammaBar_UU.xx * tmp1173;
double tmp1397 = tmp1394 + tmp1395;
double tmp1398 = tmp1396 + tmp1397;
double tmp1406 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].xx;
double tmp1407 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].xy;
double tmp1408 = gammaBar_UU.xy * tmp1407;
double tmp1409 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].xz;
double tmp1410 = gammaBar_UU.xz * tmp1409;
double tmp1411 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[0].xy;
double tmp1412 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[0].xz;
double tmp1413 = gammaBar_UU.yz * tmp1412;
double tmp1414 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[0].xz;
double tmp1415 = 2. * tmp1413;
double tmp1416 = gammaBar_UU.zz * tmp1414;
double tmp1417 = gammaBar_UU.yy * tmp1411;
double tmp1418 = tmp1415 + tmp1416;
double tmp1419 = 2. * tmp1410;
double tmp1420 = tmp1417 + tmp1418;
double tmp1421 = 2. * tmp1408;
double tmp1422 = tmp1419 + tmp1420;
double tmp1423 = gammaBar_UU.xx * tmp1406;
double tmp1424 = tmp1421 + tmp1422;
double tmp1425 = tmp1423 + tmp1424;
double tmp1427 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].yy;
double tmp1428 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].yz;
double tmp1430 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[0].yy;
double tmp1431 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[0].yz;
double tmp1433 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[0].yy;
double tmp1434 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[0].yz;
double tmp1435 = gammaBar_UU.yz * tmp1433;
double tmp1436 = gammaBar_UU.zz * tmp1434;
double tmp1437 = gammaBar_UU.xz * tmp1412;
double tmp1438 = tmp1435 + tmp1436;
double tmp1439 = gammaBar_UU.yz * tmp1431;
double tmp1440 = tmp1437 + tmp1438;
double tmp1441 = gammaBar_UU.yy * tmp1430;
double tmp1442 = tmp1439 + tmp1440;
double tmp1443 = gammaBar_UU.xy * tmp1411;
double tmp1444 = tmp1441 + tmp1442;
double tmp1445 = gammaBar_UU.xz * tmp1428;
double tmp1446 = tmp1443 + tmp1444;
double tmp1447 = gammaBar_UU.xy * tmp1427;
double tmp1448 = tmp1445 + tmp1446;
double tmp1449 = gammaBar_UU.xx * tmp1407;
double tmp1450 = tmp1447 + tmp1448;
double tmp1451 = tmp1449 + tmp1450;
double tmp1452 = gammaBar_UU.xy * tmp1451;
double tmp1455 = partial_gammaBar_LLl[0].xx * partial_gammaBar_LLl[0].zz;
double tmp1458 = partial_gammaBar_LLl[0].xy * partial_gammaBar_LLl[0].zz;
double tmp1461 = partial_gammaBar_LLl[0].xz * partial_gammaBar_LLl[0].zz;
double tmp1462 = gammaBar_UU.yz * tmp1434;
double tmp1463 = gammaBar_UU.zz * tmp1461;
double tmp1464 = gammaBar_UU.xz * tmp1414;
double tmp1465 = tmp1462 + tmp1463;
double tmp1466 = gammaBar_UU.yz * tmp1458;
double tmp1467 = tmp1464 + tmp1465;
double tmp1468 = gammaBar_UU.yy * tmp1431;
double tmp1469 = tmp1466 + tmp1467;
double tmp1470 = gammaBar_UU.xy * tmp1412;
double tmp1471 = tmp1468 + tmp1469;
double tmp1472 = gammaBar_UU.xz * tmp1455;
double tmp1473 = tmp1470 + tmp1471;
double tmp1474 = gammaBar_UU.xy * tmp1428;
double tmp1475 = tmp1472 + tmp1473;
double tmp1476 = gammaBar_UU.xx * tmp1409;
double tmp1477 = tmp1474 + tmp1475;
double tmp1478 = tmp1476 + tmp1477;
double tmp1479 = gammaBar_UU.xz * tmp1478;
double tmp1482 = gammaBar_UU.xy * tmp1430;
double tmp1484 = gammaBar_UU.xz * tmp1431;
double tmp1485 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[0].yy;
double tmp1486 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[0].yz;
double tmp1487 = gammaBar_UU.yz * tmp1486;
double tmp1488 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[0].yz;
double tmp1489 = 2. * tmp1487;
double tmp1490 = gammaBar_UU.zz * tmp1488;
double tmp1491 = gammaBar_UU.yy * tmp1485;
double tmp1492 = tmp1489 + tmp1490;
double tmp1493 = 2. * tmp1484;
double tmp1494 = tmp1491 + tmp1492;
double tmp1495 = 2. * tmp1482;
double tmp1496 = tmp1493 + tmp1494;
double tmp1497 = gammaBar_UU.xx * tmp1411;
double tmp1498 = tmp1495 + tmp1496;
double tmp1499 = tmp1497 + tmp1498;
double tmp1505 = partial_gammaBar_LLl[0].yy * partial_gammaBar_LLl[0].zz;
double tmp1508 = partial_gammaBar_LLl[0].yz * partial_gammaBar_LLl[0].zz;
double tmp1509 = gammaBar_UU.yz * tmp1488;
double tmp1510 = gammaBar_UU.zz * tmp1508;
double tmp1511 = gammaBar_UU.xz * tmp1434;
double tmp1512 = tmp1509 + tmp1510;
double tmp1513 = gammaBar_UU.yz * tmp1505;
double tmp1514 = tmp1511 + tmp1512;
double tmp1515 = gammaBar_UU.yy * tmp1486;
double tmp1516 = tmp1513 + tmp1514;
double tmp1517 = gammaBar_UU.xy * tmp1433;
double tmp1518 = tmp1515 + tmp1516;
double tmp1519 = gammaBar_UU.xz * tmp1458;
double tmp1520 = tmp1517 + tmp1518;
double tmp1521 = gammaBar_UU.xy * tmp1431;
double tmp1522 = tmp1519 + tmp1520;
double tmp1523 = gammaBar_UU.xx * tmp1412;
double tmp1524 = tmp1521 + tmp1522;
double tmp1525 = tmp1523 + tmp1524;
double tmp1526 = gammaBar_UU.yz * tmp1525;
double tmp1529 = gammaBar_UU.xy * tmp1434;
double tmp1531 = gammaBar_UU.xz * tmp1461;
double tmp1534 = gammaBar_UU.yz * tmp1508;
double tmp1535 = partial_gammaBar_LLl[0].zz * partial_gammaBar_LLl[0].zz;
double tmp1536 = 2. * tmp1534;
double tmp1537 = gammaBar_UU.zz * tmp1535;
double tmp1538 = gammaBar_UU.yy * tmp1488;
double tmp1539 = tmp1536 + tmp1537;
double tmp1540 = 2. * tmp1531;
double tmp1541 = tmp1538 + tmp1539;
double tmp1542 = 2. * tmp1529;
double tmp1543 = tmp1540 + tmp1541;
double tmp1544 = gammaBar_UU.xx * tmp1414;
double tmp1545 = tmp1542 + tmp1543;
double tmp1546 = tmp1544 + tmp1545;
double tmp1547 = 2. * tmp1526;
double tmp1548 = gammaBar_UU.zz * tmp1546;
double tmp1549 = gammaBar_UU.yy * tmp1499;
double tmp1550 = tmp1547 + tmp1548;
double tmp1551 = 2. * tmp1479;
double tmp1552 = tmp1549 + tmp1550;
double tmp1553 = 2. * tmp1452;
double tmp1554 = tmp1551 + tmp1552;
double tmp1555 = gammaBar_UU.xx * tmp1425;
double tmp1556 = tmp1553 + tmp1554;
double tmp1557 = tmp1555 + tmp1556;
double tmp1570 = tmp758 + tmp755;
double tmp1572 = tmp1570 + tmp764;
double tmp1574 = tmp1572 + tmp754;
double tmp1576 = tmp1574 + tmp760;
double tmp1578 = tmp1576 + tmp766;
double tmp1580 = tmp1578 + tmp756;
double tmp1582 = tmp1580 + tmp762;
double tmp1583 = tmp1582 + tmp768;
double tmp1596 = tmp836 + tmp833;
double tmp1598 = tmp1596 + tmp842;
double tmp1600 = tmp1598 + tmp832;
double tmp1602 = tmp1600 + tmp838;
double tmp1604 = tmp1602 + tmp788;
double tmp1606 = tmp1604 + tmp834;
double tmp1608 = tmp1606 + tmp840;
double tmp1609 = tmp1608 + tmp846;
double tmp1622 = tmp914 + tmp911;
double tmp1624 = tmp1622 + tmp808;
double tmp1626 = tmp1624 + tmp910;
double tmp1628 = tmp1626 + tmp916;
double tmp1630 = tmp1628 + tmp922;
double tmp1632 = tmp1630 + tmp912;
double tmp1634 = tmp1632 + tmp918;
double tmp1635 = tmp1634 + tmp924;
double tmp1648 = tmp784 + tmp781;
double tmp1650 = tmp1648 + tmp790;
double tmp1652 = tmp1650 + tmp780;
double tmp1654 = tmp1652 + tmp786;
double tmp1656 = tmp1654 + tmp792;
double tmp1658 = tmp1656 + tmp782;
double tmp1660 = tmp1658 + tmp788;
double tmp1661 = tmp1660 + tmp794;
double tmp1674 = tmp862 + tmp859;
double tmp1676 = tmp1674 + tmp868;
double tmp1678 = tmp1676 + tmp858;
double tmp1680 = tmp1678 + tmp864;
double tmp1682 = tmp1680 + tmp870;
double tmp1684 = tmp1682 + tmp860;
double tmp1686 = tmp1684 + tmp866;
double tmp1687 = tmp1686 + tmp872;
double tmp1700 = tmp884 + tmp937;
double tmp1702 = tmp1700 + tmp946;
double tmp1704 = tmp1702 + tmp936;
double tmp1706 = tmp1704 + tmp942;
double tmp1708 = tmp1706 + tmp948;
double tmp1710 = tmp1708 + tmp938;
double tmp1712 = tmp1710 + tmp944;
double tmp1713 = tmp1712 + tmp950;
double tmp1726 = tmp810 + tmp807;
double tmp1728 = tmp1726 + tmp816;
double tmp1730 = tmp1728 + tmp806;
double tmp1732 = tmp1730 + tmp812;
double tmp1734 = tmp1732 + tmp818;
double tmp1736 = tmp1734 + tmp808;
double tmp1738 = tmp1736 + tmp814;
double tmp1739 = tmp1738 + tmp820;
double tmp1752 = tmp888 + tmp885;
double tmp1754 = tmp1752 + tmp894;
double tmp1756 = tmp1754 + tmp884;
double tmp1758 = tmp1756 + tmp890;
double tmp1760 = tmp1758 + tmp896;
double tmp1762 = tmp1760 + tmp886;
double tmp1764 = tmp1762 + tmp892;
double tmp1765 = tmp1764 + tmp898;
double tmp1778 = tmp966 + tmp963;
double tmp1780 = tmp1778 + tmp972;
double tmp1782 = tmp1780 + tmp962;
double tmp1784 = tmp1782 + tmp968;
double tmp1786 = tmp1784 + tmp974;
double tmp1788 = tmp1786 + tmp964;
double tmp1790 = tmp1788 + tmp970;
double tmp1791 = tmp1790 + tmp976;
double tmp1792 = gammaBar_UU.yz * tmp1765;
double tmp1793 = gammaBar_UU.zz * tmp1791;
double tmp1794 = gammaBar_UU.xz * tmp1739;
double tmp1795 = tmp1792 + tmp1793;
double tmp1796 = gammaBar_UU.yz * tmp1713;
double tmp1797 = tmp1794 + tmp1795;
double tmp1798 = gammaBar_UU.yy * tmp1687;
double tmp1799 = tmp1796 + tmp1797;
double tmp1800 = gammaBar_UU.xy * tmp1661;
double tmp1801 = tmp1798 + tmp1799;
double tmp1802 = gammaBar_UU.xz * tmp1635;
double tmp1803 = tmp1800 + tmp1801;
double tmp1804 = gammaBar_UU.xy * tmp1609;
double tmp1805 = tmp1802 + tmp1803;
double tmp1806 = gammaBar_UU.xx * tmp1583;
double tmp1807 = tmp1804 + tmp1805;
double tmp1808 = tmp1806 + tmp1807;
double tmp1821 = tmp97 + tmp94;
double tmp1823 = tmp1821 + tmp103;
double tmp1825 = tmp1823 + tmp93;
double tmp1827 = tmp1825 + tmp99;
double tmp1829 = tmp1827 + tmp105;
double tmp1831 = tmp1829 + tmp95;
double tmp1833 = tmp1831 + tmp101;
double tmp1834 = tmp1833 + tmp107;
double tmp1847 = tmp175 + tmp172;
double tmp1849 = tmp1847 + tmp181;
double tmp1851 = tmp1849 + tmp171;
double tmp1853 = tmp1851 + tmp177;
double tmp1855 = tmp1853 + tmp127;
double tmp1857 = tmp1855 + tmp173;
double tmp1859 = tmp1857 + tmp179;
double tmp1860 = tmp1859 + tmp185;
double tmp1873 = tmp253 + tmp250;
double tmp1875 = tmp1873 + tmp147;
double tmp1877 = tmp1875 + tmp249;
double tmp1879 = tmp1877 + tmp255;
double tmp1881 = tmp1879 + tmp261;
double tmp1883 = tmp1881 + tmp251;
double tmp1885 = tmp1883 + tmp257;
double tmp1886 = tmp1885 + tmp263;
double tmp1899 = tmp123 + tmp120;
double tmp1901 = tmp1899 + tmp129;
double tmp1903 = tmp1901 + tmp119;
double tmp1905 = tmp1903 + tmp125;
double tmp1907 = tmp1905 + tmp131;
double tmp1909 = tmp1907 + tmp121;
double tmp1911 = tmp1909 + tmp127;
double tmp1912 = tmp1911 + tmp133;
double tmp1925 = tmp201 + tmp198;
double tmp1927 = tmp1925 + tmp207;
double tmp1929 = tmp1927 + tmp197;
double tmp1931 = tmp1929 + tmp203;
double tmp1933 = tmp1931 + tmp209;
double tmp1935 = tmp1933 + tmp199;
double tmp1937 = tmp1935 + tmp205;
double tmp1938 = tmp1937 + tmp211;
double tmp1951 = tmp223 + tmp276;
double tmp1953 = tmp1951 + tmp285;
double tmp1955 = tmp1953 + tmp275;
double tmp1957 = tmp1955 + tmp281;
double tmp1959 = tmp1957 + tmp287;
double tmp1961 = tmp1959 + tmp277;
double tmp1963 = tmp1961 + tmp283;
double tmp1964 = tmp1963 + tmp289;
double tmp1977 = tmp149 + tmp146;
double tmp1979 = tmp1977 + tmp155;
double tmp1981 = tmp1979 + tmp145;
double tmp1983 = tmp1981 + tmp151;
double tmp1985 = tmp1983 + tmp157;
double tmp1987 = tmp1985 + tmp147;
double tmp1989 = tmp1987 + tmp153;
double tmp1990 = tmp1989 + tmp159;
double tmp2003 = tmp227 + tmp224;
double tmp2005 = tmp2003 + tmp233;
double tmp2007 = tmp2005 + tmp223;
double tmp2009 = tmp2007 + tmp229;
double tmp2011 = tmp2009 + tmp235;
double tmp2013 = tmp2011 + tmp225;
double tmp2015 = tmp2013 + tmp231;
double tmp2016 = tmp2015 + tmp237;
double tmp2029 = tmp305 + tmp302;
double tmp2031 = tmp2029 + tmp311;
double tmp2033 = tmp2031 + tmp301;
double tmp2035 = tmp2033 + tmp307;
double tmp2037 = tmp2035 + tmp313;
double tmp2039 = tmp2037 + tmp303;
double tmp2041 = tmp2039 + tmp309;
double tmp2042 = tmp2041 + tmp315;
double tmp2043 = gammaBar_UU.yz * tmp2016;
double tmp2044 = gammaBar_UU.zz * tmp2042;
double tmp2045 = gammaBar_UU.xz * tmp1990;
double tmp2046 = tmp2043 + tmp2044;
double tmp2047 = gammaBar_UU.yz * tmp1964;
double tmp2048 = tmp2045 + tmp2046;
double tmp2049 = gammaBar_UU.yy * tmp1938;
double tmp2050 = tmp2047 + tmp2048;
double tmp2051 = gammaBar_UU.xy * tmp1912;
double tmp2052 = tmp2049 + tmp2050;
double tmp2053 = gammaBar_UU.xz * tmp1886;
double tmp2054 = tmp2051 + tmp2052;
double tmp2055 = gammaBar_UU.xy * tmp1860;
double tmp2056 = tmp2053 + tmp2054;
double tmp2057 = gammaBar_UU.xx * tmp1834;
double tmp2058 = tmp2055 + tmp2056;
double tmp2059 = tmp2057 + tmp2058;
double tmp2071 = gammaBar_UU.xy * partial2_gammaBar_LLll[0][0].xy;
double tmp2072 = gammaBar_UU.xz * partial2_gammaBar_LLll[0][0].xz;
double tmp2073 = gammaBar_UU.yz * partial2_gammaBar_LLll[0][0].yz;
double tmp2074 = 2. * tmp2073;
double tmp2075 = gammaBar_UU.zz * partial2_gammaBar_LLll[0][0].zz;
double tmp2076 = gammaBar_UU.yy * partial2_gammaBar_LLll[0][0].yy;
double tmp2077 = tmp2074 + tmp2075;
double tmp2078 = 2. * tmp2072;
double tmp2079 = tmp2076 + tmp2077;
double tmp2080 = 2. * tmp2071;
double tmp2081 = tmp2078 + tmp2079;
double tmp2082 = gammaBar_UU.xx * partial2_gammaBar_LLll[0][0].xx;
double tmp2083 = tmp2080 + tmp2081;
double tmp2084 = tmp2082 + tmp2083;
double tmp2085 = gammaBar_UU.xy * partial2_gammaBar_LLll[0][1].xy;
double tmp2086 = gammaBar_UU.xz * partial2_gammaBar_LLll[0][1].xz;
double tmp2087 = gammaBar_UU.yz * partial2_gammaBar_LLll[0][1].yz;
double tmp2088 = 2. * tmp2087;
double tmp2089 = gammaBar_UU.zz * partial2_gammaBar_LLll[0][1].zz;
double tmp2090 = gammaBar_UU.yy * partial2_gammaBar_LLll[0][1].yy;
double tmp2091 = tmp2088 + tmp2089;
double tmp2092 = 2. * tmp2086;
double tmp2093 = tmp2090 + tmp2091;
double tmp2094 = 2. * tmp2085;
double tmp2095 = tmp2092 + tmp2093;
double tmp2096 = gammaBar_UU.xx * partial2_gammaBar_LLll[0][1].xx;
double tmp2097 = tmp2094 + tmp2095;
double tmp2098 = tmp2096 + tmp2097;
double tmp2099 = gammaBar_UU.xy * partial2_gammaBar_LLll[0][2].xy;
double tmp2100 = gammaBar_UU.xz * partial2_gammaBar_LLll[0][2].xz;
double tmp2101 = gammaBar_UU.yz * partial2_gammaBar_LLll[0][2].yz;
double tmp2102 = 2. * tmp2101;
double tmp2103 = gammaBar_UU.zz * partial2_gammaBar_LLll[0][2].zz;
double tmp2104 = gammaBar_UU.yy * partial2_gammaBar_LLll[0][2].yy;
double tmp2105 = tmp2102 + tmp2103;
double tmp2106 = 2. * tmp2100;
double tmp2107 = tmp2104 + tmp2105;
double tmp2108 = 2. * tmp2099;
double tmp2109 = tmp2106 + tmp2107;
double tmp2110 = gammaBar_UU.xx * partial2_gammaBar_LLll[0][2].xx;
double tmp2111 = tmp2108 + tmp2109;
double tmp2112 = tmp2110 + tmp2111;
double tmp2118 = gammaBar_UU.xy * partial2_gammaBar_LLll[1][0].xy;
double tmp2119 = gammaBar_UU.xz * partial2_gammaBar_LLll[1][0].xz;
double tmp2120 = gammaBar_UU.yz * partial2_gammaBar_LLll[1][0].yz;
double tmp2121 = 2. * tmp2120;
double tmp2122 = gammaBar_UU.zz * partial2_gammaBar_LLll[1][0].zz;
double tmp2123 = gammaBar_UU.yy * partial2_gammaBar_LLll[1][0].yy;
double tmp2124 = tmp2121 + tmp2122;
double tmp2125 = 2. * tmp2119;
double tmp2126 = tmp2123 + tmp2124;
double tmp2127 = 2. * tmp2118;
double tmp2128 = tmp2125 + tmp2126;
double tmp2129 = gammaBar_UU.xx * partial2_gammaBar_LLll[1][0].xx;
double tmp2130 = tmp2127 + tmp2128;
double tmp2131 = tmp2129 + tmp2130;
double tmp2132 = gammaBar_UU.xy * partial2_gammaBar_LLll[1][1].xy;
double tmp2133 = gammaBar_UU.xz * partial2_gammaBar_LLll[1][1].xz;
double tmp2134 = gammaBar_UU.yz * partial2_gammaBar_LLll[1][1].yz;
double tmp2135 = 2. * tmp2134;
double tmp2136 = gammaBar_UU.zz * partial2_gammaBar_LLll[1][1].zz;
double tmp2137 = gammaBar_UU.yy * partial2_gammaBar_LLll[1][1].yy;
double tmp2138 = tmp2135 + tmp2136;
double tmp2139 = 2. * tmp2133;
double tmp2140 = tmp2137 + tmp2138;
double tmp2141 = 2. * tmp2132;
double tmp2142 = tmp2139 + tmp2140;
double tmp2143 = gammaBar_UU.xx * partial2_gammaBar_LLll[1][1].xx;
double tmp2144 = tmp2141 + tmp2142;
double tmp2145 = tmp2143 + tmp2144;
double tmp2146 = gammaBar_UU.xy * partial2_gammaBar_LLll[1][2].xy;
double tmp2147 = gammaBar_UU.xz * partial2_gammaBar_LLll[1][2].xz;
double tmp2148 = gammaBar_UU.yz * partial2_gammaBar_LLll[1][2].yz;
double tmp2149 = 2. * tmp2148;
double tmp2150 = gammaBar_UU.zz * partial2_gammaBar_LLll[1][2].zz;
double tmp2151 = gammaBar_UU.yy * partial2_gammaBar_LLll[1][2].yy;
double tmp2152 = tmp2149 + tmp2150;
double tmp2153 = 2. * tmp2147;
double tmp2154 = tmp2151 + tmp2152;
double tmp2155 = 2. * tmp2146;
double tmp2156 = tmp2153 + tmp2154;
double tmp2157 = gammaBar_UU.xx * partial2_gammaBar_LLll[1][2].xx;
double tmp2158 = tmp2155 + tmp2156;
double tmp2159 = tmp2157 + tmp2158;
double tmp2165 = gammaBar_UU.xy * partial2_gammaBar_LLll[2][0].xy;
double tmp2166 = gammaBar_UU.xz * partial2_gammaBar_LLll[2][0].xz;
double tmp2167 = gammaBar_UU.yz * partial2_gammaBar_LLll[2][0].yz;
double tmp2168 = 2. * tmp2167;
double tmp2169 = gammaBar_UU.zz * partial2_gammaBar_LLll[2][0].zz;
double tmp2170 = gammaBar_UU.yy * partial2_gammaBar_LLll[2][0].yy;
double tmp2171 = tmp2168 + tmp2169;
double tmp2172 = 2. * tmp2166;
double tmp2173 = tmp2170 + tmp2171;
double tmp2174 = 2. * tmp2165;
double tmp2175 = tmp2172 + tmp2173;
double tmp2176 = gammaBar_UU.xx * partial2_gammaBar_LLll[2][0].xx;
double tmp2177 = tmp2174 + tmp2175;
double tmp2178 = tmp2176 + tmp2177;
double tmp2179 = gammaBar_UU.xy * partial2_gammaBar_LLll[2][1].xy;
double tmp2180 = gammaBar_UU.xz * partial2_gammaBar_LLll[2][1].xz;
double tmp2181 = gammaBar_UU.yz * partial2_gammaBar_LLll[2][1].yz;
double tmp2182 = 2. * tmp2181;
double tmp2183 = gammaBar_UU.zz * partial2_gammaBar_LLll[2][1].zz;
double tmp2184 = gammaBar_UU.yy * partial2_gammaBar_LLll[2][1].yy;
double tmp2185 = tmp2182 + tmp2183;
double tmp2186 = 2. * tmp2180;
double tmp2187 = tmp2184 + tmp2185;
double tmp2188 = 2. * tmp2179;
double tmp2189 = tmp2186 + tmp2187;
double tmp2190 = gammaBar_UU.xx * partial2_gammaBar_LLll[2][1].xx;
double tmp2191 = tmp2188 + tmp2189;
double tmp2192 = tmp2190 + tmp2191;
double tmp2193 = gammaBar_UU.xy * partial2_gammaBar_LLll[2][2].xy;
double tmp2194 = gammaBar_UU.xz * partial2_gammaBar_LLll[2][2].xz;
double tmp2195 = gammaBar_UU.yz * partial2_gammaBar_LLll[2][2].yz;
double tmp2196 = 2. * tmp2195;
double tmp2197 = gammaBar_UU.zz * partial2_gammaBar_LLll[2][2].zz;
double tmp2198 = gammaBar_UU.yy * partial2_gammaBar_LLll[2][2].yy;
double tmp2199 = tmp2196 + tmp2197;
double tmp2200 = 2. * tmp2194;
double tmp2201 = tmp2198 + tmp2199;
double tmp2202 = 2. * tmp2193;
double tmp2203 = tmp2200 + tmp2201;
double tmp2204 = gammaBar_UU.xx * partial2_gammaBar_LLll[2][2].xx;
double tmp2205 = tmp2202 + tmp2203;
double tmp2206 = tmp2204 + tmp2205;
double tmp2219 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xy;
double tmp2220 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xz;
double tmp2221 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xz;
double tmp2222 = tmp2219 + tmp2220;
double tmp2223 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xy;
double tmp2224 = tmp2221 + tmp2222;
double tmp2225 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xx;
double tmp2226 = tmp2223 + tmp2224;
double tmp2228 = tmp2225 + tmp2226;
double tmp2229 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xx;
double tmp2230 = tmp2228 + tmp2;
double tmp2232 = tmp2229 + tmp2230;
double tmp2234 = tmp2232 + tmp1;
double tmp2235 = tmp2234 + tmp3;
double tmp2238 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yy;
double tmp2239 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yz;
double tmp2240 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yz;
double tmp2241 = tmp2238 + tmp2239;
double tmp2242 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yy;
double tmp2243 = tmp2240 + tmp2241;
double tmp2244 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xy;
double tmp2245 = tmp2242 + tmp2243;
double tmp2247 = tmp2244 + tmp2245;
double tmp2249 = tmp2247 + tmp7;
double tmp2251 = tmp2249 + tmp11;
double tmp2253 = tmp2251 + tmp6;
double tmp2254 = tmp2253 + tmp8;
double tmp2257 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yz;
double tmp2258 = gammaBar_UU.zz * partial_gammaBar_LLl[2].zz;
double tmp2259 = gammaBar_UU.yz * partial_gammaBar_LLl[1].zz;
double tmp2260 = tmp2257 + tmp2258;
double tmp2261 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yz;
double tmp2262 = tmp2259 + tmp2260;
double tmp2264 = tmp2261 + tmp2262;
double tmp2266 = tmp2264 + tmp22;
double tmp2267 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xz;
double tmp2268 = tmp2266 + tmp17;
double tmp2270 = tmp2267 + tmp2268;
double tmp2272 = tmp2270 + tmp16;
double tmp2273 = tmp2272 + tmp18;
double tmp2391 = gammaBar_UU.xx * gammaBar_UU.xy;
double tmp2393 = gammaBar_UU.xx * gammaBar_UU.xz;
double tmp2395 = gammaBar_UU.xy * gammaBar_UU.xy;
double tmp2396 = gammaBar_UU.xy * gammaBar_UU.xz;
double tmp2398 = gammaBar_UU.xz * gammaBar_UU.xz;
double tmp2411 = gammaBar_UU.xx * gammaBar_UU.yy;
double tmp2412 = gammaBar_UU.xx * gammaBar_UU.yz;
double tmp2414 = gammaBar_UU.xy * gammaBar_UU.yy;
double tmp2415 = gammaBar_UU.xy * gammaBar_UU.yz;
double tmp2417 = gammaBar_UU.xz * gammaBar_UU.yy;
double tmp2418 = gammaBar_UU.xz * gammaBar_UU.yz;
double tmp2419 = ABar_LL.yz * tmp2417;
double tmp2420 = ABar_LL.zz * tmp2418;
double tmp2421 = ABar_LL.xz * tmp2396;
double tmp2423 = ABar_LL.yz * tmp2415;
double tmp2425 = ABar_LL.yy * tmp2414;
double tmp2427 = ABar_LL.xy * tmp2395;
double tmp2429 = ABar_LL.xz * tmp2412;
double tmp2431 = ABar_LL.xy * tmp2411;
double tmp2433 = ABar_LL.xx * tmp2391;
double tmp2438 = gammaBar_UU.xx * gammaBar_UU.zz;
double tmp2441 = gammaBar_UU.xy * gammaBar_UU.zz;
double tmp2444 = gammaBar_UU.xz * gammaBar_UU.zz;
double tmp2445 = ABar_LL.yz * tmp2418;
double tmp2446 = ABar_LL.zz * tmp2444;
double tmp2447 = ABar_LL.xz * tmp2398;
double tmp2449 = ABar_LL.yz * tmp2441;
double tmp2451 = ABar_LL.yy * tmp2415;
double tmp2453 = ABar_LL.xy * tmp2396;
double tmp2455 = ABar_LL.xz * tmp2438;
double tmp2457 = ABar_LL.xy * tmp2412;
double tmp2459 = ABar_LL.xx * tmp2393;
double tmp2467 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].xx;
double tmp2468 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].xx;
double tmp2469 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].xx;
double tmp2470 = tmp2467 + tmp2468;
double tmp2471 = tmp2469 + tmp2470;
double tmp2472 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].xy;
double tmp2473 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].xy;
double tmp2474 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].xy;
double tmp2475 = tmp2472 + tmp2473;
double tmp2476 = tmp2474 + tmp2475;
double tmp2477 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].xz;
double tmp2478 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].xz;
double tmp2479 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].xz;
double tmp2480 = tmp2477 + tmp2478;
double tmp2481 = tmp2479 + tmp2480;
double tmp2482 = gammaBar_UU.xy * tmp2476;
double tmp2483 = gammaBar_UU.xz * tmp2481;
double tmp2484 = gammaBar_UU.xx * tmp2471;
double tmp2493 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].yy;
double tmp2494 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].yy;
double tmp2495 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].yy;
double tmp2496 = tmp2493 + tmp2494;
double tmp2497 = tmp2495 + tmp2496;
double tmp2498 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].yz;
double tmp2499 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].yz;
double tmp2500 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].yz;
double tmp2501 = tmp2498 + tmp2499;
double tmp2502 = tmp2500 + tmp2501;
double tmp2503 = gammaBar_UU.xy * tmp2497;
double tmp2504 = gammaBar_UU.xz * tmp2502;
double tmp2505 = gammaBar_UU.xx * tmp2476;
double tmp2519 = partial_beta_Ul[0].y * partial_gammaBar_LLl[1].zz;
double tmp2520 = partial_beta_Ul[0].z * partial_gammaBar_LLl[2].zz;
double tmp2521 = partial_beta_Ul[0].x * partial_gammaBar_LLl[0].zz;
double tmp2522 = tmp2519 + tmp2520;
double tmp2523 = tmp2521 + tmp2522;
double tmp2524 = gammaBar_UU.xy * tmp2502;
double tmp2525 = gammaBar_UU.xz * tmp2523;
double tmp2526 = gammaBar_UU.xx * tmp2481;
double tmp2530 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].xx;
double tmp2531 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].xx;
double tmp2532 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].xx;
double tmp2533 = tmp2530 + tmp2531;
double tmp2534 = tmp2532 + tmp2533;
double tmp2535 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].xy;
double tmp2536 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].xy;
double tmp2537 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].xy;
double tmp2538 = tmp2535 + tmp2536;
double tmp2539 = tmp2537 + tmp2538;
double tmp2540 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].xz;
double tmp2541 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].xz;
double tmp2542 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].xz;
double tmp2543 = tmp2540 + tmp2541;
double tmp2544 = tmp2542 + tmp2543;
double tmp2545 = gammaBar_UU.xy * tmp2539;
double tmp2546 = gammaBar_UU.xz * tmp2544;
double tmp2556 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].yy;
double tmp2557 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].yy;
double tmp2558 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].yy;
double tmp2559 = tmp2556 + tmp2557;
double tmp2560 = tmp2558 + tmp2559;
double tmp2561 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].yz;
double tmp2562 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].yz;
double tmp2563 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].yz;
double tmp2564 = tmp2561 + tmp2562;
double tmp2565 = tmp2563 + tmp2564;
double tmp2582 = partial_beta_Ul[1].y * partial_gammaBar_LLl[1].zz;
double tmp2583 = partial_beta_Ul[1].z * partial_gammaBar_LLl[2].zz;
double tmp2584 = partial_beta_Ul[1].x * partial_gammaBar_LLl[0].zz;
double tmp2585 = tmp2582 + tmp2583;
double tmp2586 = tmp2584 + tmp2585;
double tmp2593 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].xx;
double tmp2594 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].xx;
double tmp2595 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].xx;
double tmp2596 = tmp2593 + tmp2594;
double tmp2597 = tmp2595 + tmp2596;
double tmp2598 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].xy;
double tmp2599 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].xy;
double tmp2600 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].xy;
double tmp2601 = tmp2598 + tmp2599;
double tmp2602 = tmp2600 + tmp2601;
double tmp2603 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].xz;
double tmp2604 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].xz;
double tmp2605 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].xz;
double tmp2606 = tmp2603 + tmp2604;
double tmp2607 = tmp2605 + tmp2606;
double tmp2608 = gammaBar_UU.xy * tmp2602;
double tmp2609 = gammaBar_UU.xz * tmp2607;
double tmp2619 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].yy;
double tmp2620 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].yy;
double tmp2621 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].yy;
double tmp2622 = tmp2619 + tmp2620;
double tmp2623 = tmp2621 + tmp2622;
double tmp2624 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].yz;
double tmp2625 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].yz;
double tmp2626 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].yz;
double tmp2627 = tmp2624 + tmp2625;
double tmp2628 = tmp2626 + tmp2627;
double tmp2645 = partial_beta_Ul[2].y * partial_gammaBar_LLl[1].zz;
double tmp2646 = partial_beta_Ul[2].z * partial_gammaBar_LLl[2].zz;
double tmp2647 = partial_beta_Ul[2].x * partial_gammaBar_LLl[0].zz;
double tmp2648 = tmp2645 + tmp2646;
double tmp2649 = tmp2647 + tmp2648;
double tmp2701 = gammaBar_UU.yz * tmp2544;
double tmp2702 = gammaBar_UU.zz * tmp2607;
double tmp2704 = tmp2701 + tmp2702;
double tmp2705 = gammaBar_UU.yz * tmp2602;
double tmp2706 = tmp2704 + tmp2483;
double tmp2707 = gammaBar_UU.yy * tmp2539;
double tmp2708 = tmp2705 + tmp2706;
double tmp2710 = tmp2707 + tmp2708;
double tmp2711 = gammaBar_UU.xz * tmp2597;
double tmp2712 = tmp2710 + tmp2482;
double tmp2713 = gammaBar_UU.xy * tmp2534;
double tmp2714 = tmp2711 + tmp2712;
double tmp2716 = tmp2713 + tmp2714;
double tmp2717 = tmp2716 + tmp2484;
double tmp2763 = gammaBar_UU.yz * tmp2565;
double tmp2764 = gammaBar_UU.zz * tmp2628;
double tmp2766 = tmp2763 + tmp2764;
double tmp2767 = gammaBar_UU.yz * tmp2623;
double tmp2768 = tmp2766 + tmp2504;
double tmp2769 = gammaBar_UU.yy * tmp2560;
double tmp2770 = tmp2767 + tmp2768;
double tmp2772 = tmp2769 + tmp2770;
double tmp2773 = gammaBar_UU.xz * tmp2602;
double tmp2774 = tmp2772 + tmp2503;
double tmp2776 = tmp2773 + tmp2774;
double tmp2778 = tmp2776 + tmp2545;
double tmp2779 = tmp2778 + tmp2505;
double tmp2825 = gammaBar_UU.yz * tmp2586;
double tmp2826 = gammaBar_UU.zz * tmp2649;
double tmp2828 = tmp2825 + tmp2826;
double tmp2829 = gammaBar_UU.yz * tmp2628;
double tmp2830 = tmp2828 + tmp2525;
double tmp2831 = gammaBar_UU.yy * tmp2565;
double tmp2832 = tmp2829 + tmp2830;
double tmp2834 = tmp2831 + tmp2832;
double tmp2836 = tmp2834 + tmp2524;
double tmp2837 = gammaBar_UU.xy * tmp2544;
double tmp2838 = tmp2836 + tmp2609;
double tmp2840 = tmp2837 + tmp2838;
double tmp2841 = tmp2840 + tmp2526;
double tmp2844 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yz;
double tmp2845 = 2. * tmp2844;
double tmp2846 = gammaBar_UU.zz * partial_gammaBar_LLl[0].zz;
double tmp2847 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yy;
double tmp2848 = tmp2845 + tmp2846;
double tmp2849 = 2. * tmp2;
double tmp2850 = tmp2847 + tmp2848;
double tmp2851 = 2. * tmp1;
double tmp2852 = tmp2849 + tmp2850;
double tmp2854 = tmp2851 + tmp2852;
double tmp2855 = tmp2854 + tmp3;
double tmp2859 = 2. * tmp2240;
double tmp2860 = gammaBar_UU.zz * partial_gammaBar_LLl[1].zz;
double tmp2862 = tmp2859 + tmp2860;
double tmp2863 = 2. * tmp12;
double tmp2864 = tmp2862 + tmp2242;
double tmp2865 = 2. * tmp11;
double tmp2866 = tmp2863 + tmp2864;
double tmp2868 = tmp2865 + tmp2866;
double tmp2869 = tmp2868 + tmp13;
double tmp2873 = 2. * tmp2257;
double tmp2875 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yy;
double tmp2876 = tmp2873 + tmp2258;
double tmp2877 = 2. * tmp22;
double tmp2878 = tmp2875 + tmp2876;
double tmp2879 = 2. * tmp21;
double tmp2880 = tmp2877 + tmp2878;
double tmp2882 = tmp2879 + tmp2880;
double tmp2883 = tmp2882 + tmp23;
double tmp2884 = U->beta_U.y * tmp2869;
double tmp2885 = U->beta_U.z * tmp2883;
double tmp2886 = U->beta_U.x * tmp2855;
double tmp2887 = tmp2884 + tmp2885;
double tmp2949 = tmp2886 + tmp2887;
double tmp2961 = gammaBar_UU.yz * tmp747;
double tmp2962 = gammaBar_UU.zz * tmp86;
double tmp2964 = tmp2961 + tmp2962;
double tmp2965 = gammaBar_UU.yz * tmp85;
double tmp2966 = tmp2964 + tmp1410;
double tmp2967 = gammaBar_UU.yy * tmp746;
double tmp2968 = tmp2965 + tmp2966;
double tmp2970 = tmp2967 + tmp2968;
double tmp2971 = gammaBar_UU.xz * tmp84;
double tmp2972 = tmp2970 + tmp1408;
double tmp2973 = gammaBar_UU.xy * tmp745;
double tmp2974 = tmp2971 + tmp2972;
double tmp2976 = tmp2973 + tmp2974;
double tmp2977 = tmp2976 + tmp1423;
double tmp2988 = gammaBar_UU.zz * tmp89;
double tmp2990 = tmp2988 + tmp758;
double tmp2991 = gammaBar_UU.yz * tmp88;
double tmp2992 = tmp2990 + tmp1437;
double tmp2994 = tmp2991 + tmp2992;
double tmp2996 = tmp2994 + tmp760;
double tmp2997 = gammaBar_UU.xz * tmp87;
double tmp2998 = tmp2996 + tmp1443;
double tmp3000 = tmp2997 + tmp2998;
double tmp3002 = tmp3000 + tmp762;
double tmp3003 = tmp3002 + tmp1449;
double tmp3013 = gammaBar_UU.yz * tmp753;
double tmp3016 = tmp3013 + tmp94;
double tmp3018 = tmp3016 + tmp1464;
double tmp3019 = gammaBar_UU.yy * tmp752;
double tmp3020 = tmp3018 + tmp93;
double tmp3022 = tmp3019 + tmp3020;
double tmp3024 = tmp3022 + tmp1470;
double tmp3025 = gammaBar_UU.xy * tmp751;
double tmp3026 = tmp3024 + tmp95;
double tmp3028 = tmp3025 + tmp3026;
double tmp3029 = tmp3028 + tmp1476;
double tmp3030 = gammaBar_UU.xy * tmp3003;
double tmp3031 = gammaBar_UU.xz * tmp3029;
double tmp3044 = gammaBar_UU.yz * tmp773;
double tmp3045 = gammaBar_UU.zz * tmp112;
double tmp3047 = tmp3044 + tmp3045;
double tmp3048 = gammaBar_UU.yz * tmp111;
double tmp3049 = tmp3047 + tmp1445;
double tmp3050 = gammaBar_UU.yy * tmp772;
double tmp3051 = tmp3048 + tmp3049;
double tmp3053 = tmp3050 + tmp3051;
double tmp3054 = gammaBar_UU.xz * tmp85;
double tmp3055 = tmp3053 + tmp1447;
double tmp3057 = tmp3054 + tmp3055;
double tmp3059 = tmp3057 + tmp766;
double tmp3060 = tmp3059 + tmp1449;
double tmp3071 = gammaBar_UU.zz * tmp115;
double tmp3073 = tmp3071 + tmp784;
double tmp3074 = gammaBar_UU.yz * tmp114;
double tmp3075 = tmp3073 + tmp1484;
double tmp3077 = tmp3074 + tmp3075;
double tmp3079 = tmp3077 + tmp786;
double tmp3080 = gammaBar_UU.xz * tmp88;
double tmp3081 = tmp3079 + tmp1482;
double tmp3083 = tmp3080 + tmp3081;
double tmp3085 = tmp3083 + tmp788;
double tmp3086 = tmp3085 + tmp1497;
double tmp3099 = tmp806 + tmp120;
double tmp3101 = tmp3099 + tmp1511;
double tmp3102 = gammaBar_UU.yy * tmp778;
double tmp3103 = tmp3101 + tmp119;
double tmp3105 = tmp3102 + tmp3103;
double tmp3107 = tmp3105 + tmp1517;
double tmp3109 = tmp3107 + tmp121;
double tmp3111 = tmp3109 + tmp922;
double tmp3112 = tmp3111 + tmp1523;
double tmp3113 = gammaBar_UU.xy * tmp3086;
double tmp3114 = gammaBar_UU.xz * tmp3112;
double tmp3127 = gammaBar_UU.yz * tmp799;
double tmp3128 = gammaBar_UU.zz * tmp138;
double tmp3130 = tmp3127 + tmp3128;
double tmp3131 = gammaBar_UU.yz * tmp112;
double tmp3132 = tmp3130 + tmp1472;
double tmp3133 = gammaBar_UU.yy * tmp773;
double tmp3134 = tmp3131 + tmp3132;
double tmp3136 = tmp3133 + tmp3134;
double tmp3138 = tmp3136 + tmp1474;
double tmp3139 = gammaBar_UU.xy * tmp747;
double tmp3140 = tmp3138 + tmp103;
double tmp3142 = tmp3139 + tmp3140;
double tmp3143 = tmp3142 + tmp1476;
double tmp3154 = gammaBar_UU.zz * tmp141;
double tmp3156 = tmp3154 + tmp810;
double tmp3158 = tmp3156 + tmp1519;
double tmp3160 = tmp3158 + tmp123;
double tmp3162 = tmp3160 + tmp812;
double tmp3164 = tmp3162 + tmp1521;
double tmp3166 = tmp3164 + tmp181;
double tmp3168 = tmp3166 + tmp814;
double tmp3169 = tmp3168 + tmp1523;
double tmp3179 = gammaBar_UU.yz * tmp805;
double tmp3182 = tmp3179 + tmp146;
double tmp3184 = tmp3182 + tmp1531;
double tmp3185 = gammaBar_UU.yy * tmp779;
double tmp3186 = tmp3184 + tmp145;
double tmp3188 = tmp3185 + tmp3186;
double tmp3190 = tmp3188 + tmp1529;
double tmp3191 = gammaBar_UU.xy * tmp753;
double tmp3192 = tmp3190 + tmp147;
double tmp3194 = tmp3191 + tmp3192;
double tmp3195 = tmp3194 + tmp1544;
double tmp3196 = gammaBar_UU.xy * tmp3169;
double tmp3197 = gammaBar_UU.xz * tmp3195;
double tmp3237 = gammaBar_UU.zz * tmp167;
double tmp3238 = gammaBar_UU.xz * tmp1433;
double tmp3239 = tmp3237 + tmp836;
double tmp3240 = gammaBar_UU.yz * tmp166;
double tmp3241 = tmp3238 + tmp3239;
double tmp3243 = tmp3240 + tmp3241;
double tmp3245 = tmp3243 + tmp838;
double tmp3246 = gammaBar_UU.xz * tmp165;
double tmp3247 = tmp3245 + tmp1482;
double tmp3249 = tmp3246 + tmp3247;
double tmp3250 = gammaBar_UU.xx * tmp1427;
double tmp3251 = tmp3249 + tmp840;
double tmp3252 = tmp3250 + tmp3251;
double tmp3265 = tmp914 + tmp172;
double tmp3267 = tmp3265 + tmp1511;
double tmp3269 = tmp3267 + tmp171;
double tmp3271 = tmp3269 + tmp916;
double tmp3273 = tmp3271 + tmp1521;
double tmp3275 = tmp3273 + tmp173;
double tmp3276 = gammaBar_UU.xx * tmp1428;
double tmp3277 = tmp3275 + tmp918;
double tmp3278 = tmp3276 + tmp3277;
double tmp3320 = gammaBar_UU.zz * tmp193;
double tmp3321 = gammaBar_UU.xz * tmp1486;
double tmp3322 = tmp3320 + tmp862;
double tmp3323 = gammaBar_UU.yz * tmp192;
double tmp3324 = tmp3321 + tmp3322;
double tmp3326 = tmp3323 + tmp3324;
double tmp3327 = gammaBar_UU.xy * tmp1485;
double tmp3328 = tmp3326 + tmp864;
double tmp3329 = gammaBar_UU.xz * tmp166;
double tmp3330 = tmp3327 + tmp3328;
double tmp3332 = tmp3329 + tmp3330;
double tmp3333 = gammaBar_UU.xx * tmp1430;
double tmp3334 = tmp3332 + tmp866;
double tmp3335 = tmp3333 + tmp3334;
double tmp3347 = gammaBar_UU.xz * tmp1488;
double tmp3348 = tmp884 + tmp198;
double tmp3350 = tmp3347 + tmp3348;
double tmp3352 = tmp3350 + tmp197;
double tmp3353 = gammaBar_UU.xy * tmp1486;
double tmp3354 = tmp3352 + tmp942;
double tmp3356 = tmp3353 + tmp3354;
double tmp3358 = tmp3356 + tmp199;
double tmp3359 = gammaBar_UU.xx * tmp1431;
double tmp3360 = tmp3358 + tmp944;
double tmp3361 = tmp3359 + tmp3360;
double tmp3403 = gammaBar_UU.zz * tmp219;
double tmp3404 = gammaBar_UU.xz * tmp1505;
double tmp3405 = tmp3403 + tmp888;
double tmp3407 = tmp3404 + tmp3405;
double tmp3409 = tmp3407 + tmp201;
double tmp3411 = tmp3409 + tmp890;
double tmp3412 = gammaBar_UU.xz * tmp167;
double tmp3413 = tmp3411 + tmp3353;
double tmp3415 = tmp3412 + tmp3413;
double tmp3416 = gammaBar_UU.xx * tmp1433;
double tmp3417 = tmp3415 + tmp892;
double tmp3418 = tmp3416 + tmp3417;
double tmp3430 = gammaBar_UU.xz * tmp1508;
double tmp3431 = tmp966 + tmp224;
double tmp3433 = tmp3430 + tmp3431;
double tmp3435 = tmp3433 + tmp223;
double tmp3436 = gammaBar_UU.xy * tmp1488;
double tmp3437 = tmp3435 + tmp968;
double tmp3439 = tmp3436 + tmp3437;
double tmp3441 = tmp3439 + tmp225;
double tmp3442 = gammaBar_UU.xx * tmp1434;
double tmp3443 = tmp3441 + tmp970;
double tmp3444 = tmp3442 + tmp3443;
double tmp3511 = gammaBar_UU.yz * tmp909;
double tmp3514 = tmp3511 + tmp250;
double tmp3516 = tmp3514 + tmp1531;
double tmp3517 = gammaBar_UU.yy * tmp908;
double tmp3518 = tmp3516 + tmp249;
double tmp3519 = gammaBar_UU.xy * tmp1458;
double tmp3520 = tmp3517 + tmp3518;
double tmp3522 = tmp3519 + tmp3520;
double tmp3523 = gammaBar_UU.xy * tmp907;
double tmp3524 = tmp3522 + tmp251;
double tmp3525 = gammaBar_UU.xx * tmp1455;
double tmp3526 = tmp3523 + tmp3524;
double tmp3527 = tmp3525 + tmp3526;
double tmp3597 = tmp962 + tmp276;
double tmp3599 = tmp3597 + tmp3430;
double tmp3600 = gammaBar_UU.yy * tmp934;
double tmp3601 = tmp3599 + tmp275;
double tmp3602 = gammaBar_UU.xy * tmp1505;
double tmp3603 = tmp3600 + tmp3601;
double tmp3605 = tmp3602 + tmp3603;
double tmp3606 = gammaBar_UU.xy * tmp908;
double tmp3607 = tmp3605 + tmp277;
double tmp3608 = gammaBar_UU.xx * tmp1458;
double tmp3609 = tmp3606 + tmp3607;
double tmp3610 = tmp3608 + tmp3609;
double tmp3677 = gammaBar_UU.yz * tmp961;
double tmp3679 = gammaBar_UU.xz * tmp1535;
double tmp3680 = tmp3677 + tmp302;
double tmp3682 = tmp3679 + tmp3680;
double tmp3683 = gammaBar_UU.yy * tmp935;
double tmp3684 = tmp3682 + tmp301;
double tmp3685 = gammaBar_UU.xy * tmp1508;
double tmp3686 = tmp3683 + tmp3684;
double tmp3688 = tmp3685 + tmp3686;
double tmp3689 = gammaBar_UU.xy * tmp909;
double tmp3690 = tmp3688 + tmp303;
double tmp3691 = gammaBar_UU.xx * tmp1461;
double tmp3692 = tmp3689 + tmp3690;
double tmp3693 = tmp3691 + tmp3692;
double tmp3726 = gammaBar_UU.yz * tmp999;
double tmp3727 = gammaBar_UU.zz * tmp337;
double tmp3729 = tmp3726 + tmp3727;
double tmp3730 = gammaBar_UU.yz * tmp336;
double tmp3731 = tmp3729 + tmp756;
double tmp3732 = gammaBar_UU.yy * tmp997;
double tmp3733 = tmp3730 + tmp3731;
double tmp3735 = tmp3732 + tmp3733;
double tmp3736 = gammaBar_UU.xz * tmp335;
double tmp3737 = tmp3735 + tmp762;
double tmp3738 = gammaBar_UU.xy * tmp996;
double tmp3739 = tmp3736 + tmp3737;
double tmp3741 = tmp3738 + tmp3739;
double tmp3742 = tmp3741 + tmp768;
double tmp3753 = gammaBar_UU.zz * tmp340;
double tmp3755 = tmp3753 + tmp1003;
double tmp3756 = gammaBar_UU.yz * tmp339;
double tmp3757 = tmp3755 + tmp782;
double tmp3759 = tmp3756 + tmp3757;
double tmp3761 = tmp3759 + tmp1007;
double tmp3762 = gammaBar_UU.xz * tmp338;
double tmp3763 = tmp3761 + tmp788;
double tmp3765 = tmp3762 + tmp3763;
double tmp3767 = tmp3765 + tmp998;
double tmp3768 = tmp3767 + tmp794;
double tmp3778 = gammaBar_UU.yz * tmp1004;
double tmp3781 = tmp3778 + tmp345;
double tmp3783 = tmp3781 + tmp808;
double tmp3784 = gammaBar_UU.yy * tmp1002;
double tmp3785 = tmp3783 + tmp344;
double tmp3787 = tmp3784 + tmp3785;
double tmp3789 = tmp3787 + tmp814;
double tmp3790 = gammaBar_UU.xy * tmp999;
double tmp3791 = tmp3789 + tmp346;
double tmp3793 = tmp3790 + tmp3791;
double tmp3794 = tmp3793 + tmp820;
double tmp3795 = gammaBar_UU.xy * tmp3768;
double tmp3796 = gammaBar_UU.xz * tmp3794;
double tmp3809 = gammaBar_UU.yz * tmp1018;
double tmp3810 = gammaBar_UU.zz * tmp363;
double tmp3812 = tmp3809 + tmp3810;
double tmp3813 = gammaBar_UU.yz * tmp362;
double tmp3814 = tmp3812 + tmp834;
double tmp3815 = gammaBar_UU.yy * tmp1017;
double tmp3816 = tmp3813 + tmp3814;
double tmp3818 = tmp3815 + tmp3816;
double tmp3819 = gammaBar_UU.xz * tmp336;
double tmp3820 = tmp3818 + tmp840;
double tmp3822 = tmp3819 + tmp3820;
double tmp3824 = tmp3822 + tmp998;
double tmp3825 = tmp3824 + tmp846;
double tmp3836 = gammaBar_UU.zz * tmp366;
double tmp3838 = tmp3836 + tmp1029;
double tmp3839 = gammaBar_UU.yz * tmp365;
double tmp3840 = tmp3838 + tmp860;
double tmp3842 = tmp3839 + tmp3840;
double tmp3844 = tmp3842 + tmp1031;
double tmp3845 = gammaBar_UU.xz * tmp339;
double tmp3846 = tmp3844 + tmp866;
double tmp3848 = tmp3845 + tmp3846;
double tmp3850 = tmp3848 + tmp1033;
double tmp3851 = tmp3850 + tmp872;
double tmp3864 = tmp1052 + tmp371;
double tmp3866 = tmp3864 + tmp886;
double tmp3867 = gammaBar_UU.yy * tmp1023;
double tmp3868 = tmp3866 + tmp370;
double tmp3870 = tmp3867 + tmp3868;
double tmp3872 = tmp3870 + tmp892;
double tmp3874 = tmp3872 + tmp372;
double tmp3876 = tmp3874 + tmp1060;
double tmp3877 = tmp3876 + tmp898;
double tmp3878 = gammaBar_UU.xy * tmp3851;
double tmp3879 = gammaBar_UU.xz * tmp3877;
double tmp3892 = gammaBar_UU.yz * tmp1045;
double tmp3893 = gammaBar_UU.zz * tmp389;
double tmp3895 = tmp3892 + tmp3893;
double tmp3896 = gammaBar_UU.yz * tmp363;
double tmp3897 = tmp3895 + tmp912;
double tmp3898 = gammaBar_UU.yy * tmp1018;
double tmp3899 = tmp3896 + tmp3897;
double tmp3901 = tmp3898 + tmp3899;
double tmp3903 = tmp3901 + tmp918;
double tmp3905 = tmp3903 + tmp354;
double tmp3907 = tmp3905 + tmp3790;
double tmp3908 = tmp3907 + tmp924;
double tmp3919 = gammaBar_UU.zz * tmp392;
double tmp3921 = tmp3919 + tmp1056;
double tmp3923 = tmp3921 + tmp938;
double tmp3925 = tmp3923 + tmp374;
double tmp3927 = tmp3925 + tmp1058;
double tmp3929 = tmp3927 + tmp944;
double tmp3931 = tmp3929 + tmp432;
double tmp3933 = tmp3931 + tmp1060;
double tmp3934 = tmp3933 + tmp950;
double tmp3944 = gammaBar_UU.yz * tmp1051;
double tmp3947 = tmp3944 + tmp397;
double tmp3949 = tmp3947 + tmp964;
double tmp3950 = gammaBar_UU.yy * tmp1024;
double tmp3951 = tmp3949 + tmp396;
double tmp3953 = tmp3950 + tmp3951;
double tmp3955 = tmp3953 + tmp970;
double tmp3956 = gammaBar_UU.xy * tmp1004;
double tmp3957 = tmp3955 + tmp398;
double tmp3959 = tmp3956 + tmp3957;
double tmp3960 = tmp3959 + tmp976;
double tmp3961 = gammaBar_UU.xy * tmp3934;
double tmp3962 = gammaBar_UU.xz * tmp3960;
double tmp4002 = gammaBar_UU.zz * tmp418;
double tmp4003 = gammaBar_UU.xz * tmp778;
double tmp4004 = tmp4002 + tmp1025;
double tmp4005 = gammaBar_UU.yz * tmp417;
double tmp4006 = tmp4003 + tmp4004;
double tmp4008 = tmp4005 + tmp4006;
double tmp4010 = tmp4008 + tmp1031;
double tmp4011 = gammaBar_UU.xz * tmp416;
double tmp4012 = tmp4010 + tmp870;
double tmp4014 = tmp4011 + tmp4012;
double tmp4015 = gammaBar_UU.xx * tmp772;
double tmp4016 = tmp4014 + tmp1037;
double tmp4017 = tmp4015 + tmp4016;
double tmp4030 = tmp1052 + tmp423;
double tmp4032 = tmp4030 + tmp946;
double tmp4034 = tmp4032 + tmp422;
double tmp4036 = tmp4034 + tmp1058;
double tmp4038 = tmp4036 + tmp896;
double tmp4040 = tmp4038 + tmp424;
double tmp4041 = gammaBar_UU.xx * tmp773;
double tmp4042 = tmp4040 + tmp1064;
double tmp4043 = tmp4041 + tmp4042;
double tmp4085 = gammaBar_UU.zz * tmp444;
double tmp4086 = gammaBar_UU.xz * tmp856;
double tmp4087 = tmp4085 + tmp1077;
double tmp4088 = gammaBar_UU.yz * tmp443;
double tmp4089 = tmp4086 + tmp4087;
double tmp4091 = tmp4088 + tmp4089;
double tmp4092 = gammaBar_UU.xy * tmp853;
double tmp4093 = tmp4091 + tmp1081;
double tmp4094 = gammaBar_UU.xz * tmp417;
double tmp4095 = tmp4092 + tmp4093;
double tmp4097 = tmp4094 + tmp4095;
double tmp4098 = gammaBar_UU.xx * tmp775;
double tmp4099 = tmp4097 + tmp1072;
double tmp4100 = tmp4098 + tmp4099;
double tmp4112 = gammaBar_UU.xz * tmp857;
double tmp4113 = tmp1099 + tmp449;
double tmp4115 = tmp4112 + tmp4113;
double tmp4117 = tmp4115 + tmp448;
double tmp4118 = gammaBar_UU.xy * tmp854;
double tmp4119 = tmp4117 + tmp1105;
double tmp4121 = tmp4118 + tmp4119;
double tmp4123 = tmp4121 + tmp450;
double tmp4124 = gammaBar_UU.xx * tmp776;
double tmp4125 = tmp4123 + tmp1111;
double tmp4126 = tmp4124 + tmp4125;
double tmp4168 = gammaBar_UU.zz * tmp470;
double tmp4169 = gammaBar_UU.xz * tmp934;
double tmp4170 = tmp4168 + tmp1103;
double tmp4172 = tmp4169 + tmp4170;
double tmp4174 = tmp4172 + tmp452;
double tmp4175 = gammaBar_UU.xy * tmp856;
double tmp4176 = tmp4174 + tmp1105;
double tmp4177 = gammaBar_UU.xz * tmp418;
double tmp4178 = tmp4175 + tmp4176;
double tmp4180 = tmp4177 + tmp4178;
double tmp4181 = gammaBar_UU.xx * tmp778;
double tmp4182 = tmp4180 + tmp1107;
double tmp4183 = tmp4181 + tmp4182;
double tmp4195 = gammaBar_UU.xz * tmp935;
double tmp4196 = tmp1124 + tmp475;
double tmp4198 = tmp4195 + tmp4196;
double tmp4200 = tmp4198 + tmp474;
double tmp4201 = gammaBar_UU.xy * tmp857;
double tmp4202 = tmp4200 + tmp1128;
double tmp4204 = tmp4201 + tmp4202;
double tmp4206 = tmp4204 + tmp476;
double tmp4207 = gammaBar_UU.xx * tmp779;
double tmp4208 = tmp4206 + tmp1119;
double tmp4209 = tmp4207 + tmp4208;
double tmp4279 = tmp3944 + tmp501;
double tmp4281 = tmp4279 + tmp972;
double tmp4282 = gammaBar_UU.yy * tmp1048;
double tmp4283 = tmp4281 + tmp500;
double tmp4284 = gammaBar_UU.xy * tmp802;
double tmp4285 = tmp4282 + tmp4283;
double tmp4287 = tmp4284 + tmp4285;
double tmp4288 = gammaBar_UU.xy * tmp1045;
double tmp4289 = tmp4287 + tmp502;
double tmp4290 = gammaBar_UU.xx * tmp799;
double tmp4291 = tmp4288 + tmp4289;
double tmp4292 = tmp4290 + tmp4291;
double tmp4361 = gammaBar_UU.xz * tmp883;
double tmp4362 = tmp1124 + tmp527;
double tmp4364 = tmp4361 + tmp4362;
double tmp4365 = gammaBar_UU.yy * tmp1095;
double tmp4366 = tmp4364 + tmp526;
double tmp4367 = gammaBar_UU.xy * tmp880;
double tmp4368 = tmp4365 + tmp4366;
double tmp4370 = tmp4367 + tmp4368;
double tmp4371 = gammaBar_UU.xy * tmp1048;
double tmp4372 = tmp4370 + tmp528;
double tmp4373 = gammaBar_UU.xx * tmp802;
double tmp4374 = tmp4371 + tmp4372;
double tmp4375 = tmp4373 + tmp4374;
double tmp4442 = gammaBar_UU.yz * tmp1125;
double tmp4444 = gammaBar_UU.xz * tmp961;
double tmp4445 = tmp4442 + tmp553;
double tmp4447 = tmp4444 + tmp4445;
double tmp4448 = gammaBar_UU.yy * tmp1098;
double tmp4449 = tmp4447 + tmp552;
double tmp4450 = gammaBar_UU.xy * tmp883;
double tmp4451 = tmp4448 + tmp4449;
double tmp4453 = tmp4450 + tmp4451;
double tmp4454 = gammaBar_UU.xy * tmp1051;
double tmp4455 = tmp4453 + tmp554;
double tmp4456 = gammaBar_UU.xx * tmp805;
double tmp4457 = tmp4454 + tmp4455;
double tmp4458 = tmp4456 + tmp4457;
double tmp4491 = gammaBar_UU.yz * tmp341;
double tmp4492 = gammaBar_UU.zz * tmp589;
double tmp4494 = tmp4491 + tmp4492;
double tmp4495 = gammaBar_UU.yz * tmp587;
double tmp4496 = tmp4494 + tmp95;
double tmp4497 = gammaBar_UU.yy * tmp338;
double tmp4498 = tmp4495 + tmp4496;
double tmp4500 = tmp4497 + tmp4498;
double tmp4501 = gammaBar_UU.xz * tmp586;
double tmp4502 = tmp4500 + tmp101;
double tmp4503 = gammaBar_UU.xy * tmp335;
double tmp4504 = tmp4501 + tmp4502;
double tmp4506 = tmp4503 + tmp4504;
double tmp4507 = tmp4506 + tmp107;
double tmp4518 = gammaBar_UU.zz * tmp592;
double tmp4520 = tmp4518 + tmp344;
double tmp4521 = gammaBar_UU.yz * tmp591;
double tmp4522 = tmp4520 + tmp121;
double tmp4524 = tmp4521 + tmp4522;
double tmp4526 = tmp4524 + tmp350;
double tmp4527 = gammaBar_UU.xz * tmp587;
double tmp4528 = tmp4526 + tmp127;
double tmp4530 = tmp4527 + tmp4528;
double tmp4532 = tmp4530 + tmp356;
double tmp4533 = tmp4532 + tmp133;
double tmp4543 = gammaBar_UU.yz * tmp343;
double tmp4546 = tmp4543 + tmp596;
double tmp4548 = tmp4546 + tmp147;
double tmp4549 = gammaBar_UU.yy * tmp340;
double tmp4550 = tmp4548 + tmp593;
double tmp4552 = tmp4549 + tmp4550;
double tmp4554 = tmp4552 + tmp153;
double tmp4555 = gammaBar_UU.xy * tmp337;
double tmp4556 = tmp4554 + tmp590;
double tmp4558 = tmp4555 + tmp4556;
double tmp4559 = tmp4558 + tmp159;
double tmp4560 = gammaBar_UU.xy * tmp4533;
double tmp4561 = gammaBar_UU.xz * tmp4559;
double tmp4574 = gammaBar_UU.yz * tmp419;
double tmp4575 = gammaBar_UU.zz * tmp608;
double tmp4577 = tmp4574 + tmp4575;
double tmp4578 = gammaBar_UU.yz * tmp607;
double tmp4579 = tmp4577 + tmp173;
double tmp4580 = gammaBar_UU.yy * tmp416;
double tmp4581 = tmp4578 + tmp4579;
double tmp4583 = tmp4580 + tmp4581;
double tmp4585 = tmp4583 + tmp179;
double tmp4587 = tmp4585 + tmp4527;
double tmp4589 = tmp4587 + tmp352;
double tmp4590 = tmp4589 + tmp185;
double tmp4601 = gammaBar_UU.zz * tmp611;
double tmp4603 = tmp4601 + tmp422;
double tmp4604 = gammaBar_UU.yz * tmp610;
double tmp4605 = tmp4603 + tmp199;
double tmp4607 = tmp4604 + tmp4605;
double tmp4609 = tmp4607 + tmp428;
double tmp4610 = gammaBar_UU.xz * tmp591;
double tmp4611 = tmp4609 + tmp205;
double tmp4613 = tmp4610 + tmp4611;
double tmp4615 = tmp4613 + tmp378;
double tmp4616 = tmp4615 + tmp211;
double tmp4629 = tmp504 + tmp616;
double tmp4631 = tmp4629 + tmp225;
double tmp4632 = gammaBar_UU.yy * tmp418;
double tmp4633 = tmp4631 + tmp615;
double tmp4635 = tmp4632 + tmp4633;
double tmp4637 = tmp4635 + tmp231;
double tmp4639 = tmp4637 + tmp617;
double tmp4641 = tmp4639 + tmp404;
double tmp4642 = tmp4641 + tmp237;
double tmp4643 = gammaBar_UU.xy * tmp4616;
double tmp4644 = gammaBar_UU.xz * tmp4642;
double tmp4657 = gammaBar_UU.yz * tmp497;
double tmp4658 = gammaBar_UU.zz * tmp635;
double tmp4660 = tmp4657 + tmp4658;
double tmp4661 = gammaBar_UU.yz * tmp608;
double tmp4662 = tmp4660 + tmp251;
double tmp4663 = gammaBar_UU.yy * tmp419;
double tmp4664 = tmp4661 + tmp4662;
double tmp4666 = tmp4663 + tmp4664;
double tmp4668 = tmp4666 + tmp257;
double tmp4669 = gammaBar_UU.xy * tmp341;
double tmp4670 = tmp4668 + tmp590;
double tmp4672 = tmp4669 + tmp4670;
double tmp4673 = tmp4672 + tmp263;
double tmp4684 = gammaBar_UU.zz * tmp638;
double tmp4686 = tmp4684 + tmp500;
double tmp4688 = tmp4686 + tmp277;
double tmp4690 = tmp4688 + tmp619;
double tmp4692 = tmp4690 + tmp506;
double tmp4694 = tmp4692 + tmp283;
double tmp4696 = tmp4694 + tmp617;
double tmp4698 = tmp4696 + tmp512;
double tmp4699 = tmp4698 + tmp289;
double tmp4709 = gammaBar_UU.yz * tmp499;
double tmp4712 = tmp4709 + tmp643;
double tmp4714 = tmp4712 + tmp303;
double tmp4715 = gammaBar_UU.yy * tmp421;
double tmp4716 = tmp4714 + tmp642;
double tmp4718 = tmp4715 + tmp4716;
double tmp4720 = tmp4718 + tmp309;
double tmp4721 = gammaBar_UU.xy * tmp343;
double tmp4722 = tmp4720 + tmp644;
double tmp4724 = tmp4721 + tmp4722;
double tmp4725 = tmp4724 + tmp315;
double tmp4726 = gammaBar_UU.xy * tmp4699;
double tmp4727 = gammaBar_UU.xz * tmp4725;
double tmp4767 = gammaBar_UU.zz * tmp613;
double tmp4768 = gammaBar_UU.xz * tmp117;
double tmp4769 = tmp4767 + tmp370;
double tmp4771 = tmp4768 + tmp4769;
double tmp4773 = tmp4771 + tmp4604;
double tmp4775 = tmp4773 + tmp376;
double tmp4776 = gammaBar_UU.xz * tmp607;
double tmp4777 = tmp4775 + tmp209;
double tmp4779 = tmp4776 + tmp4777;
double tmp4780 = gammaBar_UU.xx * tmp111;
double tmp4781 = tmp4779 + tmp382;
double tmp4782 = tmp4780 + tmp4781;
double tmp4795 = tmp396 + tmp616;
double tmp4797 = tmp4795 + tmp285;
double tmp4799 = tmp4797 + tmp619;
double tmp4801 = tmp4799 + tmp402;
double tmp4803 = tmp4801 + tmp235;
double tmp4805 = tmp4803 + tmp625;
double tmp4806 = gammaBar_UU.xx * tmp112;
double tmp4807 = tmp4805 + tmp408;
double tmp4808 = tmp4806 + tmp4807;
double tmp4850 = gammaBar_UU.zz * tmp666;
double tmp4851 = gammaBar_UU.xz * tmp195;
double tmp4852 = tmp4850 + tmp448;
double tmp4853 = gammaBar_UU.yz * tmp665;
double tmp4854 = tmp4851 + tmp4852;
double tmp4856 = tmp4853 + tmp4854;
double tmp4857 = gammaBar_UU.xy * tmp192;
double tmp4858 = tmp4856 + tmp454;
double tmp4859 = gammaBar_UU.xz * tmp610;
double tmp4860 = tmp4857 + tmp4858;
double tmp4862 = tmp4859 + tmp4860;
double tmp4863 = gammaBar_UU.xx * tmp114;
double tmp4864 = tmp4862 + tmp460;
double tmp4865 = tmp4863 + tmp4864;
double tmp4877 = gammaBar_UU.xz * tmp196;
double tmp4878 = tmp474 + tmp670;
double tmp4880 = tmp4877 + tmp4878;
double tmp4882 = tmp4880 + tmp667;
double tmp4883 = gammaBar_UU.xy * tmp193;
double tmp4884 = tmp4882 + tmp480;
double tmp4886 = tmp4883 + tmp4884;
double tmp4888 = tmp4886 + tmp664;
double tmp4889 = gammaBar_UU.xx * tmp115;
double tmp4890 = tmp4888 + tmp486;
double tmp4891 = tmp4889 + tmp4890;
double tmp4933 = gammaBar_UU.zz * tmp685;
double tmp4934 = gammaBar_UU.xz * tmp273;
double tmp4935 = tmp4933 + tmp526;
double tmp4937 = tmp4934 + tmp4935;
double tmp4939 = tmp4937 + tmp667;
double tmp4940 = gammaBar_UU.xy * tmp195;
double tmp4941 = tmp4939 + tmp532;
double tmp4942 = gammaBar_UU.xz * tmp613;
double tmp4943 = tmp4940 + tmp4941;
double tmp4945 = tmp4942 + tmp4943;
double tmp4946 = gammaBar_UU.xx * tmp117;
double tmp4947 = tmp4945 + tmp538;
double tmp4948 = tmp4946 + tmp4947;
double tmp4960 = gammaBar_UU.xz * tmp274;
double tmp4961 = tmp552 + tmp690;
double tmp4963 = tmp4960 + tmp4961;
double tmp4965 = tmp4963 + tmp689;
double tmp4966 = gammaBar_UU.xy * tmp196;
double tmp4967 = tmp4965 + tmp558;
double tmp4969 = tmp4966 + tmp4967;
double tmp4971 = tmp4969 + tmp691;
double tmp4972 = gammaBar_UU.xx * tmp118;
double tmp4973 = tmp4971 + tmp564;
double tmp4974 = tmp4972 + tmp4973;
double tmp5041 = gammaBar_UU.yz * tmp395;
double tmp5044 = tmp5041 + tmp643;
double tmp5046 = tmp5044 + tmp311;
double tmp5047 = gammaBar_UU.yy * tmp392;
double tmp5048 = tmp5046 + tmp646;
double tmp5049 = gammaBar_UU.xy * tmp141;
double tmp5050 = tmp5047 + tmp5048;
double tmp5052 = tmp5049 + tmp5050;
double tmp5053 = gammaBar_UU.xy * tmp389;
double tmp5054 = tmp5052 + tmp652;
double tmp5055 = gammaBar_UU.xx * tmp138;
double tmp5056 = tmp5053 + tmp5054;
double tmp5057 = tmp5055 + tmp5056;
double tmp5126 = gammaBar_UU.xz * tmp222;
double tmp5127 = tmp556 + tmp690;
double tmp5129 = tmp5126 + tmp5127;
double tmp5130 = gammaBar_UU.yy * tmp470;
double tmp5131 = tmp5129 + tmp693;
double tmp5132 = gammaBar_UU.xy * tmp219;
double tmp5133 = tmp5130 + tmp5131;
double tmp5135 = tmp5132 + tmp5133;
double tmp5136 = gammaBar_UU.xy * tmp392;
double tmp5137 = tmp5135 + tmp699;
double tmp5138 = gammaBar_UU.xx * tmp141;
double tmp5139 = tmp5136 + tmp5137;
double tmp5140 = tmp5138 + tmp5139;
double tmp5207 = gammaBar_UU.yz * tmp551;
double tmp5209 = gammaBar_UU.xz * tmp300;
double tmp5210 = tmp5207 + tmp717;
double tmp5212 = tmp5209 + tmp5210;
double tmp5213 = gammaBar_UU.yy * tmp473;
double tmp5214 = tmp5212 + tmp714;
double tmp5215 = gammaBar_UU.xy * tmp222;
double tmp5216 = tmp5213 + tmp5214;
double tmp5218 = tmp5215 + tmp5216;
double tmp5219 = gammaBar_UU.xy * tmp395;
double tmp5220 = tmp5218 + tmp711;
double tmp5221 = gammaBar_UU.xx * tmp144;
double tmp5222 = tmp5219 + tmp5220;
double tmp5223 = tmp5221 + tmp5222;
double tmp5451 = tmp58 + tmp54;
double tmp5452 = tmp5451 + tmp60;
double tmp5468 = gammaBar_UU.xy * tmp30;
double tmp5469 = gammaBar_UU.xz * tmp35;
double tmp5470 = gammaBar_UU.xx * tmp15;
double tmp5471 = tmp5468 + tmp5469;
double tmp5472 = tmp5470 + tmp5471;
double tmp5488 = gammaBar_UU.xy * tmp40;
double tmp5489 = gammaBar_UU.xz * tmp45;
double tmp5490 = gammaBar_UU.xx * tmp25;
double tmp5491 = tmp5488 + tmp5489;
double tmp5492 = tmp5490 + tmp5491;
double tmp5498 = gammaBar_UU.yy * partial_gammaBar_LLl[0].xy;
double tmp5499 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xz;
double tmp5500 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xx;
double tmp5501 = tmp5498 + tmp5499;
double tmp5502 = tmp5500 + tmp5501;
double tmp5506 = tmp2847 + tmp2844;
double tmp5507 = tmp5506 + tmp1;
double tmp5508 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yz;
double tmp5509 = gammaBar_UU.yz * partial_gammaBar_LLl[0].zz;
double tmp5510 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xz;
double tmp5511 = tmp5508 + tmp5509;
double tmp5512 = tmp5510 + tmp5511;
double tmp5513 = gammaBar_UU.xy * tmp5507;
double tmp5514 = gammaBar_UU.xz * tmp5512;
double tmp5515 = gammaBar_UU.xx * tmp5502;
double tmp5516 = tmp5513 + tmp5514;
double tmp5517 = tmp5515 + tmp5516;
double tmp5521 = tmp2223 + tmp2221;
double tmp5522 = tmp5521 + tmp2229;
double tmp5526 = tmp2242 + tmp2240;
double tmp5527 = tmp5526 + tmp11;
double tmp5531 = tmp2261 + tmp2259;
double tmp5532 = tmp5531 + tmp2267;
double tmp5533 = gammaBar_UU.xy * tmp5527;
double tmp5534 = gammaBar_UU.xz * tmp5532;
double tmp5535 = gammaBar_UU.xx * tmp5522;
double tmp5536 = tmp5533 + tmp5534;
double tmp5537 = tmp5535 + tmp5536;
double tmp5538 = gammaBar_UU.yy * partial_gammaBar_LLl[2].xy;
double tmp5539 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xz;
double tmp5540 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xx;
double tmp5541 = tmp5538 + tmp5539;
double tmp5542 = tmp5540 + tmp5541;
double tmp5546 = tmp2875 + tmp2257;
double tmp5547 = tmp5546 + tmp21;
double tmp5548 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yz;
double tmp5549 = gammaBar_UU.yz * partial_gammaBar_LLl[2].zz;
double tmp5550 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xz;
double tmp5551 = tmp5548 + tmp5549;
double tmp5552 = tmp5550 + tmp5551;
double tmp5553 = gammaBar_UU.xy * tmp5547;
double tmp5554 = gammaBar_UU.xz * tmp5552;
double tmp5555 = gammaBar_UU.xx * tmp5542;
double tmp5556 = tmp5553 + tmp5554;
double tmp5557 = tmp5555 + tmp5556;
double tmp5578 = gammaBar_UU.yy * tmp10;
double tmp5579 = gammaBar_UU.yz * tmp20;
double tmp5580 = gammaBar_UU.xy * tmp5;
double tmp5581 = tmp5578 + tmp5579;
double tmp5582 = tmp5580 + tmp5581;
double tmp5601 = tmp50 + tmp48;
double tmp5602 = tmp5601 + tmp56;
double tmp5618 = gammaBar_UU.yy * tmp40;
double tmp5619 = gammaBar_UU.yz * tmp45;
double tmp5620 = gammaBar_UU.xy * tmp25;
double tmp5621 = tmp5618 + tmp5619;
double tmp5622 = tmp5620 + tmp5621;
double tmp5628 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xy;
double tmp5629 = gammaBar_UU.zz * partial_gammaBar_LLl[0].xz;
double tmp5630 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xx;
double tmp5631 = tmp5628 + tmp5629;
double tmp5632 = tmp5630 + tmp5631;
double tmp5633 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yy;
double tmp5634 = gammaBar_UU.zz * partial_gammaBar_LLl[0].yz;
double tmp5635 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xy;
double tmp5636 = tmp5633 + tmp5634;
double tmp5637 = tmp5635 + tmp5636;
double tmp5641 = tmp2844 + tmp2846;
double tmp5642 = tmp5641 + tmp2;
double tmp5643 = gammaBar_UU.xy * tmp5637;
double tmp5644 = gammaBar_UU.xz * tmp5642;
double tmp5645 = gammaBar_UU.xx * tmp5632;
double tmp5646 = tmp5643 + tmp5644;
double tmp5647 = tmp5645 + tmp5646;
double tmp5648 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xy;
double tmp5649 = gammaBar_UU.zz * partial_gammaBar_LLl[1].xz;
double tmp5650 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xx;
double tmp5651 = tmp5648 + tmp5649;
double tmp5652 = tmp5650 + tmp5651;
double tmp5653 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yy;
double tmp5654 = gammaBar_UU.zz * partial_gammaBar_LLl[1].yz;
double tmp5655 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xy;
double tmp5656 = tmp5653 + tmp5654;
double tmp5657 = tmp5655 + tmp5656;
double tmp5661 = tmp2240 + tmp2860;
double tmp5662 = tmp5661 + tmp12;
double tmp5663 = gammaBar_UU.xy * tmp5657;
double tmp5664 = gammaBar_UU.xz * tmp5662;
double tmp5665 = gammaBar_UU.xx * tmp5652;
double tmp5666 = tmp5663 + tmp5664;
double tmp5667 = tmp5665 + tmp5666;
double tmp5672 = tmp2225 + tmp2222;
double tmp5677 = tmp2244 + tmp2241;
double tmp5682 = tmp22 + tmp2260;
double tmp5683 = gammaBar_UU.xy * tmp5677;
double tmp5684 = gammaBar_UU.xz * tmp5682;
double tmp5685 = gammaBar_UU.xx * tmp5672;
double tmp5686 = tmp5683 + tmp5684;
double tmp5687 = tmp5685 + tmp5686;
double tmp5708 = gammaBar_UU.yz * tmp10;
double tmp5709 = gammaBar_UU.zz * tmp20;
double tmp5710 = gammaBar_UU.xz * tmp5;
double tmp5711 = tmp5708 + tmp5709;
double tmp5712 = tmp5710 + tmp5711;
double tmp5728 = gammaBar_UU.yz * tmp30;
double tmp5729 = gammaBar_UU.zz * tmp35;
double tmp5730 = gammaBar_UU.xz * tmp15;
double tmp5731 = tmp5728 + tmp5729;
double tmp5732 = tmp5730 + tmp5731;
double tmp5752 = tmp52 + tmp49;
double tmp5773 = gammaBar_UU.yy * tmp5507;
double tmp5774 = gammaBar_UU.yz * tmp5512;
double tmp5775 = gammaBar_UU.xy * tmp5502;
double tmp5776 = tmp5773 + tmp5774;
double tmp5777 = tmp5775 + tmp5776;
double tmp5793 = gammaBar_UU.yy * tmp5527;
double tmp5794 = gammaBar_UU.yz * tmp5532;
double tmp5795 = gammaBar_UU.xy * tmp5522;
double tmp5796 = tmp5793 + tmp5794;
double tmp5797 = tmp5795 + tmp5796;
double tmp5813 = gammaBar_UU.yy * tmp5547;
double tmp5814 = gammaBar_UU.yz * tmp5552;
double tmp5815 = gammaBar_UU.xy * tmp5542;
double tmp5816 = tmp5813 + tmp5814;
double tmp5817 = tmp5815 + tmp5816;
double tmp5838 = gammaBar_UU.yy * tmp5637;
double tmp5839 = gammaBar_UU.yz * tmp5642;
double tmp5840 = gammaBar_UU.xy * tmp5632;
double tmp5841 = tmp5838 + tmp5839;
double tmp5842 = tmp5840 + tmp5841;
double tmp5858 = gammaBar_UU.yy * tmp5657;
double tmp5859 = gammaBar_UU.yz * tmp5662;
double tmp5860 = gammaBar_UU.xy * tmp5652;
double tmp5861 = tmp5858 + tmp5859;
double tmp5862 = tmp5860 + tmp5861;
double tmp5878 = gammaBar_UU.yy * tmp5677;
double tmp5879 = gammaBar_UU.yz * tmp5682;
double tmp5880 = gammaBar_UU.xy * tmp5672;
double tmp5881 = tmp5878 + tmp5879;
double tmp5882 = tmp5880 + tmp5881;
double tmp5903 = gammaBar_UU.yz * tmp5507;
double tmp5904 = gammaBar_UU.zz * tmp5512;
double tmp5905 = gammaBar_UU.xz * tmp5502;
double tmp5906 = tmp5903 + tmp5904;
double tmp5907 = tmp5905 + tmp5906;
double tmp5923 = gammaBar_UU.yz * tmp5527;
double tmp5924 = gammaBar_UU.zz * tmp5532;
double tmp5925 = gammaBar_UU.xz * tmp5522;
double tmp5926 = tmp5923 + tmp5924;
double tmp5927 = tmp5925 + tmp5926;
double tmp5943 = gammaBar_UU.yz * tmp5547;
double tmp5944 = gammaBar_UU.zz * tmp5552;
double tmp5945 = gammaBar_UU.xz * tmp5542;
double tmp5946 = tmp5943 + tmp5944;
double tmp5947 = tmp5945 + tmp5946;
double tmp5968 = gammaBar_UU.yz * tmp5637;
double tmp5969 = gammaBar_UU.zz * tmp5642;
double tmp5970 = gammaBar_UU.xz * tmp5632;
double tmp5971 = tmp5968 + tmp5969;
double tmp5972 = tmp5970 + tmp5971;
double tmp5988 = gammaBar_UU.yz * tmp5657;
double tmp5989 = gammaBar_UU.zz * tmp5662;
double tmp5990 = gammaBar_UU.xz * tmp5652;
double tmp5991 = tmp5988 + tmp5989;
double tmp5992 = tmp5990 + tmp5991;
double tmp6008 = gammaBar_UU.yz * tmp5677;
double tmp6009 = gammaBar_UU.zz * tmp5682;
double tmp6010 = gammaBar_UU.xz * tmp5672;
double tmp6011 = tmp6008 + tmp6009;
double tmp6012 = tmp6010 + tmp6011;
double tmp6054 = tmp56 + tmp52;
double tmp6055 = tmp6054 + tmp60;
double tmp6072 = gammaBar_UU.xz * tmp40;
double tmp6073 = gammaBar_UU.xx * tmp10;
double tmp6074 = tmp6072 + tmp5468;
double tmp6075 = tmp6073 + tmp6074;
double tmp6091 = gammaBar_UU.xy * tmp35;
double tmp6093 = gammaBar_UU.xx * tmp20;
double tmp6094 = tmp6091 + tmp5489;
double tmp6095 = tmp6093 + tmp6094;
double tmp6116 = gammaBar_UU.yy * tmp15;
double tmp6117 = gammaBar_UU.yz * tmp25;
double tmp6119 = tmp6116 + tmp6117;
double tmp6120 = tmp6119 + tmp5580;
double tmp6139 = tmp50 + tmp46;
double tmp6140 = tmp6139 + tmp58;
double tmp6156 = gammaBar_UU.yy * tmp35;
double tmp6158 = gammaBar_UU.xy * tmp20;
double tmp6159 = tmp6156 + tmp5619;
double tmp6160 = tmp6158 + tmp6159;
double tmp6246 = gammaBar_UU.yz * tmp15;
double tmp6247 = gammaBar_UU.zz * tmp25;
double tmp6249 = tmp6246 + tmp6247;
double tmp6250 = tmp6249 + tmp5710;
double tmp6267 = gammaBar_UU.zz * tmp40;
double tmp6268 = gammaBar_UU.xz * tmp10;
double tmp6269 = tmp6267 + tmp5728;
double tmp6270 = tmp6268 + tmp6269;
double tmp6289 = tmp48 + tmp47;
double tmp6290 = tmp6289 + tmp54;
double tmp6642 = tmp2220 + tmp3;
double tmp6644 = tmp6642 + tmp2219;
double tmp6646 = tmp6644 + tmp2221;
double tmp6648 = tmp6646 + tmp2223;
double tmp6650 = tmp6648 + tmp2225;
double tmp6652 = tmp6650 + tmp2;
double tmp6654 = tmp6652 + tmp2229;
double tmp6655 = tmp6654 + tmp1;
double tmp6659 = tmp2239 + tmp8;
double tmp6661 = tmp6659 + tmp2238;
double tmp6663 = tmp6661 + tmp2240;
double tmp6665 = tmp6663 + tmp2242;
double tmp6667 = tmp6665 + tmp2244;
double tmp6669 = tmp6667 + tmp7;
double tmp6671 = tmp6669 + tmp11;
double tmp6672 = tmp6671 + tmp6;
double tmp6676 = tmp2258 + tmp18;
double tmp6678 = tmp6676 + tmp2257;
double tmp6680 = tmp6678 + tmp2259;
double tmp6682 = tmp6680 + tmp2261;
double tmp6684 = tmp6682 + tmp22;
double tmp6686 = tmp6684 + tmp17;
double tmp6688 = tmp6686 + tmp2267;
double tmp6689 = tmp6688 + tmp16;
double tmp6756 = tmp1 + tmp2229;
double tmp6758 = tmp6756 + tmp2220;
double tmp6760 = tmp6758 + tmp2219;
double tmp6762 = tmp6760 + tmp2221;
double tmp6764 = tmp6762 + tmp2223;
double tmp6766 = tmp6764 + tmp2225;
double tmp6768 = tmp6766 + tmp2;
double tmp6769 = tmp6768 + tmp3;
double tmp6773 = tmp6 + tmp11;
double tmp6775 = tmp6773 + tmp2239;
double tmp6777 = tmp6775 + tmp2238;
double tmp6779 = tmp6777 + tmp2240;
double tmp6781 = tmp6779 + tmp2242;
double tmp6783 = tmp6781 + tmp2244;
double tmp6785 = tmp6783 + tmp7;
double tmp6786 = tmp6785 + tmp8;
double tmp6790 = tmp16 + tmp2267;
double tmp6792 = tmp6790 + tmp2258;
double tmp6794 = tmp6792 + tmp2257;
double tmp6796 = tmp6794 + tmp2259;
double tmp6798 = tmp6796 + tmp2261;
double tmp6800 = tmp6798 + tmp22;
double tmp6802 = tmp6800 + tmp17;
double tmp6803 = tmp6802 + tmp18;
double tmp6804 = gammaBar_UU.xy * tmp6786;
double tmp6805 = gammaBar_UU.xz * tmp6803;
double tmp6806 = gammaBar_UU.xx * tmp6769;
double tmp6807 = tmp6804 + tmp6805;
double tmp6808 = tmp6806 + tmp6807;
double tmp6809 = gammaBar_UU.xy * tmp6808;
double tmp6870 = tmp2 + tmp2225;
double tmp6872 = tmp6870 + tmp2220;
double tmp6874 = tmp6872 + tmp2219;
double tmp6876 = tmp6874 + tmp2221;
double tmp6878 = tmp6876 + tmp2223;
double tmp6880 = tmp6878 + tmp2229;
double tmp6882 = tmp6880 + tmp1;
double tmp6883 = tmp6882 + tmp3;
double tmp6887 = tmp7 + tmp2244;
double tmp6889 = tmp6887 + tmp2239;
double tmp6891 = tmp6889 + tmp2238;
double tmp6893 = tmp6891 + tmp2240;
double tmp6895 = tmp6893 + tmp2242;
double tmp6897 = tmp6895 + tmp11;
double tmp6899 = tmp6897 + tmp6;
double tmp6900 = tmp6899 + tmp8;
double tmp6904 = tmp17 + tmp22;
double tmp6906 = tmp6904 + tmp2258;
double tmp6908 = tmp6906 + tmp2257;
double tmp6910 = tmp6908 + tmp2259;
double tmp6912 = tmp6910 + tmp2261;
double tmp6914 = tmp6912 + tmp2267;
double tmp6916 = tmp6914 + tmp16;
double tmp6917 = tmp6916 + tmp18;
double tmp6918 = gammaBar_UU.xy * tmp6900;
double tmp6919 = gammaBar_UU.xz * tmp6917;
double tmp6920 = gammaBar_UU.xx * tmp6883;
double tmp6921 = tmp6918 + tmp6919;
double tmp6922 = tmp6920 + tmp6921;
double tmp6923 = gammaBar_UU.xz * tmp6922;
double tmp6975 = gammaBar_UU.yy * tmp6786;
double tmp6976 = gammaBar_UU.yz * tmp6803;
double tmp6977 = gammaBar_UU.xy * tmp6769;
double tmp6978 = tmp6975 + tmp6976;
double tmp6979 = tmp6977 + tmp6978;
double tmp6980 = gammaBar_UU.xy * tmp6979;
double tmp7032 = gammaBar_UU.yz * tmp6786;
double tmp7033 = gammaBar_UU.zz * tmp6803;
double tmp7034 = gammaBar_UU.xz * tmp6769;
double tmp7035 = tmp7032 + tmp7033;
double tmp7036 = tmp7034 + tmp7035;
double tmp7037 = gammaBar_UU.xy * tmp7036;
double tmp7089 = gammaBar_UU.yy * tmp6900;
double tmp7090 = gammaBar_UU.yz * tmp6917;
double tmp7091 = gammaBar_UU.xy * tmp6883;
double tmp7092 = tmp7089 + tmp7090;
double tmp7093 = tmp7091 + tmp7092;
double tmp7094 = gammaBar_UU.xz * tmp7093;
double tmp7146 = gammaBar_UU.yz * tmp6900;
double tmp7147 = gammaBar_UU.zz * tmp6917;
double tmp7148 = gammaBar_UU.xz * tmp6883;
double tmp7149 = tmp7146 + tmp7147;
double tmp7150 = tmp7148 + tmp7149;
double tmp7151 = gammaBar_UU.xz * tmp7150;
double tmp7170 = gammaBar_UU.xy * partial_ABar_LLl[0].xy;
double tmp7171 = gammaBar_UU.xz * partial_ABar_LLl[0].xz;
double tmp7172 = gammaBar_UU.yz * partial_ABar_LLl[0].yz;
double tmp7173 = 2. * tmp7172;
double tmp7174 = gammaBar_UU.zz * partial_ABar_LLl[0].zz;
double tmp7175 = gammaBar_UU.yy * partial_ABar_LLl[0].yy;
double tmp7176 = tmp7173 + tmp7174;
double tmp7177 = 2. * tmp7171;
double tmp7178 = tmp7175 + tmp7176;
double tmp7179 = 2. * tmp7170;
double tmp7180 = tmp7177 + tmp7178;
double tmp7181 = gammaBar_UU.xx * partial_ABar_LLl[0].xx;
double tmp7182 = tmp7179 + tmp7180;
double tmp7183 = tmp7181 + tmp7182;
double tmp7184 = gammaBar_UU.xy * partial_ABar_LLl[1].xy;
double tmp7185 = gammaBar_UU.xz * partial_ABar_LLl[1].xz;
double tmp7186 = gammaBar_UU.yz * partial_ABar_LLl[1].yz;
double tmp7187 = 2. * tmp7186;
double tmp7188 = gammaBar_UU.zz * partial_ABar_LLl[1].zz;
double tmp7189 = gammaBar_UU.yy * partial_ABar_LLl[1].yy;
double tmp7190 = tmp7187 + tmp7188;
double tmp7191 = 2. * tmp7185;
double tmp7192 = tmp7189 + tmp7190;
double tmp7193 = 2. * tmp7184;
double tmp7194 = tmp7191 + tmp7192;
double tmp7195 = gammaBar_UU.xx * partial_ABar_LLl[1].xx;
double tmp7196 = tmp7193 + tmp7194;
double tmp7197 = tmp7195 + tmp7196;
double tmp7198 = gammaBar_UU.xy * partial_ABar_LLl[2].xy;
double tmp7199 = gammaBar_UU.xz * partial_ABar_LLl[2].xz;
double tmp7200 = gammaBar_UU.yz * partial_ABar_LLl[2].yz;
double tmp7201 = 2. * tmp7200;
double tmp7202 = gammaBar_UU.zz * partial_ABar_LLl[2].zz;
double tmp7203 = gammaBar_UU.yy * partial_ABar_LLl[2].yy;
double tmp7204 = tmp7201 + tmp7202;
double tmp7205 = 2. * tmp7199;
double tmp7206 = tmp7203 + tmp7204;
double tmp7207 = 2. * tmp7198;
double tmp7208 = tmp7205 + tmp7206;
double tmp7209 = gammaBar_UU.xx * partial_ABar_LLl[2].xx;
double tmp7210 = tmp7207 + tmp7208;
double tmp7211 = tmp7209 + tmp7210;
double tmp7212 = gammaBar_UU.yz * partial_ABar_LLl[2].xy;
double tmp7213 = gammaBar_UU.zz * partial_ABar_LLl[2].xz;
double tmp7214 = gammaBar_UU.yz * partial_ABar_LLl[1].xz;
double tmp7215 = tmp7212 + tmp7213;
double tmp7216 = gammaBar_UU.yy * partial_ABar_LLl[1].xy;
double tmp7217 = tmp7214 + tmp7215;
double tmp7218 = gammaBar_UU.xz * partial_ABar_LLl[2].xx;
double tmp7219 = tmp7216 + tmp7217;
double tmp7221 = tmp7218 + tmp7219;
double tmp7222 = gammaBar_UU.xy * partial_ABar_LLl[1].xx;
double tmp7223 = tmp7221 + tmp7171;
double tmp7225 = tmp7222 + tmp7223;
double tmp7227 = tmp7225 + tmp7170;
double tmp7228 = tmp7227 + tmp7181;
double tmp7229 = gammaBar_UU.yz * partial_ABar_LLl[2].yy;
double tmp7230 = gammaBar_UU.zz * partial_ABar_LLl[2].yz;
double tmp7232 = tmp7229 + tmp7230;
double tmp7234 = tmp7232 + tmp7186;
double tmp7235 = gammaBar_UU.xz * partial_ABar_LLl[2].xy;
double tmp7236 = tmp7234 + tmp7189;
double tmp7237 = gammaBar_UU.xz * partial_ABar_LLl[0].yz;
double tmp7238 = tmp7235 + tmp7236;
double tmp7240 = tmp7237 + tmp7238;
double tmp7241 = gammaBar_UU.xy * partial_ABar_LLl[0].yy;
double tmp7242 = tmp7240 + tmp7184;
double tmp7243 = gammaBar_UU.xx * partial_ABar_LLl[0].xy;
double tmp7244 = tmp7241 + tmp7242;
double tmp7245 = tmp7243 + tmp7244;
double tmp7248 = gammaBar_UU.yz * partial_ABar_LLl[1].zz;
double tmp7249 = tmp7200 + tmp7202;
double tmp7250 = gammaBar_UU.yy * partial_ABar_LLl[1].yz;
double tmp7251 = tmp7248 + tmp7249;
double tmp7253 = tmp7250 + tmp7251;
double tmp7254 = gammaBar_UU.xz * partial_ABar_LLl[0].zz;
double tmp7255 = tmp7253 + tmp7199;
double tmp7256 = gammaBar_UU.xy * partial_ABar_LLl[1].xz;
double tmp7257 = tmp7254 + tmp7255;
double tmp7258 = gammaBar_UU.xy * partial_ABar_LLl[0].yz;
double tmp7259 = tmp7256 + tmp7257;
double tmp7260 = gammaBar_UU.xx * partial_ABar_LLl[0].xz;
double tmp7261 = tmp7258 + tmp7259;
double tmp7262 = tmp7260 + tmp7261;
double tmp7357 = 1. / det_gammaBar;
double tmp7358 = 1. / 6.;
double tmp7420 = tmp5794 + tmp5946;
double tmp7422 = tmp7420 + tmp5793;
double tmp7424 = tmp7422 + tmp5945;
double tmp7426 = tmp7424 + tmp5514;
double tmp7428 = tmp7426 + tmp5795;
double tmp7430 = tmp7428 + tmp5513;
double tmp7432 = tmp7430 + tmp5515;
double tmp9791 = gammaBar_UU.yy * gammaBar_UU.yz;
double tmp9793 = gammaBar_UU.yz * gammaBar_UU.yz;
double tmp9810 = gammaBar_UU.yy * gammaBar_UU.zz;
double tmp9813 = gammaBar_UU.yz * gammaBar_UU.zz;
double tmp9814 = ABar_LL.yz * tmp9793;
double tmp9815 = ABar_LL.zz * tmp9813;
double tmp9816 = ABar_LL.xz * tmp2418;
double tmp9818 = ABar_LL.yz * tmp9810;
double tmp9820 = ABar_LL.yy * tmp9791;
double tmp9822 = ABar_LL.xy * tmp2417;
double tmp9824 = ABar_LL.xz * tmp2441;
double tmp9826 = ABar_LL.xy * tmp2415;
double tmp9828 = ABar_LL.xx * tmp2396;
double tmp9873 = gammaBar_UU.yz * tmp2502;
double tmp10649 = gammaBar_UU.yz * tmp3278;
double tmp10732 = gammaBar_UU.yz * tmp3361;
double tmp10815 = gammaBar_UU.yz * tmp3444;
double tmp11414 = gammaBar_UU.yz * tmp4043;
double tmp11497 = gammaBar_UU.yz * tmp4126;
double tmp11580 = gammaBar_UU.yz * tmp4209;
double tmp12179 = gammaBar_UU.yz * tmp4808;
double tmp12262 = gammaBar_UU.yz * tmp4891;
double tmp12345 = gammaBar_UU.yz * tmp4974;
double tmp13423 = tmp5795 + tmp5945;
double tmp13424 = tmp13423 + tmp5515;
double tmp13441 = gammaBar_UU.xz * tmp5547;
double tmp13442 = gammaBar_UU.xx * tmp5507;
double tmp13443 = tmp13441 + tmp5533;
double tmp13444 = tmp13442 + tmp13443;
double tmp13460 = gammaBar_UU.xy * tmp5532;
double tmp13462 = gammaBar_UU.xx * tmp5512;
double tmp13463 = tmp13460 + tmp5554;
double tmp13464 = tmp13462 + tmp13463;
double tmp13485 = gammaBar_UU.yy * tmp5522;
double tmp13486 = gammaBar_UU.yz * tmp5542;
double tmp13488 = tmp13485 + tmp13486;
double tmp13489 = tmp13488 + tmp5775;
double tmp13508 = tmp5793 + tmp5943;
double tmp13509 = tmp13508 + tmp5513;
double tmp13525 = gammaBar_UU.yy * tmp5532;
double tmp13527 = gammaBar_UU.xy * tmp5512;
double tmp13528 = tmp13525 + tmp5814;
double tmp13529 = tmp13527 + tmp13528;
double tmp13615 = gammaBar_UU.yz * tmp5522;
double tmp13616 = gammaBar_UU.zz * tmp5542;
double tmp13618 = tmp13615 + tmp13616;
double tmp13619 = tmp13618 + tmp5905;
double tmp13636 = gammaBar_UU.zz * tmp5547;
double tmp13637 = gammaBar_UU.xz * tmp5507;
double tmp13638 = tmp13636 + tmp5923;
double tmp13639 = tmp13637 + tmp13638;
double tmp13658 = tmp5794 + tmp5944;
double tmp13659 = tmp13658 + tmp5514;
double tmp14125 = tmp2220 + tmp2223;
double tmp14127 = tmp14125 + tmp2219;
double tmp14129 = tmp14127 + tmp2221;
double tmp14131 = tmp14129 + tmp2225;
double tmp14133 = tmp14131 + tmp2;
double tmp14135 = tmp14133 + tmp2229;
double tmp14137 = tmp14135 + tmp1;
double tmp14138 = tmp14137 + tmp3;
double tmp14142 = tmp2239 + tmp2242;
double tmp14144 = tmp14142 + tmp2238;
double tmp14146 = tmp14144 + tmp2240;
double tmp14148 = tmp14146 + tmp2244;
double tmp14150 = tmp14148 + tmp7;
double tmp14152 = tmp14150 + tmp11;
double tmp14154 = tmp14152 + tmp6;
double tmp14155 = tmp14154 + tmp8;
double tmp14159 = tmp2258 + tmp2261;
double tmp14161 = tmp14159 + tmp2257;
double tmp14163 = tmp14161 + tmp2259;
double tmp14165 = tmp14163 + tmp22;
double tmp14167 = tmp14165 + tmp17;
double tmp14169 = tmp14167 + tmp2267;
double tmp14171 = tmp14169 + tmp16;
double tmp14172 = tmp14171 + tmp18;
double tmp14239 = tmp2221 + tmp2219;
double tmp14241 = tmp14239 + tmp2220;
double tmp14243 = tmp14241 + tmp2223;
double tmp14245 = tmp14243 + tmp2225;
double tmp14247 = tmp14245 + tmp2;
double tmp14249 = tmp14247 + tmp2229;
double tmp14251 = tmp14249 + tmp1;
double tmp14252 = tmp14251 + tmp3;
double tmp14256 = tmp2240 + tmp2238;
double tmp14258 = tmp14256 + tmp2239;
double tmp14260 = tmp14258 + tmp2242;
double tmp14262 = tmp14260 + tmp2244;
double tmp14264 = tmp14262 + tmp7;
double tmp14266 = tmp14264 + tmp11;
double tmp14268 = tmp14266 + tmp6;
double tmp14269 = tmp14268 + tmp8;
double tmp14273 = tmp2259 + tmp2257;
double tmp14275 = tmp14273 + tmp2258;
double tmp14277 = tmp14275 + tmp2261;
double tmp14279 = tmp14277 + tmp22;
double tmp14281 = tmp14279 + tmp17;
double tmp14283 = tmp14281 + tmp2267;
double tmp14285 = tmp14283 + tmp16;
double tmp14286 = tmp14285 + tmp18;
double tmp14287 = gammaBar_UU.xy * tmp14269;
double tmp14288 = gammaBar_UU.xz * tmp14286;
double tmp14289 = gammaBar_UU.xx * tmp14252;
double tmp14290 = tmp14287 + tmp14288;
double tmp14291 = tmp14289 + tmp14290;
double tmp14292 = gammaBar_UU.yz * tmp14291;
double tmp14458 = gammaBar_UU.yy * tmp14269;
double tmp14459 = gammaBar_UU.yz * tmp14286;
double tmp14460 = gammaBar_UU.xy * tmp14252;
double tmp14461 = tmp14458 + tmp14459;
double tmp14462 = tmp14460 + tmp14461;
double tmp14463 = gammaBar_UU.yz * tmp14462;
double tmp14515 = gammaBar_UU.yz * tmp14269;
double tmp14516 = gammaBar_UU.zz * tmp14286;
double tmp14517 = gammaBar_UU.xz * tmp14252;
double tmp14518 = tmp14515 + tmp14516;
double tmp14519 = tmp14517 + tmp14518;
double tmp14520 = gammaBar_UU.yz * tmp14519;
double tmp14789 = tmp5859 + tmp6011;
double tmp14791 = tmp14789 + tmp5858;
double tmp14793 = tmp14791 + tmp6010;
double tmp14795 = tmp14793 + tmp5644;
double tmp14797 = tmp14795 + tmp5860;
double tmp14799 = tmp14797 + tmp5643;
double tmp14801 = tmp14799 + tmp5645;
double tmp20792 = tmp5860 + tmp6010;
double tmp20793 = tmp20792 + tmp5645;
double tmp20810 = gammaBar_UU.xz * tmp5677;
double tmp20811 = gammaBar_UU.xx * tmp5637;
double tmp20812 = tmp20810 + tmp5663;
double tmp20813 = tmp20811 + tmp20812;
double tmp20829 = gammaBar_UU.xy * tmp5662;
double tmp20831 = gammaBar_UU.xx * tmp5642;
double tmp20832 = tmp20829 + tmp5684;
double tmp20833 = tmp20831 + tmp20832;
double tmp20854 = gammaBar_UU.yy * tmp5652;
double tmp20855 = gammaBar_UU.yz * tmp5672;
double tmp20857 = tmp20854 + tmp20855;
double tmp20858 = tmp20857 + tmp5840;
double tmp20877 = tmp5858 + tmp6008;
double tmp20878 = tmp20877 + tmp5643;
double tmp20894 = gammaBar_UU.yy * tmp5662;
double tmp20896 = gammaBar_UU.xy * tmp5642;
double tmp20897 = tmp20894 + tmp5879;
double tmp20898 = tmp20896 + tmp20897;
double tmp20984 = gammaBar_UU.yz * tmp5652;
double tmp20985 = gammaBar_UU.zz * tmp5672;
double tmp20987 = tmp20984 + tmp20985;
double tmp20988 = tmp20987 + tmp5970;
double tmp21005 = gammaBar_UU.zz * tmp5677;
double tmp21006 = gammaBar_UU.xz * tmp5637;
double tmp21007 = tmp21005 + tmp5988;
double tmp21008 = tmp21006 + tmp21007;
double tmp21027 = tmp5859 + tmp6009;
double tmp21028 = tmp21027 + tmp5644;
double dt_LambdaBar_U.x = tmp7358 * U->beta_U.x * tmp7357 + U->alpha * (-2. * (gammaBar_UU.xz * tmp7262 + gammaBar_UU.xy * tmp7245 + gammaBar_UU.xx * tmp7228) + gammaBar_UU.xz * tmp7211 + gammaBar_UU.xy * tmp7197 + gammaBar_UU.xx * tmp7183) + 2. * U->alpha * (ABar_LL.zz * tmp7151 + ABar_LL.yz * tmp7094 + ABar_LL.yz * tmp7037 + ABar_LL.yy * tmp6980 + ABar_LL.xz * tmp6923 + ABar_LL.xz * gammaBar_UU.xx * (gammaBar_UU.zz * tmp6689 + gammaBar_UU.yz * tmp6672 + gammaBar_UU.xz * tmp6655) + ABar_LL.xy * tmp6809 + ABar_LL.xy * gammaBar_UU.xx * (gammaBar_UU.yz * tmp6689 + gammaBar_UU.yy * tmp6672 + gammaBar_UU.xy * tmp6655) + ABar_LL.xx * gammaBar_UU.xx * (gammaBar_UU.xz * tmp6689 + gammaBar_UU.xy * tmp6672 + gammaBar_UU.xx * tmp6655)) + 2. * U->alpha * (ABar_LL.zz * (gammaBar_UU.zz * tmp6290 + gammaBar_UU.yz * tmp6270 + gammaBar_UU.xz * tmp6250) + ABar_LL.yz * (gammaBar_UU.zz * tmp6160 + gammaBar_UU.yz * tmp6140 + gammaBar_UU.xz * tmp6120) + ABar_LL.yz * (gammaBar_UU.yz * tmp6290 + gammaBar_UU.yy * tmp6270 + gammaBar_UU.xy * tmp6250) + ABar_LL.yy * (gammaBar_UU.yz * tmp6160 + gammaBar_UU.yy * tmp6140 + gammaBar_UU.xy * tmp6120) + ABar_LL.xz * (gammaBar_UU.zz * tmp6095 + gammaBar_UU.yz * tmp6075 + gammaBar_UU.xz * tmp6055) + ABar_LL.xz * (gammaBar_UU.xz * tmp6290 + gammaBar_UU.xy * tmp6270 + gammaBar_UU.xx * tmp6250) + ABar_LL.xy * (gammaBar_UU.yz * tmp6095 + gammaBar_UU.yy * tmp6075 + gammaBar_UU.xy * tmp6055) + ABar_LL.xy * (gammaBar_UU.xz * tmp6160 + gammaBar_UU.xy * tmp6140 + gammaBar_UU.xx * tmp6120) + ABar_LL.xx * (gammaBar_UU.xz * tmp6095 + gammaBar_UU.xy * tmp6075 + gammaBar_UU.xx * tmp6055)) + -1. * U->alpha * (ABar_LL.zz * (gammaBar_UU.xz * tmp6012 + gammaBar_UU.xy * tmp5992 + gammaBar_UU.xx * tmp5972) + ABar_LL.yz * (gammaBar_UU.xz * tmp5947 + gammaBar_UU.xy * tmp5927 + gammaBar_UU.xx * tmp5907) + ABar_LL.yz * (gammaBar_UU.xz * tmp5882 + gammaBar_UU.xy * tmp5862 + gammaBar_UU.xx * tmp5842) + ABar_LL.yy * (gammaBar_UU.xz * tmp5817 + gammaBar_UU.xy * tmp5797 + gammaBar_UU.xx * tmp5777) + ABar_LL.xz * (gammaBar_UU.xz * tmp5752 + gammaBar_UU.xy * tmp5732 + gammaBar_UU.xx * tmp5712) + ABar_LL.xz * (gammaBar_UU.xz * tmp5687 + gammaBar_UU.xy * tmp5667 + gammaBar_UU.xx * tmp5647) + ABar_LL.xy * (gammaBar_UU.xz * tmp5622 + gammaBar_UU.xy * tmp5602 + gammaBar_UU.xx * tmp5582) + ABar_LL.xy * (gammaBar_UU.xz * tmp5557 + gammaBar_UU.xy * tmp5537 + gammaBar_UU.xx * tmp5517) + ABar_LL.xx * (gammaBar_UU.xz * tmp5492 + gammaBar_UU.xy * tmp5472 + gammaBar_UU.xx * tmp5452)) + U->beta_U.z * (gammaBar_UU.zz * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][2].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][2].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[2][2].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][1].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][1].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[2][1].xz) + gammaBar_UU.xz * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][0].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][0].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[2][0].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][2].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[2][2].xy) + gammaBar_UU.yy * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][1].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[2][1].xy) + gammaBar_UU.xy * (gammaBar_UU.xz * partial2_gammaBar_LLll[2][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][0].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[2][0].xy) + gammaBar_UU.xz * (tmp2204 + tmp2193 + tmp2194) + gammaBar_UU.xy * (tmp2190 + tmp2179 + tmp2180) + gammaBar_UU.xx * (tmp2176 + tmp2165 + tmp2166)) + U->beta_U.y * (gammaBar_UU.zz * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][2].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][2].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[1][2].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][1].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][1].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[1][1].xz) + gammaBar_UU.xz * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][0].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][0].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[1][0].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][2].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[1][2].xy) + gammaBar_UU.yy * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][1].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[1][1].xy) + gammaBar_UU.xy * (gammaBar_UU.xz * partial2_gammaBar_LLll[1][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][0].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[1][0].xy) + gammaBar_UU.xz * (tmp2157 + tmp2146 + tmp2147) + gammaBar_UU.xy * (tmp2143 + tmp2132 + tmp2133) + gammaBar_UU.xx * (tmp2129 + tmp2118 + tmp2119)) + U->beta_U.x * (gammaBar_UU.zz * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][2].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][2].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[0][2].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][1].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][1].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[0][1].xz) + gammaBar_UU.xz * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][0].zz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][0].yz + gammaBar_UU.xx * partial2_gammaBar_LLll[0][0].xz) + gammaBar_UU.yz * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][2].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[0][2].xy) + gammaBar_UU.yy * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][1].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[0][1].xy) + gammaBar_UU.xy * (gammaBar_UU.xz * partial2_gammaBar_LLll[0][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][0].yy + gammaBar_UU.xx * partial2_gammaBar_LLll[0][0].xy) + gammaBar_UU.xz * (tmp2110 + tmp2099 + tmp2100) + gammaBar_UU.xy * (tmp2096 + tmp2085 + tmp2086) + gammaBar_UU.xx * (tmp2082 + tmp2071 + tmp2072)) + -1. * U->beta_U.z * (gammaBar_UU.zz * (gammaBar_UU.xz * tmp5223 + gammaBar_UU.xy * tmp4974 + gammaBar_UU.xx * tmp4725) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp5140 + gammaBar_UU.xy * tmp4891 + gammaBar_UU.xx * tmp4642) + gammaBar_UU.xz * (gammaBar_UU.xz * tmp5057 + gammaBar_UU.xy * tmp4808 + gammaBar_UU.xx * tmp4559) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp4974 + gammaBar_UU.xy * tmp4948 + gammaBar_UU.xx * tmp4699) + gammaBar_UU.yy * (gammaBar_UU.xz * tmp4891 + gammaBar_UU.xy * tmp4865 + gammaBar_UU.xx * tmp4616) + gammaBar_UU.xy * (gammaBar_UU.xz * tmp4808 + gammaBar_UU.xy * tmp4782 + gammaBar_UU.xx * tmp4533) + gammaBar_UU.xz * (tmp4726 + tmp4727 + gammaBar_UU.xx * tmp4673) + gammaBar_UU.xy * (tmp4643 + tmp4644 + gammaBar_UU.xx * tmp4590) + gammaBar_UU.xx * (tmp4560 + tmp4561 + gammaBar_UU.xx * tmp4507)) + -1. * U->beta_U.y * (gammaBar_UU.zz * (gammaBar_UU.xz * tmp4458 + gammaBar_UU.xy * tmp4209 + gammaBar_UU.xx * tmp3960) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp4375 + gammaBar_UU.xy * tmp4126 + gammaBar_UU.xx * tmp3877) + gammaBar_UU.xz * (gammaBar_UU.xz * tmp4292 + gammaBar_UU.xy * tmp4043 + gammaBar_UU.xx * tmp3794) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp4209 + gammaBar_UU.xy * tmp4183 + gammaBar_UU.xx * tmp3934) + gammaBar_UU.yy * (gammaBar_UU.xz * tmp4126 + gammaBar_UU.xy * tmp4100 + gammaBar_UU.xx * tmp3851) + gammaBar_UU.xy * (gammaBar_UU.xz * tmp4043 + gammaBar_UU.xy * tmp4017 + gammaBar_UU.xx * tmp3768) + gammaBar_UU.xz * (tmp3961 + tmp3962 + gammaBar_UU.xx * tmp3908) + gammaBar_UU.xy * (tmp3878 + tmp3879 + gammaBar_UU.xx * tmp3825) + gammaBar_UU.xx * (tmp3795 + tmp3796 + gammaBar_UU.xx * tmp3742)) + -1. * U->beta_U.x * (gammaBar_UU.zz * (gammaBar_UU.xz * tmp3693 + gammaBar_UU.xy * tmp3444 + gammaBar_UU.xx * tmp3195) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp3610 + gammaBar_UU.xy * tmp3361 + gammaBar_UU.xx * tmp3112) + gammaBar_UU.xz * (gammaBar_UU.xz * tmp3527 + gammaBar_UU.xy * tmp3278 + gammaBar_UU.xx * tmp3029) + gammaBar_UU.yz * (gammaBar_UU.xz * tmp3444 + gammaBar_UU.xy * tmp3418 + gammaBar_UU.xx * tmp3169) + gammaBar_UU.yy * (gammaBar_UU.xz * tmp3361 + gammaBar_UU.xy * tmp3335 + gammaBar_UU.xx * tmp3086) + gammaBar_UU.xy * (gammaBar_UU.xz * tmp3278 + gammaBar_UU.xy * tmp3252 + gammaBar_UU.xx * tmp3003) + gammaBar_UU.xz * (tmp3196 + tmp3197 + gammaBar_UU.xx * tmp3143) + gammaBar_UU.xy * (tmp3113 + tmp3114 + gammaBar_UU.xx * tmp3060) + gammaBar_UU.xx * (tmp3030 + tmp3031 + gammaBar_UU.xx * tmp2977)) + -1. * tmp2949 * tmp63 + gammaBar_UU.xz * tmp2841 + gammaBar_UU.xy * tmp2779 + gammaBar_UU.xx * tmp2717 + -1. * gammaBar_UU.zz * (gammaBar_UU.xz * tmp2649 + gammaBar_UU.xy * tmp2628 + gammaBar_UU.xx * tmp2607) + -1. * gammaBar_UU.yz * (gammaBar_UU.xz * tmp2628 + gammaBar_UU.xy * tmp2623 + gammaBar_UU.xx * tmp2602) + -1. * gammaBar_UU.xz * (tmp2608 + tmp2609 + gammaBar_UU.xx * tmp2597) + -1. * gammaBar_UU.yz * (gammaBar_UU.xz * tmp2586 + gammaBar_UU.xy * tmp2565 + gammaBar_UU.xx * tmp2544) + -1. * gammaBar_UU.yy * (gammaBar_UU.xz * tmp2565 + gammaBar_UU.xy * tmp2560 + gammaBar_UU.xx * tmp2539) + -1. * gammaBar_UU.xy * (tmp2545 + tmp2546 + gammaBar_UU.xx * tmp2534) + -1. * gammaBar_UU.xz * (tmp2526 + tmp2524 + tmp2525) + -1. * gammaBar_UU.xy * (tmp2505 + tmp2503 + tmp2504) + -1. * gammaBar_UU.xx * (tmp2484 + tmp2482 + tmp2483) + gammaBar_UU.zz * partial2_beta_Ull[2][2].x + gammaBar_UU.yz * partial2_beta_Ull[2][1].x + gammaBar_UU.xz * partial2_beta_Ull[2][0].x + gammaBar_UU.yz * partial2_beta_Ull[1][2].x + gammaBar_UU.yy * partial2_beta_Ull[1][1].x + gammaBar_UU.xy * partial2_beta_Ull[1][0].x + gammaBar_UU.xz * partial2_beta_Ull[0][2].x + gammaBar_UU.xy * partial2_beta_Ull[0][1].x + gammaBar_UU.xx * partial2_beta_Ull[0][0].x + -2. * (partial_alpha_l.z * (tmp2459 + tmp2457 + tmp2455 + tmp2453 + tmp2451 + tmp2449 + tmp2447 + tmp2445 + tmp2446) + partial_alpha_l.y * (tmp2433 + tmp2431 + tmp2429 + tmp2427 + tmp2425 + tmp2423 + tmp2421 + tmp2419 + tmp2420) + partial_alpha_l.x * (ABar_LL.zz * tmp2398 + 2. * ABar_LL.yz * tmp2396 + ABar_LL.yy * tmp2395 + 2. * ABar_LL.xz * tmp2393 + 2. * ABar_LL.xy * tmp2391 + ABar_LL.xx * gammaBar_UU.xx * gammaBar_UU.xx)) + -1. * gammaBar_UU.zz * partial_beta_Ul[2].x * tmp2273 + -1. * gammaBar_UU.yz * partial_beta_Ul[2].x * tmp2254 + -1. * gammaBar_UU.xz * partial_beta_Ul[2].x * tmp2235 + -1. * gammaBar_UU.yz * partial_beta_Ul[1].x * tmp2273 + -1. * gammaBar_UU.yy * partial_beta_Ul[1].x * tmp2254 + -1. * gammaBar_UU.xy * partial_beta_Ul[1].x * tmp2235 + -1. * gammaBar_UU.xz * partial_beta_Ul[0].x * tmp2273 + -1. * gammaBar_UU.xy * partial_beta_Ul[0].x * tmp2254 + -1. * gammaBar_UU.xx * partial_beta_Ul[0].x * tmp2235 + -1. * tmp743 * (U->beta_U.z * (gammaBar_UU.xz * tmp2206 + gammaBar_UU.xy * tmp2192 + gammaBar_UU.xx * tmp2178) + U->beta_U.y * (gammaBar_UU.xz * tmp2159 + gammaBar_UU.xy * tmp2145 + gammaBar_UU.xx * tmp2131) + U->beta_U.x * (gammaBar_UU.xz * tmp2112 + gammaBar_UU.xy * tmp2098 + gammaBar_UU.xx * tmp2084)) + tmp743 * U->beta_U.x * (gammaBar_UU.xz * tmp2059 + gammaBar_UU.xy * tmp1808 + gammaBar_UU.xx * tmp1557) + tmp743 * U->beta_U.y * (gammaBar_UU.xz * tmp1398 + gammaBar_UU.xy * tmp1147 + gammaBar_UU.xx * tmp995) + tmp743 * U->beta_U.z * (gammaBar_UU.xz * tmp737 + gammaBar_UU.xy * tmp585 + gammaBar_UU.xx * tmp334) + tmp65 * gammaBar_UU.xx * tmp77 + tmp65 * gammaBar_UU.xy * tmp73 + tmp65 * gammaBar_UU.xz * tmp69 + 2. * tmp65 * tmp63 * tmp64;
double dt_LambdaBar_U.y = tmp7358 * U->beta_U.y * tmp7357 + U->alpha * (-2. * (gammaBar_UU.yz * tmp7262 + gammaBar_UU.yy * tmp7245 + gammaBar_UU.xy * tmp7228) + gammaBar_UU.yz * tmp7211 + gammaBar_UU.yy * tmp7197 + gammaBar_UU.xy * tmp7183) + 2. * U->alpha * (ABar_LL.zz * tmp14520 + ABar_LL.yz * tmp14463 + ABar_LL.yz * gammaBar_UU.yy * (gammaBar_UU.zz * tmp14172 + gammaBar_UU.yz * tmp14155 + gammaBar_UU.xz * tmp14138) + ABar_LL.yy * gammaBar_UU.yy * (gammaBar_UU.yz * tmp14172 + gammaBar_UU.yy * tmp14155 + gammaBar_UU.xy * tmp14138) + ABar_LL.xz * tmp14292 + ABar_LL.xz * tmp7037 + ABar_LL.xy * gammaBar_UU.yy * (gammaBar_UU.xz * tmp14172 + gammaBar_UU.xy * tmp14155 + gammaBar_UU.xx * tmp14138) + ABar_LL.xy * tmp6980 + ABar_LL.xx * tmp6809) + 2. * U->alpha * (ABar_LL.zz * (gammaBar_UU.zz * tmp13659 + gammaBar_UU.yz * tmp13639 + gammaBar_UU.xz * tmp13619) + ABar_LL.yz * (gammaBar_UU.zz * tmp13529 + gammaBar_UU.yz * tmp13509 + gammaBar_UU.xz * tmp13489) + ABar_LL.yz * (gammaBar_UU.yz * tmp13659 + gammaBar_UU.yy * tmp13639 + gammaBar_UU.xy * tmp13619) + ABar_LL.yy * (gammaBar_UU.yz * tmp13529 + gammaBar_UU.yy * tmp13509 + gammaBar_UU.xy * tmp13489) + ABar_LL.xz * (gammaBar_UU.zz * tmp13464 + gammaBar_UU.yz * tmp13444 + gammaBar_UU.xz * tmp13424) + ABar_LL.xz * (gammaBar_UU.xz * tmp13659 + gammaBar_UU.xy * tmp13639 + gammaBar_UU.xx * tmp13619) + ABar_LL.xy * (gammaBar_UU.yz * tmp13464 + gammaBar_UU.yy * tmp13444 + gammaBar_UU.xy * tmp13424) + ABar_LL.xy * (gammaBar_UU.xz * tmp13529 + gammaBar_UU.xy * tmp13509 + gammaBar_UU.xx * tmp13489) + ABar_LL.xx * (gammaBar_UU.xz * tmp13464 + gammaBar_UU.xy * tmp13444 + gammaBar_UU.xx * tmp13424)) + -1. * U->alpha * (ABar_LL.zz * (gammaBar_UU.yz * tmp6012 + gammaBar_UU.yy * tmp5992 + gammaBar_UU.xy * tmp5972) + ABar_LL.yz * (gammaBar_UU.yz * tmp5947 + gammaBar_UU.yy * tmp5927 + gammaBar_UU.xy * tmp5907) + ABar_LL.yz * (gammaBar_UU.yz * tmp5882 + gammaBar_UU.yy * tmp5862 + gammaBar_UU.xy * tmp5842) + ABar_LL.yy * (gammaBar_UU.yz * tmp5817 + gammaBar_UU.yy * tmp5797 + gammaBar_UU.xy * tmp5777) + ABar_LL.xz * (gammaBar_UU.yz * tmp5752 + gammaBar_UU.yy * tmp5732 + gammaBar_UU.xy * tmp5712) + ABar_LL.xz * (gammaBar_UU.yz * tmp5687 + gammaBar_UU.yy * tmp5667 + gammaBar_UU.xy * tmp5647) + ABar_LL.xy * (gammaBar_UU.yz * tmp5622 + gammaBar_UU.yy * tmp5602 + gammaBar_UU.xy * tmp5582) + ABar_LL.xy * (gammaBar_UU.yz * tmp5557 + gammaBar_UU.yy * tmp5537 + gammaBar_UU.xy * tmp5517) + ABar_LL.xx * (gammaBar_UU.yz * tmp5492 + gammaBar_UU.yy * tmp5472 + gammaBar_UU.xy * tmp5452)) + U->beta_U.z * (gammaBar_UU.zz * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][2].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][2].xz) + gammaBar_UU.yz * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][1].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][1].xz) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][0].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[2][0].xz) + gammaBar_UU.yz * (tmp2193 + tmp2198 + tmp2195) + gammaBar_UU.yy * (tmp2179 + tmp2184 + tmp2181) + gammaBar_UU.xy * (tmp2165 + tmp2170 + tmp2167) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][2].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][2].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[2][2].xx) + gammaBar_UU.xy * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][1].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][1].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[2][1].xx) + gammaBar_UU.xx * (gammaBar_UU.yz * partial2_gammaBar_LLll[2][0].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[2][0].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[2][0].xx)) + U->beta_U.y * (gammaBar_UU.zz * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][2].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][2].xz) + gammaBar_UU.yz * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][1].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][1].xz) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][0].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[1][0].xz) + gammaBar_UU.yz * (tmp2146 + tmp2151 + tmp2148) + gammaBar_UU.yy * (tmp2132 + tmp2137 + tmp2134) + gammaBar_UU.xy * (tmp2118 + tmp2123 + tmp2120) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][2].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][2].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[1][2].xx) + gammaBar_UU.xy * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][1].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][1].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[1][1].xx) + gammaBar_UU.xx * (gammaBar_UU.yz * partial2_gammaBar_LLll[1][0].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[1][0].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[1][0].xx)) + U->beta_U.x * (gammaBar_UU.zz * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][2].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][2].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][2].xz) + gammaBar_UU.yz * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][1].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][1].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][1].xz) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][0].zz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][0].yz + gammaBar_UU.xy * partial2_gammaBar_LLll[0][0].xz) + gammaBar_UU.yz * (tmp2099 + tmp2104 + tmp2101) + gammaBar_UU.yy * (tmp2085 + tmp2090 + tmp2087) + gammaBar_UU.xy * (tmp2071 + tmp2076 + tmp2073) + gammaBar_UU.xz * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][2].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][2].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[0][2].xx) + gammaBar_UU.xy * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][1].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][1].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[0][1].xx) + gammaBar_UU.xx * (gammaBar_UU.yz * partial2_gammaBar_LLll[0][0].xz + gammaBar_UU.yy * partial2_gammaBar_LLll[0][0].xy + gammaBar_UU.xy * partial2_gammaBar_LLll[0][0].xx)) + -1. * U->beta_U.z * (gammaBar_UU.zz * (gammaBar_UU.yz * tmp5223 + gammaBar_UU.yy * tmp4974 + gammaBar_UU.xy * tmp4725) + gammaBar_UU.yz * (gammaBar_UU.yz * tmp5140 + gammaBar_UU.yy * tmp4891 + gammaBar_UU.xy * tmp4642) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp5057 + gammaBar_UU.yy * tmp4808 + gammaBar_UU.xy * tmp4559) + gammaBar_UU.yz * (tmp4726 + tmp12345 + gammaBar_UU.yy * tmp4948) + gammaBar_UU.yy * (tmp4643 + tmp12262 + gammaBar_UU.yy * tmp4865) + gammaBar_UU.xy * (tmp4560 + tmp12179 + gammaBar_UU.yy * tmp4782) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp4725 + gammaBar_UU.yy * tmp4699 + gammaBar_UU.xy * tmp4673) + gammaBar_UU.xy * (gammaBar_UU.yz * tmp4642 + gammaBar_UU.yy * tmp4616 + gammaBar_UU.xy * tmp4590) + gammaBar_UU.xx * (gammaBar_UU.yz * tmp4559 + gammaBar_UU.yy * tmp4533 + gammaBar_UU.xy * tmp4507)) + -1. * U->beta_U.y * (gammaBar_UU.zz * (gammaBar_UU.yz * tmp4458 + gammaBar_UU.yy * tmp4209 + gammaBar_UU.xy * tmp3960) + gammaBar_UU.yz * (gammaBar_UU.yz * tmp4375 + gammaBar_UU.yy * tmp4126 + gammaBar_UU.xy * tmp3877) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp4292 + gammaBar_UU.yy * tmp4043 + gammaBar_UU.xy * tmp3794) + gammaBar_UU.yz * (tmp3961 + tmp11580 + gammaBar_UU.yy * tmp4183) + gammaBar_UU.yy * (tmp3878 + tmp11497 + gammaBar_UU.yy * tmp4100) + gammaBar_UU.xy * (tmp3795 + tmp11414 + gammaBar_UU.yy * tmp4017) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp3960 + gammaBar_UU.yy * tmp3934 + gammaBar_UU.xy * tmp3908) + gammaBar_UU.xy * (gammaBar_UU.yz * tmp3877 + gammaBar_UU.yy * tmp3851 + gammaBar_UU.xy * tmp3825) + gammaBar_UU.xx * (gammaBar_UU.yz * tmp3794 + gammaBar_UU.yy * tmp3768 + gammaBar_UU.xy * tmp3742)) + -1. * U->beta_U.x * (gammaBar_UU.zz * (gammaBar_UU.yz * tmp3693 + gammaBar_UU.yy * tmp3444 + gammaBar_UU.xy * tmp3195) + gammaBar_UU.yz * (gammaBar_UU.yz * tmp3610 + gammaBar_UU.yy * tmp3361 + gammaBar_UU.xy * tmp3112) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp3527 + gammaBar_UU.yy * tmp3278 + gammaBar_UU.xy * tmp3029) + gammaBar_UU.yz * (tmp3196 + tmp10815 + gammaBar_UU.yy * tmp3418) + gammaBar_UU.yy * (tmp3113 + tmp10732 + gammaBar_UU.yy * tmp3335) + gammaBar_UU.xy * (tmp3030 + tmp10649 + gammaBar_UU.yy * tmp3252) + gammaBar_UU.xz * (gammaBar_UU.yz * tmp3195 + gammaBar_UU.yy * tmp3169 + gammaBar_UU.xy * tmp3143) + gammaBar_UU.xy * (gammaBar_UU.yz * tmp3112 + gammaBar_UU.yy * tmp3086 + gammaBar_UU.xy * tmp3060) + gammaBar_UU.xx * (gammaBar_UU.yz * tmp3029 + gammaBar_UU.yy * tmp3003 + gammaBar_UU.xy * tmp2977)) + -1. * tmp2949 * tmp7432 + gammaBar_UU.yz * tmp2841 + gammaBar_UU.yy * tmp2779 + gammaBar_UU.xy * tmp2717 + -1. * gammaBar_UU.zz * (gammaBar_UU.yz * tmp2649 + gammaBar_UU.yy * tmp2628 + gammaBar_UU.xy * tmp2607) + -1. * gammaBar_UU.yz * (tmp2608 + tmp2829 + gammaBar_UU.yy * tmp2623) + -1. * gammaBar_UU.xz * (gammaBar_UU.yz * tmp2607 + gammaBar_UU.yy * tmp2602 + gammaBar_UU.xy * tmp2597) + -1. * gammaBar_UU.yz * (tmp2837 + tmp2831 + tmp2825) + -1. * gammaBar_UU.yy * (tmp2545 + tmp2769 + tmp2763) + -1. * gammaBar_UU.xy * (tmp2713 + tmp2707 + tmp2701) + -1. * gammaBar_UU.xz * (gammaBar_UU.yz * tmp2523 + gammaBar_UU.yy * tmp2502 + gammaBar_UU.xy * tmp2481) + -1. * gammaBar_UU.xy * (tmp2482 + tmp9873 + gammaBar_UU.yy * tmp2497) + -1. * gammaBar_UU.xx * (gammaBar_UU.yz * tmp2481 + gammaBar_UU.yy * tmp2476 + gammaBar_UU.xy * tmp2471) + gammaBar_UU.zz * partial2_beta_Ull[2][2].y + gammaBar_UU.yz * partial2_beta_Ull[2][1].y + gammaBar_UU.xz * partial2_beta_Ull[2][0].y + gammaBar_UU.yz * partial2_beta_Ull[1][2].y + gammaBar_UU.yy * partial2_beta_Ull[1][1].y + gammaBar_UU.xy * partial2_beta_Ull[1][0].y + gammaBar_UU.xz * partial2_beta_Ull[0][2].y + gammaBar_UU.xy * partial2_beta_Ull[0][1].y + gammaBar_UU.xx * partial2_beta_Ull[0][0].y + -2. * (partial_alpha_l.z * (tmp9828 + tmp9826 + tmp9824 + tmp9822 + tmp9820 + tmp9818 + tmp9816 + tmp9814 + tmp9815) + partial_alpha_l.y * (ABar_LL.zz * tmp9793 + 2. * ABar_LL.yz * tmp9791 + ABar_LL.yy * gammaBar_UU.yy * gammaBar_UU.yy + 2. * ABar_LL.xz * tmp2415 + 2. * ABar_LL.xy * tmp2414 + ABar_LL.xx * tmp2395) + partial_alpha_l.x * (tmp2433 + tmp2427 + tmp2421 + tmp2431 + tmp2425 + tmp2419 + tmp2429 + tmp2423 + tmp2420)) + -1. * gammaBar_UU.zz * partial_beta_Ul[2].y * tmp2273 + -1. * gammaBar_UU.yz * partial_beta_Ul[2].y * tmp2254 + -1. * gammaBar_UU.xz * partial_beta_Ul[2].y * tmp2235 + -1. * gammaBar_UU.yz * partial_beta_Ul[1].y * tmp2273 + -1. * gammaBar_UU.yy * partial_beta_Ul[1].y * tmp2254 + -1. * gammaBar_UU.xy * partial_beta_Ul[1].y * tmp2235 + -1. * gammaBar_UU.xz * partial_beta_Ul[0].y * tmp2273 + -1. * gammaBar_UU.xy * partial_beta_Ul[0].y * tmp2254 + -1. * gammaBar_UU.xx * partial_beta_Ul[0].y * tmp2235 + -1. * tmp743 * (U->beta_U.z * (gammaBar_UU.yz * tmp2206 + gammaBar_UU.yy * tmp2192 + gammaBar_UU.xy * tmp2178) + U->beta_U.y * (gammaBar_UU.yz * tmp2159 + gammaBar_UU.yy * tmp2145 + gammaBar_UU.xy * tmp2131) + U->beta_U.x * (gammaBar_UU.yz * tmp2112 + gammaBar_UU.yy * tmp2098 + gammaBar_UU.xy * tmp2084)) + tmp743 * U->beta_U.x * (gammaBar_UU.yz * tmp2059 + gammaBar_UU.yy * tmp1808 + gammaBar_UU.xy * tmp1557) + tmp743 * U->beta_U.y * (gammaBar_UU.yz * tmp1398 + gammaBar_UU.yy * tmp1147 + gammaBar_UU.xy * tmp995) + tmp743 * U->beta_U.z * (gammaBar_UU.yz * tmp737 + gammaBar_UU.yy * tmp585 + gammaBar_UU.xy * tmp334) + tmp65 * gammaBar_UU.xy * tmp77 + tmp65 * gammaBar_UU.yy * tmp73 + tmp65 * gammaBar_UU.yz * tmp69 + 2. * tmp65 * tmp7432 * tmp64;
double dt_LambdaBar_U.z = tmp7358 * U->beta_U.z * tmp7357 + U->alpha * (-2. * (gammaBar_UU.zz * tmp7262 + gammaBar_UU.yz * tmp7245 + gammaBar_UU.xz * tmp7228) + gammaBar_UU.zz * tmp7211 + gammaBar_UU.yz * tmp7197 + gammaBar_UU.xz * tmp7183) + 2. * U->alpha * (ABar_LL.zz * gammaBar_UU.zz * (gammaBar_UU.zz * tmp2273 + gammaBar_UU.yz * tmp2254 + gammaBar_UU.xz * tmp2235) + ABar_LL.yz * gammaBar_UU.zz * (gammaBar_UU.yz * tmp2273 + gammaBar_UU.yy * tmp2254 + gammaBar_UU.xy * tmp2235) + ABar_LL.yz * tmp14520 + ABar_LL.yy * tmp14463 + ABar_LL.xz * gammaBar_UU.zz * (gammaBar_UU.xz * tmp2273 + gammaBar_UU.xy * tmp2254 + gammaBar_UU.xx * tmp2235) + ABar_LL.xz * tmp7151 + ABar_LL.xy * tmp14292 + ABar_LL.xy * tmp7094 + ABar_LL.xx * tmp6923) + 2. * U->alpha * (ABar_LL.zz * (gammaBar_UU.zz * tmp21028 + gammaBar_UU.yz * tmp21008 + gammaBar_UU.xz * tmp20988) + ABar_LL.yz * (gammaBar_UU.zz * tmp20898 + gammaBar_UU.yz * tmp20878 + gammaBar_UU.xz * tmp20858) + ABar_LL.yz * (gammaBar_UU.yz * tmp21028 + gammaBar_UU.yy * tmp21008 + gammaBar_UU.xy * tmp20988) + ABar_LL.yy * (gammaBar_UU.yz * tmp20898 + gammaBar_UU.yy * tmp20878 + gammaBar_UU.xy * tmp20858) + ABar_LL.xz * (gammaBar_UU.zz * tmp20833 + gammaBar_UU.yz * tmp20813 + gammaBar_UU.xz * tmp20793) + ABar_LL.xz * (gammaBar_UU.xz * tmp21028 + gammaBar_UU.xy * tmp21008 + gammaBar_UU.xx * tmp20988) + ABar_LL.xy * (gammaBar_UU.yz * tmp20833 + gammaBar_UU.yy * tmp20813 + gammaBar_UU.xy * tmp20793) + ABar_LL.xy * (gammaBar_UU.xz * tmp20898 + gammaBar_UU.xy * tmp20878 + gammaBar_UU.xx * tmp20858) + ABar_LL.xx * (gammaBar_UU.xz * tmp20833 + gammaBar_UU.xy * tmp20813 + gammaBar_UU.xx * tmp20793)) + -1. * U->alpha * (ABar_LL.zz * (gammaBar_UU.zz * tmp6012 + gammaBar_UU.yz * tmp5992 + gammaBar_UU.xz * tmp5972) + ABar_LL.yz * (gammaBar_UU.zz * tmp5947 + gammaBar_UU.yz * tmp5927 + gammaBar_UU.xz * tmp5907) + ABar_LL.yz * (gammaBar_UU.zz * tmp5882 + gammaBar_UU.yz * tmp5862 + gammaBar_UU.xz * tmp5842) + ABar_LL.yy * (gammaBar_UU.zz * tmp5817 + gammaBar_UU.yz * tmp5797 + gammaBar_UU.xz * tmp5777) + ABar_LL.xz * (gammaBar_UU.zz * tmp5752 + gammaBar_UU.yz * tmp5732 + gammaBar_UU.xz * tmp5712) + ABar_LL.xz * (gammaBar_UU.zz * tmp5687 + gammaBar_UU.yz * tmp5667 + gammaBar_UU.xz * tmp5647) + ABar_LL.xy * (gammaBar_UU.zz * tmp5622 + gammaBar_UU.yz * tmp5602 + gammaBar_UU.xz * tmp5582) + ABar_LL.xy * (gammaBar_UU.zz * tmp5557 + gammaBar_UU.yz * tmp5537 + gammaBar_UU.xz * tmp5517) + ABar_LL.xx * (gammaBar_UU.zz * tmp5492 + gammaBar_UU.yz * tmp5472 + gammaBar_UU.xz * tmp5452)) + U->beta_U.z * (gammaBar_UU.zz * (tmp2194 + tmp2195 + tmp2197) + gammaBar_UU.yz * (tmp2180 + tmp2181 + tmp2183) + gammaBar_UU.xz * (tmp2166 + tmp2167 + tmp2169) + gammaBar_UU.yz * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][2].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][2].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][2].xy) + gammaBar_UU.yy * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][1].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][1].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][1].xy) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][0].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][0].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][0].xy) + gammaBar_UU.xz * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][2].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][2].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][2].xx) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][1].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][1].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][1].xx) + gammaBar_UU.xx * (gammaBar_UU.zz * partial2_gammaBar_LLll[2][0].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[2][0].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[2][0].xx)) + U->beta_U.y * (gammaBar_UU.zz * (tmp2147 + tmp2148 + tmp2150) + gammaBar_UU.yz * (tmp2133 + tmp2134 + tmp2136) + gammaBar_UU.xz * (tmp2119 + tmp2120 + tmp2122) + gammaBar_UU.yz * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][2].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][2].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][2].xy) + gammaBar_UU.yy * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][1].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][1].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][1].xy) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][0].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][0].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][0].xy) + gammaBar_UU.xz * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][2].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][2].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][2].xx) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][1].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][1].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][1].xx) + gammaBar_UU.xx * (gammaBar_UU.zz * partial2_gammaBar_LLll[1][0].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[1][0].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[1][0].xx)) + U->beta_U.x * (gammaBar_UU.zz * (tmp2100 + tmp2101 + tmp2103) + gammaBar_UU.yz * (tmp2086 + tmp2087 + tmp2089) + gammaBar_UU.xz * (tmp2072 + tmp2073 + tmp2075) + gammaBar_UU.yz * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][2].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][2].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][2].xy) + gammaBar_UU.yy * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][1].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][1].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][1].xy) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][0].yz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][0].yy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][0].xy) + gammaBar_UU.xz * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][2].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][2].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][2].xx) + gammaBar_UU.xy * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][1].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][1].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][1].xx) + gammaBar_UU.xx * (gammaBar_UU.zz * partial2_gammaBar_LLll[0][0].xz + gammaBar_UU.yz * partial2_gammaBar_LLll[0][0].xy + gammaBar_UU.xz * partial2_gammaBar_LLll[0][0].xx)) + -1. * U->beta_U.z * (gammaBar_UU.zz * (tmp4727 + tmp12345 + gammaBar_UU.zz * tmp5223) + gammaBar_UU.yz * (tmp4644 + tmp12262 + gammaBar_UU.zz * tmp5140) + gammaBar_UU.xz * (tmp4561 + tmp12179 + gammaBar_UU.zz * tmp5057) + gammaBar_UU.yz * (gammaBar_UU.zz * tmp4974 + gammaBar_UU.yz * tmp4948 + gammaBar_UU.xz * tmp4699) + gammaBar_UU.yy * (gammaBar_UU.zz * tmp4891 + gammaBar_UU.yz * tmp4865 + gammaBar_UU.xz * tmp4616) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp4808 + gammaBar_UU.yz * tmp4782 + gammaBar_UU.xz * tmp4533) + gammaBar_UU.xz * (gammaBar_UU.zz * tmp4725 + gammaBar_UU.yz * tmp4699 + gammaBar_UU.xz * tmp4673) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp4642 + gammaBar_UU.yz * tmp4616 + gammaBar_UU.xz * tmp4590) + gammaBar_UU.xx * (gammaBar_UU.zz * tmp4559 + gammaBar_UU.yz * tmp4533 + gammaBar_UU.xz * tmp4507)) + -1. * U->beta_U.y * (gammaBar_UU.zz * (tmp3962 + tmp11580 + gammaBar_UU.zz * tmp4458) + gammaBar_UU.yz * (tmp3879 + tmp11497 + gammaBar_UU.zz * tmp4375) + gammaBar_UU.xz * (tmp3796 + tmp11414 + gammaBar_UU.zz * tmp4292) + gammaBar_UU.yz * (gammaBar_UU.zz * tmp4209 + gammaBar_UU.yz * tmp4183 + gammaBar_UU.xz * tmp3934) + gammaBar_UU.yy * (gammaBar_UU.zz * tmp4126 + gammaBar_UU.yz * tmp4100 + gammaBar_UU.xz * tmp3851) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp4043 + gammaBar_UU.yz * tmp4017 + gammaBar_UU.xz * tmp3768) + gammaBar_UU.xz * (gammaBar_UU.zz * tmp3960 + gammaBar_UU.yz * tmp3934 + gammaBar_UU.xz * tmp3908) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp3877 + gammaBar_UU.yz * tmp3851 + gammaBar_UU.xz * tmp3825) + gammaBar_UU.xx * (gammaBar_UU.zz * tmp3794 + gammaBar_UU.yz * tmp3768 + gammaBar_UU.xz * tmp3742)) + -1. * U->beta_U.x * (gammaBar_UU.zz * (tmp3197 + tmp10815 + gammaBar_UU.zz * tmp3693) + gammaBar_UU.yz * (tmp3114 + tmp10732 + gammaBar_UU.zz * tmp3610) + gammaBar_UU.xz * (tmp3031 + tmp10649 + gammaBar_UU.zz * tmp3527) + gammaBar_UU.yz * (gammaBar_UU.zz * tmp3444 + gammaBar_UU.yz * tmp3418 + gammaBar_UU.xz * tmp3169) + gammaBar_UU.yy * (gammaBar_UU.zz * tmp3361 + gammaBar_UU.yz * tmp3335 + gammaBar_UU.xz * tmp3086) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp3278 + gammaBar_UU.yz * tmp3252 + gammaBar_UU.xz * tmp3003) + gammaBar_UU.xz * (gammaBar_UU.zz * tmp3195 + gammaBar_UU.yz * tmp3169 + gammaBar_UU.xz * tmp3143) + gammaBar_UU.xy * (gammaBar_UU.zz * tmp3112 + gammaBar_UU.yz * tmp3086 + gammaBar_UU.xz * tmp3060) + gammaBar_UU.xx * (gammaBar_UU.zz * tmp3029 + gammaBar_UU.yz * tmp3003 + gammaBar_UU.xz * tmp2977)) + -1. * tmp2949 * tmp14801 + gammaBar_UU.zz * tmp2841 + gammaBar_UU.yz * tmp2779 + gammaBar_UU.xz * tmp2717 + -1. * gammaBar_UU.zz * (tmp2609 + tmp2829 + tmp2826) + -1. * gammaBar_UU.yz * (tmp2773 + tmp2767 + tmp2764) + -1. * gammaBar_UU.xz * (tmp2711 + tmp2705 + tmp2702) + -1. * gammaBar_UU.yz * (tmp2546 + tmp2763 + gammaBar_UU.zz * tmp2586) + -1. * gammaBar_UU.yy * (gammaBar_UU.zz * tmp2565 + gammaBar_UU.yz * tmp2560 + gammaBar_UU.xz * tmp2539) + -1. * gammaBar_UU.xy * (gammaBar_UU.zz * tmp2544 + gammaBar_UU.yz * tmp2539 + gammaBar_UU.xz * tmp2534) + -1. * gammaBar_UU.xz * (tmp2483 + tmp9873 + gammaBar_UU.zz * tmp2523) + -1. * gammaBar_UU.xy * (gammaBar_UU.zz * tmp2502 + gammaBar_UU.yz * tmp2497 + gammaBar_UU.xz * tmp2476) + -1. * gammaBar_UU.xx * (gammaBar_UU.zz * tmp2481 + gammaBar_UU.yz * tmp2476 + gammaBar_UU.xz * tmp2471) + gammaBar_UU.zz * partial2_beta_Ull[2][2].z + gammaBar_UU.yz * partial2_beta_Ull[2][1].z + gammaBar_UU.xz * partial2_beta_Ull[2][0].z + gammaBar_UU.yz * partial2_beta_Ull[1][2].z + gammaBar_UU.yy * partial2_beta_Ull[1][1].z + gammaBar_UU.xy * partial2_beta_Ull[1][0].z + gammaBar_UU.xz * partial2_beta_Ull[0][2].z + gammaBar_UU.xy * partial2_beta_Ull[0][1].z + gammaBar_UU.xx * partial2_beta_Ull[0][0].z + -2. * (partial_alpha_l.z * (ABar_LL.zz * gammaBar_UU.zz * gammaBar_UU.zz + 2. * ABar_LL.yz * tmp9813 + ABar_LL.yy * tmp9793 + 2. * ABar_LL.xz * tmp2444 + 2. * ABar_LL.xy * tmp2418 + ABar_LL.xx * tmp2398) + partial_alpha_l.y * (tmp9828 + tmp9822 + tmp9816 + tmp9826 + tmp9820 + tmp9814 + tmp9824 + tmp9818 + tmp9815) + partial_alpha_l.x * (tmp2459 + tmp2453 + tmp2447 + tmp2457 + tmp2451 + tmp2445 + tmp2455 + tmp2449 + tmp2446)) + -1. * gammaBar_UU.zz * partial_beta_Ul[2].z * tmp2273 + -1. * gammaBar_UU.yz * partial_beta_Ul[2].z * tmp2254 + -1. * gammaBar_UU.xz * partial_beta_Ul[2].z * tmp2235 + -1. * gammaBar_UU.yz * partial_beta_Ul[1].z * tmp2273 + -1. * gammaBar_UU.yy * partial_beta_Ul[1].z * tmp2254 + -1. * gammaBar_UU.xy * partial_beta_Ul[1].z * tmp2235 + -1. * gammaBar_UU.xz * partial_beta_Ul[0].z * tmp2273 + -1. * gammaBar_UU.xy * partial_beta_Ul[0].z * tmp2254 + -1. * gammaBar_UU.xx * partial_beta_Ul[0].z * tmp2235 + -1. * tmp743 * (U->beta_U.z * (gammaBar_UU.zz * tmp2206 + gammaBar_UU.yz * tmp2192 + gammaBar_UU.xz * tmp2178) + U->beta_U.y * (gammaBar_UU.zz * tmp2159 + gammaBar_UU.yz * tmp2145 + gammaBar_UU.xz * tmp2131) + U->beta_U.x * (gammaBar_UU.zz * tmp2112 + gammaBar_UU.yz * tmp2098 + gammaBar_UU.xz * tmp2084)) + tmp743 * U->beta_U.x * (gammaBar_UU.zz * tmp2059 + gammaBar_UU.yz * tmp1808 + gammaBar_UU.xz * tmp1557) + tmp743 * U->beta_U.y * (gammaBar_UU.zz * tmp1398 + gammaBar_UU.yz * tmp1147 + gammaBar_UU.xz * tmp995) + tmp743 * U->beta_U.z * (gammaBar_UU.zz * tmp737 + gammaBar_UU.yz * tmp585 + gammaBar_UU.xz * tmp334) + tmp65 * gammaBar_UU.xz * tmp77 + tmp65 * gammaBar_UU.yz * tmp73 + tmp65 * gammaBar_UU.zz * tmp69 + 2. * tmp65 * tmp14801 * tmp64;

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