${{{ \eta} _I} _J} = {\overset{I\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}}$
${{{ \eta} ^I} ^J} = {\overset{I\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix} \right]}}$
${{{ \hat{\gamma}} _i} _j} = {\overset{a\downarrow b\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & {r}^{2} & 0 \\ 0 & 0 & {{{r}^{2}}} {{{\sin\left( theta\right)}^{2}}}\end{matrix} \right]}}$
${\hat{\gamma}} = {{{{r}^{4}}} {{{\sin\left( theta\right)}^{2}}}}$
${{{{ \hat{\Gamma}} _i} _j} _k} = {\overset{i\downarrow[{j\downarrow k\rightarrow}]}{\left[ \begin{matrix} \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & -{r} & 0 \\ 0 & 0 & -{{{r}} {{{\sin\left( theta\right)}^{2}}}}\end{matrix} \right]} \\ \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & r & 0 \\ r & 0 & 0 \\ 0 & 0 & -{{{{r}^{2}}} {{\sin\left( theta\right)}} {{\cos\left( theta\right)}}}\end{matrix} \right]} \\ \overset{j\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & {{r}} {{{\sin\left( theta\right)}^{2}}} \\ 0 & 0 & {{{r}^{2}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ {{r}} {{{\sin\left( theta\right)}^{2}}} & {{{r}^{2}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{{{ \hat{\Gamma}} _I} _J} _K} = {\overset{I\downarrow[{J\downarrow K\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{{{ \hat{\Gamma}} ^I} _J} _K} = {\overset{I\downarrow[{J\downarrow K\rightarrow}]}{\left[ \begin{matrix} \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{J\downarrow K\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 0\end{matrix} \right]}\end{matrix} \right]}}$
${{ \hat{\Gamma}} ^I} = {\overset{I\downarrow}{\left[ \begin{matrix} -{{\frac{1}{r}}{\left({{{gammaBar_UU.yy}} + {{gammaBar_UU.zz}}}\right)}} \\ \frac{{-{{{{gammaBar_UU.zz}}} \cdot {{\cos\left( theta\right)}}}} + {{{2}} {{{gammaBar_UU.xy}}} \cdot {{\sin\left( theta\right)}}}}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{{{2}} {{\left({{{{{gammaBar_UU.xz}}} \cdot {{\sin\left( theta\right)}}} + {{{{gammaBar_UU.yz}}} \cdot {{\cos\left( theta\right)}}}}\right)}}}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}}$
${{ \hat{\gamma}} _{,i}} = {\overset{i\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 0\end{matrix} \right]}}$
variable: $\alpha$
eqn:${{ \alpha} _{,t}} = {{{{{ \alpha} _{,i}}} {{{ \beta} ^I}} {{{{ e} ^i} _I}}} + {{{-1}} {{K}} {{f}} {{{\alpha}^{2}}}}}$
new eqn: ${{dt_alpha}} = {{{{-1}} {{f}} {{{U->alpha}^{2}}} {{U->K}}} + {{{{ \overset{i\downarrow}{\left[ \begin{matrix} {partial_alpha_l.x} \\ {partial_alpha_l.y} \\ {partial_alpha_l.z}\end{matrix} \right]}} _i}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->beta_U.x} \\ {U->beta_U.y} \\ {U->beta_U.z}\end{matrix} \right]}} ^I}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}}}}$
double tmp1 = 1. / r;
double dt_alpha = U->beta_U.z * partial_alpha_l.z * 1. / sin(theta) * tmp1 + -1. * U->K * f * U->alpha * U->alpha + U->beta_U.x * partial_alpha_l.x + U->beta_U.y * partial_alpha_l.y * tmp1;
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: ${{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_B_U.x} \\ {dt_B_U.y} \\ {dt_B_U.z}\end{matrix} \right]}} ^I} = {{{{3}} \cdot {{\frac{1}{4}}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {dt_LambdaBar_U.x} \\ {dt_LambdaBar_U.y} \\ {dt_LambdaBar_U.z}\end{matrix} \right]}} ^I}}} + {{{-1}} {{\eta}} \cdot {{{ \overset{i\downarrow}{\left[ \begin{matrix} {U->B_U.x} \\ {U->B_U.y} \\ {U->B_U.z}\end{matrix} \right]}} ^I}}}}$
double tmp1 = 1. / 4.;
double dt_B_U.x = -1. * U->B_U.x * \eta + 3. * dt_LambdaBar_U.x * tmp1;
double dt_B_U.y = -1. * U->B_U.y * \eta + 3. * dt_LambdaBar_U.y * tmp1;
double dt_B_U.z = -1. * U->B_U.z * \eta + 3. * dt_LambdaBar_U.z * tmp1;
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}} = {{{{-1}} \cdot {{\frac{1}{6}}} {{W}} {{{ \overset{i\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{3}}} {{W}} {{U->alpha}} \cdot {{U->K}}} + {{{-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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _I} _i}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}}}}$
double tmp1 = sin(theta);
double tmp2 = 1. / r;
double tmp3 = 1. / tmp1;
double tmp4 = tmp2 * tmp3;
double tmp5 = 1. / 3.;
double dt_W = -1. * W * r * (2. * U->beta_U.x * tmp1 + U->beta_U.y * cos(theta)) * 1. / det_gammaBar * r * r * tmp1 * tmp5 + ((U->beta_U.x * partial_W_l.x * r + U->beta_U.y * partial_W_l.y) * tmp1 + U->beta_U.z * partial_W_l.z) * tmp4 + U->K * U->alpha * W * tmp5 + -1. * W * (partial_beta_Ul[2].z + partial_beta_Ul[0].x * r * tmp1 + partial_beta_Ul[1].y * tmp1) * tmp4 * tmp5;
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}} = {{{{{U->K}^{2}}} {{U->alpha}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}}} + {{{{{ \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}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} -{{\frac{1}{r}}{\left({{{gammaBar_UU.yy}} + {{gammaBar_UU.zz}}}\right)}} \\ \frac{{-{{{{gammaBar_UU.zz}}} \cdot {{\cos\left( theta\right)}}}} + {{{2}} {{{gammaBar_UU.xy}}} \cdot {{\sin\left( theta\right)}}}}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{{{2}} {{\left({{{{{gammaBar_UU.xz}}} \cdot {{\sin\left( theta\right)}}} + {{{{gammaBar_UU.yz}}} \cdot {{\cos\left( theta\right)}}}}\right)}}}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^A}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{W}^{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]}} ^D} ^C}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{4}} {{S}} {{U->alpha}} \cdot {{{M_PI}}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{W}^{2}}}} + {{{-12}} {{U->alpha}} \cdot {{U->rho}} \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _d}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^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} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}}}}$
double tmp1 = sin(theta);
double tmp2 = W * W;
double tmp3 = tmp1 * tmp1;
double tmp4 = tmp2 * tmp3;
double tmp5 = r * r;
double tmp6 = tmp1 * tmp2;
double tmp7 = 1. / tmp5;
double tmp8 = 1. / tmp3;
double tmp9 = tmp7 * tmp8;
double tmp10 = partial_alpha_l.y * tmp1;
double tmp11 = r * tmp1;
double tmp12 = partial_alpha_l.x * tmp11;
double tmp13 = 1. / r;
double tmp14 = 1. / tmp1;
double tmp15 = tmp13 * tmp14;
double tmp16 = cos(theta);
double tmp17 = gammaBar_UU.xx * tmp1;
double tmp18 = gammaBar_UU.xy * tmp16;
double tmp19 = tmp17 + tmp18;
double tmp20 = gammaBar_UU.xy * tmp1;
double tmp21 = gammaBar_UU.yy * tmp16;
double tmp22 = tmp20 + tmp21;
double tmp23 = gammaBar_UU.xz * tmp1;
double tmp24 = gammaBar_UU.yz * tmp16;
double tmp25 = tmp23 + tmp24;
double tmp26 = ABar_LL.yz * tmp22;
double tmp27 = ABar_LL.zz * tmp25;
double tmp28 = ABar_LL.xz * tmp19;
double tmp29 = tmp26 + tmp27;
double tmp30 = tmp28 + tmp29;
double tmp31 = ABar_LL.yy * gammaBar_UU.xy;
double tmp32 = ABar_LL.yz * gammaBar_UU.xz;
double tmp33 = ABar_LL.xy * gammaBar_UU.xx;
double tmp34 = tmp31 + tmp32;
double tmp35 = tmp33 + tmp34;
double tmp36 = gammaBar_UU.xz * tmp19;
double tmp37 = gammaBar_UU.xx * tmp20;
double tmp38 = gammaBar_LL.xz * tmp36;
double tmp39 = gammaBar_LL.xy * tmp37;
double tmp40 = tmp38 + tmp39;
double tmp41 = gammaBar_UU.xy * gammaBar_UU.xy;
double tmp42 = tmp1 * tmp41;
double tmp43 = gammaBar_UU.xz * tmp22;
double tmp44 = gammaBar_LL.xy * tmp42;
double tmp45 = gammaBar_LL.xz * tmp43;
double tmp46 = tmp44 + tmp45;
double tmp47 = gammaBar_UU.yz * tmp19;
double tmp48 = gammaBar_UU.yy * tmp1;
double tmp49 = gammaBar_UU.xx * tmp48;
double tmp50 = gammaBar_LL.xz * tmp47;
double tmp51 = gammaBar_LL.xy * tmp49;
double tmp52 = tmp50 + tmp51;
double tmp53 = gammaBar_UU.zz * tmp19;
double tmp54 = gammaBar_UU.yz * tmp1;
double tmp55 = gammaBar_UU.xx * tmp54;
double tmp56 = gammaBar_LL.xz * tmp53;
double tmp57 = gammaBar_LL.xy * tmp55;
double tmp58 = tmp56 + tmp57;
double tmp59 = gammaBar_UU.yz * tmp22;
double tmp60 = gammaBar_UU.xy * tmp48;
double tmp61 = gammaBar_LL.xz * tmp59;
double tmp62 = gammaBar_LL.xy * tmp60;
double tmp63 = tmp61 + tmp62;
double tmp64 = gammaBar_UU.yz * tmp25;
double tmp65 = gammaBar_UU.xz * tmp48;
double tmp66 = gammaBar_LL.xz * tmp64;
double tmp67 = gammaBar_LL.xy * tmp65;
double tmp68 = tmp66 + tmp67;
double tmp69 = gammaBar_UU.zz * tmp22;
double tmp70 = gammaBar_UU.xy * tmp54;
double tmp71 = gammaBar_LL.xz * tmp69;
double tmp72 = gammaBar_LL.xy * tmp70;
double tmp73 = tmp71 + tmp72;
double tmp74 = gammaBar_UU.zz * tmp25;
double tmp75 = gammaBar_UU.xz * tmp54;
double tmp76 = gammaBar_LL.xz * tmp74;
double tmp77 = gammaBar_LL.xy * tmp75;
double tmp78 = tmp76 + tmp77;
double tmp79 = gammaBar_LL.xz * tmp25;
double tmp80 = gammaBar_LL.xy * tmp20;
double tmp81 = tmp79 + tmp80;
double tmp82 = gammaBar_UU.xz * tmp81;
double tmp83 = ABar_LL.zz * tmp78;
double tmp84 = ABar_LL.xz * tmp82;
double tmp85 = ABar_LL.yz * tmp73;
double tmp86 = tmp83 + tmp84;
double tmp87 = ABar_LL.yz * tmp68;
double tmp88 = tmp85 + tmp86;
double tmp89 = ABar_LL.yy * tmp63;
double tmp90 = tmp87 + tmp88;
double tmp91 = ABar_LL.xz * tmp58;
double tmp92 = tmp89 + tmp90;
double tmp93 = ABar_LL.xy * tmp52;
double tmp94 = tmp91 + tmp92;
double tmp95 = ABar_LL.xy * tmp46;
double tmp96 = tmp93 + tmp94;
double tmp97 = ABar_LL.xx * tmp40;
double tmp98 = tmp95 + tmp96;
double tmp99 = tmp97 + tmp98;
double tmp100 = gammaBar_LL.yz * tmp36;
double tmp101 = gammaBar_LL.yy * tmp37;
double tmp102 = tmp100 + tmp101;
double tmp103 = gammaBar_LL.yy * tmp42;
double tmp104 = gammaBar_LL.yz * tmp43;
double tmp105 = tmp103 + tmp104;
double tmp106 = gammaBar_LL.yz * tmp47;
double tmp107 = gammaBar_LL.yy * tmp49;
double tmp108 = tmp106 + tmp107;
double tmp109 = gammaBar_LL.yz * tmp53;
double tmp110 = gammaBar_LL.yy * tmp55;
double tmp111 = tmp109 + tmp110;
double tmp112 = gammaBar_LL.yz * tmp59;
double tmp113 = gammaBar_LL.yy * tmp60;
double tmp114 = tmp112 + tmp113;
double tmp115 = gammaBar_LL.yz * tmp64;
double tmp116 = gammaBar_LL.yy * tmp65;
double tmp117 = tmp115 + tmp116;
double tmp118 = gammaBar_LL.yz * tmp69;
double tmp119 = gammaBar_LL.yy * tmp70;
double tmp120 = tmp118 + tmp119;
double tmp121 = gammaBar_LL.yz * tmp74;
double tmp122 = gammaBar_LL.yy * tmp75;
double tmp123 = tmp121 + tmp122;
double tmp124 = gammaBar_LL.yz * tmp25;
double tmp125 = gammaBar_LL.yy * tmp20;
double tmp126 = tmp124 + tmp125;
double tmp127 = gammaBar_UU.xz * tmp126;
double tmp128 = ABar_LL.zz * tmp123;
double tmp129 = ABar_LL.xz * tmp127;
double tmp130 = ABar_LL.yz * tmp120;
double tmp131 = tmp128 + tmp129;
double tmp132 = ABar_LL.yz * tmp117;
double tmp133 = tmp130 + tmp131;
double tmp134 = ABar_LL.yy * tmp114;
double tmp135 = tmp132 + tmp133;
double tmp136 = ABar_LL.xz * tmp111;
double tmp137 = tmp134 + tmp135;
double tmp138 = ABar_LL.xy * tmp108;
double tmp139 = tmp136 + tmp137;
double tmp140 = ABar_LL.xy * tmp105;
double tmp141 = tmp138 + tmp139;
double tmp142 = ABar_LL.xx * tmp102;
double tmp143 = tmp140 + tmp141;
double tmp144 = tmp142 + tmp143;
double tmp145 = gammaBar_LL.zz * tmp36;
double tmp146 = gammaBar_LL.yz * tmp37;
double tmp147 = tmp145 + tmp146;
double tmp148 = gammaBar_LL.yz * tmp42;
double tmp149 = gammaBar_LL.zz * tmp43;
double tmp150 = tmp148 + tmp149;
double tmp151 = gammaBar_LL.zz * tmp47;
double tmp152 = gammaBar_LL.yz * tmp49;
double tmp153 = tmp151 + tmp152;
double tmp154 = gammaBar_LL.zz * tmp53;
double tmp155 = gammaBar_LL.yz * tmp55;
double tmp156 = tmp154 + tmp155;
double tmp157 = gammaBar_LL.zz * tmp59;
double tmp158 = gammaBar_LL.yz * tmp60;
double tmp159 = tmp157 + tmp158;
double tmp160 = gammaBar_LL.zz * tmp64;
double tmp161 = gammaBar_LL.yz * tmp65;
double tmp162 = tmp160 + tmp161;
double tmp163 = gammaBar_LL.zz * tmp69;
double tmp164 = gammaBar_LL.yz * tmp70;
double tmp165 = tmp163 + tmp164;
double tmp166 = gammaBar_LL.zz * tmp74;
double tmp167 = gammaBar_LL.yz * tmp75;
double tmp168 = tmp166 + tmp167;
double tmp169 = gammaBar_LL.zz * tmp25;
double tmp170 = gammaBar_LL.yz * tmp20;
double tmp171 = tmp169 + tmp170;
double tmp172 = gammaBar_UU.xz * tmp171;
double tmp173 = ABar_LL.zz * tmp168;
double tmp174 = ABar_LL.xz * tmp172;
double tmp175 = ABar_LL.yz * tmp165;
double tmp176 = tmp173 + tmp174;
double tmp177 = ABar_LL.yz * tmp162;
double tmp178 = tmp175 + tmp176;
double tmp179 = ABar_LL.yy * tmp159;
double tmp180 = tmp177 + tmp178;
double tmp181 = ABar_LL.xz * tmp156;
double tmp182 = tmp179 + tmp180;
double tmp183 = ABar_LL.xy * tmp153;
double tmp184 = tmp181 + tmp182;
double tmp185 = ABar_LL.xy * tmp150;
double tmp186 = tmp183 + tmp184;
double tmp187 = ABar_LL.xx * tmp147;
double tmp188 = tmp185 + tmp186;
double tmp189 = tmp187 + tmp188;
double tmp190 = partial_gammaBar_LLl[1].xx * tmp1;
double tmp191 = partial_gammaBar_LLl[0].xx * tmp11;
double tmp192 = gammaBar_UU.xy * tmp190;
double tmp193 = gammaBar_UU.xx * tmp191;
double tmp194 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xx;
double tmp195 = tmp192 + tmp193;
double tmp196 = tmp194 + tmp195;
double tmp197 = partial_gammaBar_LLl[1].xy * tmp1;
double tmp198 = partial_gammaBar_LLl[0].xy * tmp11;
double tmp199 = gammaBar_UU.xy * tmp197;
double tmp200 = gammaBar_UU.xx * tmp198;
double tmp201 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xy;
double tmp202 = tmp199 + tmp200;
double tmp203 = tmp201 + tmp202;
double tmp204 = partial_gammaBar_LLl[1].xz * tmp1;
double tmp205 = partial_gammaBar_LLl[0].xz * tmp11;
double tmp206 = gammaBar_UU.xy * tmp204;
double tmp207 = gammaBar_UU.xx * tmp205;
double tmp208 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xz;
double tmp209 = tmp206 + tmp207;
double tmp210 = tmp208 + tmp209;
double tmp211 = gammaBar_UU.xy * tmp203;
double tmp212 = gammaBar_UU.xz * tmp210;
double tmp213 = gammaBar_UU.yy * tmp190;
double tmp214 = gammaBar_UU.xy * tmp191;
double tmp215 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xx;
double tmp216 = tmp213 + tmp214;
double tmp217 = tmp215 + tmp216;
double tmp218 = gammaBar_UU.yy * tmp197;
double tmp219 = gammaBar_UU.xy * tmp198;
double tmp220 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xy;
double tmp221 = tmp218 + tmp219;
double tmp222 = tmp220 + tmp221;
double tmp223 = gammaBar_UU.yy * tmp204;
double tmp224 = gammaBar_UU.xy * tmp205;
double tmp225 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xz;
double tmp226 = tmp223 + tmp224;
double tmp227 = tmp225 + tmp226;
double tmp228 = gammaBar_UU.xy * tmp222;
double tmp229 = gammaBar_UU.xz * tmp227;
double tmp230 = gammaBar_UU.yz * tmp190;
double tmp231 = gammaBar_UU.xz * tmp191;
double tmp232 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xx;
double tmp233 = tmp230 + tmp231;
double tmp234 = tmp232 + tmp233;
double tmp235 = gammaBar_UU.yz * tmp197;
double tmp236 = gammaBar_UU.xz * tmp198;
double tmp237 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xy;
double tmp238 = tmp235 + tmp236;
double tmp239 = tmp237 + tmp238;
double tmp240 = gammaBar_UU.yz * tmp204;
double tmp241 = gammaBar_UU.xz * tmp205;
double tmp242 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xz;
double tmp243 = tmp240 + tmp241;
double tmp244 = tmp242 + tmp243;
double tmp245 = gammaBar_UU.xy * tmp239;
double tmp246 = gammaBar_UU.xz * tmp244;
double tmp247 = partial_gammaBar_LLl[1].yy * tmp1;
double tmp248 = partial_gammaBar_LLl[0].yy * tmp11;
double tmp249 = gammaBar_UU.xy * tmp247;
double tmp250 = gammaBar_UU.xx * tmp248;
double tmp251 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yy;
double tmp252 = tmp249 + tmp250;
double tmp253 = tmp251 + tmp252;
double tmp254 = partial_gammaBar_LLl[1].yz * tmp1;
double tmp255 = partial_gammaBar_LLl[0].yz * tmp11;
double tmp256 = gammaBar_UU.xy * tmp254;
double tmp257 = gammaBar_UU.xx * tmp255;
double tmp258 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yz;
double tmp259 = tmp256 + tmp257;
double tmp260 = tmp258 + tmp259;
double tmp261 = gammaBar_UU.yy * tmp247;
double tmp262 = gammaBar_UU.xy * tmp248;
double tmp263 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yy;
double tmp264 = tmp261 + tmp262;
double tmp265 = tmp263 + tmp264;
double tmp266 = gammaBar_UU.yy * tmp254;
double tmp267 = gammaBar_UU.xy * tmp255;
double tmp268 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yz;
double tmp269 = tmp266 + tmp267;
double tmp270 = tmp268 + tmp269;
double tmp271 = gammaBar_UU.yz * tmp260;
double tmp272 = gammaBar_UU.yz * tmp247;
double tmp273 = gammaBar_UU.xz * tmp248;
double tmp274 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yy;
double tmp275 = tmp272 + tmp273;
double tmp276 = tmp274 + tmp275;
double tmp277 = gammaBar_UU.yz * tmp254;
double tmp278 = gammaBar_UU.xz * tmp255;
double tmp279 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yz;
double tmp280 = tmp277 + tmp278;
double tmp281 = tmp279 + tmp280;
double tmp282 = gammaBar_UU.yz * tmp270;
double tmp283 = gammaBar_UU.yz * tmp281;
double tmp284 = partial_gammaBar_LLl[1].zz * tmp1;
double tmp285 = partial_gammaBar_LLl[0].zz * tmp11;
double tmp286 = gammaBar_UU.xy * tmp284;
double tmp287 = gammaBar_UU.xx * tmp285;
double tmp288 = gammaBar_UU.xz * partial_gammaBar_LLl[2].zz;
double tmp289 = tmp286 + tmp287;
double tmp290 = tmp288 + tmp289;
double tmp291 = gammaBar_UU.yy * tmp284;
double tmp292 = gammaBar_UU.xy * tmp285;
double tmp293 = gammaBar_UU.yz * partial_gammaBar_LLl[2].zz;
double tmp294 = tmp291 + tmp292;
double tmp295 = tmp293 + tmp294;
double tmp296 = gammaBar_UU.yz * tmp284;
double tmp297 = gammaBar_UU.xz * tmp285;
double tmp298 = gammaBar_UU.zz * partial_gammaBar_LLl[2].zz;
double tmp299 = tmp296 + tmp297;
double tmp300 = tmp298 + tmp299;
double tmp301 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xy;
double tmp302 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xx;
double tmp303 = tmp208 + tmp301;
double tmp304 = tmp302 + tmp303;
double tmp305 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yy;
double tmp306 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xy;
double tmp307 = tmp258 + tmp305;
double tmp308 = tmp306 + tmp307;
double tmp309 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yz;
double tmp310 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xz;
double tmp311 = tmp288 + tmp309;
double tmp312 = tmp310 + tmp311;
double tmp313 = gammaBar_UU.xz * tmp312;
double tmp314 = gammaBar_UU.yy * partial_gammaBar_LLl[2].xy;
double tmp315 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xx;
double tmp316 = tmp225 + tmp314;
double tmp317 = tmp315 + tmp316;
double tmp318 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yy;
double tmp319 = tmp268 + tmp318;
double tmp320 = tmp301 + tmp319;
double tmp321 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yz;
double tmp322 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xz;
double tmp323 = tmp293 + tmp321;
double tmp324 = tmp322 + tmp323;
double tmp325 = gammaBar_UU.xz * tmp324;
double tmp326 = gammaBar_UU.yz * tmp312;
double tmp327 = tmp220 + tmp242;
double tmp328 = tmp194 + tmp327;
double tmp329 = tmp263 + tmp279;
double tmp330 = tmp201 + tmp329;
double tmp331 = tmp268 + tmp298;
double tmp332 = tmp208 + tmp331;
double tmp333 = gammaBar_UU.xz * tmp332;
double tmp334 = gammaBar_UU.yz * tmp308;
double tmp335 = gammaBar_UU.zz * tmp312;
double tmp336 = gammaBar_UU.xz * tmp304;
double tmp337 = gammaBar_UU.yz * tmp324;
double tmp338 = gammaBar_UU.yz * tmp332;
double tmp339 = gammaBar_UU.yz * tmp320;
double tmp340 = gammaBar_UU.zz * tmp324;
double tmp341 = gammaBar_UU.xz * tmp317;
double tmp342 = gammaBar_UU.yz * tmp330;
double tmp343 = gammaBar_UU.zz * tmp332;
double tmp344 = gammaBar_UU.xz * tmp328;
double tmp345 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xy;
double tmp346 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xz;
double tmp347 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xx;
double tmp348 = tmp345 + tmp346;
double tmp349 = tmp347 + tmp348;
double tmp350 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yy;
double tmp351 = gammaBar_UU.xz * partial_gammaBar_LLl[1].yz;
double tmp352 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xy;
double tmp353 = tmp350 + tmp351;
double tmp354 = tmp352 + tmp353;
double tmp355 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yz;
double tmp356 = gammaBar_UU.xz * partial_gammaBar_LLl[1].zz;
double tmp357 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xz;
double tmp358 = tmp355 + tmp356;
double tmp359 = tmp357 + tmp358;
double tmp360 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xy;
double tmp361 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xz;
double tmp362 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xx;
double tmp363 = tmp360 + tmp361;
double tmp364 = tmp362 + tmp363;
double tmp365 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yy;
double tmp366 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yz;
double tmp367 = tmp365 + tmp366;
double tmp368 = tmp345 + tmp367;
double tmp369 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yz;
double tmp370 = gammaBar_UU.yz * partial_gammaBar_LLl[1].zz;
double tmp371 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xz;
double tmp372 = tmp369 + tmp370;
double tmp373 = tmp371 + tmp372;
double tmp374 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xy;
double tmp375 = gammaBar_UU.zz * partial_gammaBar_LLl[1].xz;
double tmp376 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xx;
double tmp377 = tmp374 + tmp375;
double tmp378 = tmp376 + tmp377;
double tmp379 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yy;
double tmp380 = gammaBar_UU.zz * partial_gammaBar_LLl[1].yz;
double tmp381 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xy;
double tmp382 = tmp379 + tmp380;
double tmp383 = tmp381 + tmp382;
double tmp384 = gammaBar_UU.zz * partial_gammaBar_LLl[1].zz;
double tmp385 = tmp366 + tmp384;
double tmp386 = tmp346 + tmp385;
double tmp387 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xy;
double tmp388 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xz;
double tmp389 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xx;
double tmp390 = tmp387 + tmp388;
double tmp391 = tmp389 + tmp390;
double tmp392 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yy;
double tmp393 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yz;
double tmp394 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xy;
double tmp395 = tmp392 + tmp393;
double tmp396 = tmp394 + tmp395;
double tmp397 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yz;
double tmp398 = gammaBar_UU.xz * partial_gammaBar_LLl[0].zz;
double tmp399 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xz;
double tmp400 = tmp397 + tmp398;
double tmp401 = tmp399 + tmp400;
double tmp402 = gammaBar_UU.yy * partial_gammaBar_LLl[0].xy;
double tmp403 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xz;
double tmp404 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xx;
double tmp405 = tmp402 + tmp403;
double tmp406 = tmp404 + tmp405;
double tmp407 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yy;
double tmp408 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yz;
double tmp409 = tmp407 + tmp408;
double tmp410 = tmp387 + tmp409;
double tmp411 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yz;
double tmp412 = gammaBar_UU.yz * partial_gammaBar_LLl[0].zz;
double tmp413 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xz;
double tmp414 = tmp411 + tmp412;
double tmp415 = tmp413 + tmp414;
double tmp416 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xy;
double tmp417 = gammaBar_UU.zz * partial_gammaBar_LLl[0].xz;
double tmp418 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xx;
double tmp419 = tmp416 + tmp417;
double tmp420 = tmp418 + tmp419;
double tmp421 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yy;
double tmp422 = gammaBar_UU.zz * partial_gammaBar_LLl[0].yz;
double tmp423 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xy;
double tmp424 = tmp421 + tmp422;
double tmp425 = tmp423 + tmp424;
double tmp426 = gammaBar_UU.zz * partial_gammaBar_LLl[0].zz;
double tmp427 = tmp408 + tmp426;
double tmp428 = tmp388 + tmp427;
double tmp429 = tmp1 * tmp349;
double tmp430 = tmp1 * tmp391;
double tmp431 = r * tmp430;
double tmp432 = tmp1 * tmp364;
double tmp433 = tmp1 * tmp406;
double tmp434 = r * tmp433;
double tmp435 = tmp1 * tmp378;
double tmp436 = tmp1 * tmp420;
double tmp437 = r * tmp436;
double tmp438 = tmp1 * tmp354;
double tmp439 = tmp1 * tmp396;
double tmp440 = r * tmp439;
double tmp441 = tmp1 * tmp368;
double tmp442 = tmp1 * tmp410;
double tmp443 = r * tmp442;
double tmp444 = tmp1 * tmp383;
double tmp445 = tmp1 * tmp425;
double tmp446 = r * tmp445;
double tmp447 = tmp1 * tmp359;
double tmp448 = tmp1 * tmp401;
double tmp449 = r * tmp448;
double tmp450 = tmp1 * tmp373;
double tmp451 = tmp1 * tmp415;
double tmp452 = r * tmp451;
double tmp453 = tmp1 * tmp386;
double tmp454 = tmp1 * tmp428;
double tmp455 = r * tmp454;
double dt_K = -1. * (gammaBar_UU.yy * partial2_alpha_ll.yy * tmp4 + gammaBar_UU.zz * partial2_alpha_ll.zz * tmp2 + gammaBar_UU.xx * partial2_alpha_ll.xx * tmp2 * tmp3 * tmp5 + 2. * gammaBar_UU.xy * partial2_alpha_ll.xy * r * tmp4 + 2. * gammaBar_UU.xz * partial2_alpha_ll.xz * r * tmp6 + 2. * gammaBar_UU.yz * partial2_alpha_ll.yz * tmp6) * tmp9 + W * (partial_W_l.z * (gammaBar_UU.zz * partial_alpha_l.z + gammaBar_UU.xz * tmp12 + gammaBar_UU.yz * tmp10) + partial_W_l.x * r * (gammaBar_UU.xz * partial_alpha_l.z + gammaBar_UU.xx * tmp12 + gammaBar_UU.xy * tmp10) * tmp1 + partial_W_l.y * (gammaBar_UU.yz * partial_alpha_l.z + gammaBar_UU.xy * tmp12 + gammaBar_UU.yy * tmp10) * tmp1) * tmp9 + (-1. * partial_alpha_l.x * r * (gammaBar_UU.yy + gammaBar_UU.zz) * tmp1 + partial_alpha_l.y * (2. * tmp20 + -1. * gammaBar_UU.zz * tmp16)) * tmp2 * tmp7 * tmp14 + 2. * partial_alpha_l.z * tmp2 * tmp9 * tmp25 + (U->LambdaBar_U.z * partial_alpha_l.z + U->LambdaBar_U.x * tmp12 + U->LambdaBar_U.y * tmp10) * tmp2 * tmp15 + -1. * (C_U.z * partial_alpha_l.z + C_U.x * tmp12 + C_U.y * tmp10) * tmp2 * tmp15 + -1. * (U->beta_U.y * tmp1 * tmp35 + U->beta_U.z * tmp30) * tmp15 + -1. * (U->beta_U.x * tmp99 + U->beta_U.z * tmp189 + U->beta_U.y * tmp144) * tmp15 + -1. * (U->beta_U.x * (ABar_LL.xx * (gammaBar_UU.xx * tmp196 + tmp211 + tmp212) + ABar_LL.xy * (gammaBar_UU.xx * tmp217 + tmp228 + tmp229) + ABar_LL.xy * (gammaBar_UU.xy * tmp196 + gammaBar_UU.yz * tmp210 + gammaBar_UU.yy * tmp203) + ABar_LL.xz * (gammaBar_UU.xx * tmp234 + tmp245 + tmp246) + ABar_LL.xz * (gammaBar_UU.xz * tmp196 + gammaBar_UU.zz * tmp210 + gammaBar_UU.yz * tmp203) + ABar_LL.yy * (gammaBar_UU.xy * tmp217 + gammaBar_UU.yz * tmp227 + gammaBar_UU.yy * tmp222) + ABar_LL.yz * (gammaBar_UU.xy * tmp234 + gammaBar_UU.yz * tmp244 + gammaBar_UU.yy * tmp239) + ABar_LL.zz * (gammaBar_UU.xz * tmp234 + gammaBar_UU.zz * tmp244 + gammaBar_UU.yz * tmp239) + ABar_LL.yz * (gammaBar_UU.xz * tmp217 + gammaBar_UU.zz * tmp227 + gammaBar_UU.yz * tmp222)) + U->beta_U.z * (ABar_LL.xx * (gammaBar_UU.xx * tmp210 + gammaBar_UU.xz * tmp290 + gammaBar_UU.xy * tmp260) + ABar_LL.xy * (gammaBar_UU.xx * tmp227 + gammaBar_UU.xz * tmp295 + gammaBar_UU.xy * tmp270) + ABar_LL.xy * (gammaBar_UU.xy * tmp210 + gammaBar_UU.yz * tmp290 + gammaBar_UU.yy * tmp260) + ABar_LL.xz * (gammaBar_UU.xx * tmp244 + gammaBar_UU.xz * tmp300 + gammaBar_UU.xy * tmp281) + ABar_LL.xz * (gammaBar_UU.zz * tmp290 + tmp212 + tmp271) + ABar_LL.yy * (gammaBar_UU.xy * tmp227 + gammaBar_UU.yz * tmp295 + gammaBar_UU.yy * tmp270) + ABar_LL.yz * (gammaBar_UU.xy * tmp244 + gammaBar_UU.yz * tmp300 + gammaBar_UU.yy * tmp281) + ABar_LL.zz * (gammaBar_UU.zz * tmp300 + tmp246 + tmp283) + ABar_LL.yz * (gammaBar_UU.zz * tmp295 + tmp229 + tmp282)) + U->beta_U.y * (ABar_LL.xx * (gammaBar_UU.xx * tmp203 + gammaBar_UU.xz * tmp260 + gammaBar_UU.xy * tmp253) + ABar_LL.xy * (gammaBar_UU.xx * tmp222 + gammaBar_UU.xz * tmp270 + gammaBar_UU.xy * tmp265) + ABar_LL.xy * (gammaBar_UU.yy * tmp253 + tmp211 + tmp271) + ABar_LL.xz * (gammaBar_UU.xx * tmp239 + gammaBar_UU.xz * tmp281 + gammaBar_UU.xy * tmp276) + ABar_LL.xz * (gammaBar_UU.xz * tmp203 + gammaBar_UU.zz * tmp260 + gammaBar_UU.yz * tmp253) + ABar_LL.yy * (gammaBar_UU.yy * tmp265 + tmp228 + tmp282) + ABar_LL.yz * (gammaBar_UU.yy * tmp276 + tmp245 + tmp283) + ABar_LL.zz * (gammaBar_UU.xz * tmp239 + gammaBar_UU.zz * tmp281 + gammaBar_UU.yz * tmp276) + ABar_LL.yz * (gammaBar_UU.xz * tmp222 + gammaBar_UU.zz * tmp270 + gammaBar_UU.yz * tmp265))) * tmp15 + -1. * (U->beta_U.z * (ABar_LL.xx * (gammaBar_UU.xx * tmp304 + gammaBar_UU.xy * tmp308 + tmp313) + ABar_LL.xy * (gammaBar_UU.xx * tmp317 + gammaBar_UU.xy * tmp320 + tmp325) + ABar_LL.xy * (gammaBar_UU.xy * tmp304 + gammaBar_UU.yy * tmp308 + tmp326) + ABar_LL.xz * (gammaBar_UU.xx * tmp328 + gammaBar_UU.xy * tmp330 + tmp333) + ABar_LL.xz * (tmp334 + tmp335 + tmp336) + ABar_LL.yy * (gammaBar_UU.xy * tmp317 + gammaBar_UU.yy * tmp320 + tmp337) + ABar_LL.yz * (gammaBar_UU.xy * tmp328 + gammaBar_UU.yy * tmp330 + tmp338) + ABar_LL.zz * (tmp342 + tmp343 + tmp344) + ABar_LL.yz * (tmp339 + tmp340 + tmp341)) + U->beta_U.x * r * (ABar_LL.xx * (gammaBar_UU.xx * tmp391 + gammaBar_UU.xz * tmp401 + gammaBar_UU.xy * tmp396) + ABar_LL.xy * (gammaBar_UU.xx * tmp406 + gammaBar_UU.xz * tmp415 + gammaBar_UU.xy * tmp410) + ABar_LL.xy * (gammaBar_UU.xy * tmp391 + gammaBar_UU.yz * tmp401 + gammaBar_UU.yy * tmp396) + ABar_LL.xz * (gammaBar_UU.xx * tmp420 + gammaBar_UU.xz * tmp428 + gammaBar_UU.xy * tmp425) + ABar_LL.xz * (gammaBar_UU.xz * tmp391 + gammaBar_UU.zz * tmp401 + gammaBar_UU.yz * tmp396) + ABar_LL.yy * (gammaBar_UU.xy * tmp406 + gammaBar_UU.yz * tmp415 + gammaBar_UU.yy * tmp410) + ABar_LL.yz * (gammaBar_UU.xy * tmp420 + gammaBar_UU.yz * tmp428 + gammaBar_UU.yy * tmp425) + ABar_LL.zz * (gammaBar_UU.xz * tmp420 + gammaBar_UU.zz * tmp428 + gammaBar_UU.yz * tmp425) + ABar_LL.yz * (gammaBar_UU.xz * tmp406 + gammaBar_UU.zz * tmp415 + gammaBar_UU.yz * tmp410)) * tmp1 + U->beta_U.y * (ABar_LL.xx * (gammaBar_UU.xx * tmp349 + gammaBar_UU.xz * tmp359 + gammaBar_UU.xy * tmp354) + ABar_LL.xy * (gammaBar_UU.xx * tmp364 + gammaBar_UU.xz * tmp373 + gammaBar_UU.xy * tmp368) + ABar_LL.xy * (gammaBar_UU.xy * tmp349 + gammaBar_UU.yz * tmp359 + gammaBar_UU.yy * tmp354) + ABar_LL.xz * (gammaBar_UU.xx * tmp378 + gammaBar_UU.xz * tmp386 + gammaBar_UU.xy * tmp383) + ABar_LL.xz * (gammaBar_UU.xz * tmp349 + gammaBar_UU.zz * tmp359 + gammaBar_UU.yz * tmp354) + ABar_LL.yy * (gammaBar_UU.xy * tmp364 + gammaBar_UU.yz * tmp373 + gammaBar_UU.yy * tmp368) + ABar_LL.yz * (gammaBar_UU.xy * tmp378 + gammaBar_UU.yz * tmp386 + gammaBar_UU.yy * tmp383) + ABar_LL.zz * (gammaBar_UU.xz * tmp378 + gammaBar_UU.zz * tmp386 + gammaBar_UU.yz * tmp383) + ABar_LL.yz * (gammaBar_UU.xz * tmp364 + gammaBar_UU.zz * tmp373 + gammaBar_UU.yz * tmp368)) * tmp1) * tmp15 + U->beta_U.x * tmp15 * tmp99 + U->beta_U.x * (ABar_LL.xx * (gammaBar_UU.xx * tmp431 + gammaBar_UU.xy * tmp429 + tmp336) + ABar_LL.xy * (gammaBar_UU.xx * tmp434 + gammaBar_UU.xy * tmp432 + tmp341) + ABar_LL.xy * (gammaBar_UU.yz * tmp304 + gammaBar_UU.xy * tmp431 + gammaBar_UU.yy * tmp429) + ABar_LL.xz * (gammaBar_UU.xx * tmp437 + gammaBar_UU.xy * tmp435 + tmp344) + ABar_LL.xz * (gammaBar_UU.zz * tmp304 + gammaBar_UU.xz * tmp431 + gammaBar_UU.yz * tmp429) + ABar_LL.yy * (gammaBar_UU.yz * tmp317 + gammaBar_UU.xy * tmp434 + gammaBar_UU.yy * tmp432) + ABar_LL.yz * (gammaBar_UU.yz * tmp328 + gammaBar_UU.xy * tmp437 + gammaBar_UU.yy * tmp435) + ABar_LL.zz * (gammaBar_UU.zz * tmp328 + gammaBar_UU.xz * tmp437 + gammaBar_UU.yz * tmp435) + ABar_LL.yz * (gammaBar_UU.zz * tmp317 + gammaBar_UU.xz * tmp434 + gammaBar_UU.yz * tmp432)) * tmp15 + U->beta_U.y * tmp15 * tmp144 + U->beta_U.y * (ABar_LL.xx * (gammaBar_UU.xz * tmp308 + gammaBar_UU.xx * tmp440 + gammaBar_UU.xy * tmp438) + ABar_LL.xy * (gammaBar_UU.xz * tmp320 + gammaBar_UU.xx * tmp443 + gammaBar_UU.xy * tmp441) + ABar_LL.xy * (gammaBar_UU.xy * tmp440 + gammaBar_UU.yy * tmp438 + tmp334) + ABar_LL.xz * (gammaBar_UU.xz * tmp330 + gammaBar_UU.xx * tmp446 + gammaBar_UU.xy * tmp444) + ABar_LL.xz * (gammaBar_UU.zz * tmp308 + gammaBar_UU.xz * tmp440 + gammaBar_UU.yz * tmp438) + ABar_LL.yy * (gammaBar_UU.xy * tmp443 + gammaBar_UU.yy * tmp441 + tmp339) + ABar_LL.yz * (gammaBar_UU.xy * tmp446 + gammaBar_UU.yy * tmp444 + tmp342) + ABar_LL.zz * (gammaBar_UU.zz * tmp330 + gammaBar_UU.xz * tmp446 + gammaBar_UU.yz * tmp444) + ABar_LL.yz * (gammaBar_UU.zz * tmp320 + gammaBar_UU.xz * tmp443 + gammaBar_UU.yz * tmp441)) * tmp15 + U->beta_U.z * tmp15 * tmp30 + U->beta_U.z * tmp15 * tmp189 + U->beta_U.z * (ABar_LL.xx * (gammaBar_UU.xx * tmp449 + gammaBar_UU.xy * tmp447 + tmp313) + ABar_LL.xy * (gammaBar_UU.xx * tmp452 + gammaBar_UU.xy * tmp450 + tmp325) + ABar_LL.xy * (gammaBar_UU.xy * tmp449 + gammaBar_UU.yy * tmp447 + tmp326) + ABar_LL.xz * (gammaBar_UU.xx * tmp455 + gammaBar_UU.xy * tmp453 + tmp333) + ABar_LL.xz * (gammaBar_UU.xz * tmp449 + gammaBar_UU.yz * tmp447 + tmp335) + ABar_LL.yy * (gammaBar_UU.xy * tmp452 + gammaBar_UU.yy * tmp450 + tmp337) + ABar_LL.yz * (gammaBar_UU.xy * tmp455 + gammaBar_UU.yy * tmp453 + tmp338) + ABar_LL.zz * (gammaBar_UU.xz * tmp455 + gammaBar_UU.yz * tmp453 + tmp343) + ABar_LL.yz * (gammaBar_UU.xz * tmp452 + gammaBar_UU.yz * tmp450 + tmp340)) * tmp15 + U->alpha * (U->K * U->K + (R_LL.xx * gammaBar_UU.xx + R_LL.yy * gammaBar_UU.yy + R_LL.zz * gammaBar_UU.zz + 2. * R_LL.xy * gammaBar_UU.xy + 2. * R_LL.yz * gammaBar_UU.yz + 2. * R_LL.xz * gammaBar_UU.xz) * tmp2 + -12. * M_PI * U->rho + 4. * M_PI * S) + U->beta_U.y * tmp13 * tmp35 + (U->beta_U.x * r * (gammaBar_UU.xx * partial_ABar_LLl[0].xx + gammaBar_UU.yy * partial_ABar_LLl[0].yy + gammaBar_UU.zz * partial_ABar_LLl[0].zz + 2. * gammaBar_UU.xy * partial_ABar_LLl[0].xy + 2. * gammaBar_UU.yz * partial_ABar_LLl[0].yz + 2. * gammaBar_UU.xz * partial_ABar_LLl[0].xz) + U->beta_U.y * (gammaBar_UU.xx * partial_ABar_LLl[1].xx + gammaBar_UU.yy * partial_ABar_LLl[1].yy + gammaBar_UU.zz * partial_ABar_LLl[1].zz + 2. * gammaBar_UU.xy * partial_ABar_LLl[1].xy + 2. * gammaBar_UU.yz * partial_ABar_LLl[1].yz + 2. * gammaBar_UU.xz * partial_ABar_LLl[1].xz)) * tmp13 + U->beta_U.z * (gammaBar_UU.xx * partial_ABar_LLl[2].xx + gammaBar_UU.yy * partial_ABar_LLl[2].yy + gammaBar_UU.zz * partial_ABar_LLl[2].zz + 2. * gammaBar_UU.xy * partial_ABar_LLl[2].xy + 2. * gammaBar_UU.yz * partial_ABar_LLl[2].yz + 2. * gammaBar_UU.xz * partial_ABar_LLl[2].xz) * tmp15 + (U->beta_U.x * partial_K_l.x * r + U->beta_U.y * partial_K_l.y) * tmp13 + U->beta_U.z * partial_K_l.z * tmp15;
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}} {{{{ \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}{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}} {{{{ \overset{k\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^k} _A} _j}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{k\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^k} _K}} {{\frac{1}{{det_gammaBar}}}}} + {{{-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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow k\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^k} _K}}}}$
double tmp1 = sin(theta);
double tmp2 = 1. / r;
double tmp3 = 1. / tmp1;
double tmp4 = tmp2 * tmp3;
double tmp5 = r * tmp1;
double tmp6 = partial_beta_Ul[1].y * tmp1;
double tmp7 = partial_beta_Ul[0].x * tmp5;
double tmp8 = tmp6 + tmp7;
double tmp9 = partial_beta_Ul[2].z + tmp8;
double tmp10 = tmp4 * tmp9;
double tmp11 = 1. / 3.;
double tmp12 = r * r;
double tmp13 = cos(theta);
double tmp14 = U->beta_U.x * tmp1;
double tmp15 = U->beta_U.y * tmp13;
double tmp16 = 2. * tmp14;
double tmp17 = 1. / det_gammaBar;
double tmp18 = tmp15 + tmp16;
double tmp19 = tmp1 * tmp17;
double tmp20 = r * tmp12;
double tmp21 = tmp18 * tmp19;
double tmp22 = tmp20 * tmp21;
double tmp23 = partial_gammaBar_LLl[2].xy * tmp4;
double tmp24 = partial_gammaBar_LLl[0].xy * r;
double tmp25 = U->beta_U.y * partial_gammaBar_LLl[1].xy;
double tmp26 = U->beta_U.x * tmp24;
double tmp27 = tmp25 + tmp26;
double tmp28 = U->beta_U.z * tmp23;
double tmp29 = tmp2 * tmp27;
double tmp30 = gammaBar_LL.xy * tmp10;
double tmp31 = tmp11 * tmp30;
double tmp32 = U->beta_U.y * gammaBar_LL.yy;
double tmp33 = U->beta_U.z * gammaBar_LL.yz;
double tmp34 = tmp32 + tmp33;
double tmp35 = tmp2 * tmp34;
double tmp36 = partial_beta_Ul[1].x * tmp2;
double tmp37 = partial_beta_Ul[1].y * tmp2;
double tmp38 = partial_beta_Ul[1].z * tmp2;
double tmp39 = gammaBar_LL.xy * tmp37;
double tmp40 = gammaBar_LL.xz * tmp38;
double tmp41 = gammaBar_LL.xx * tmp36;
double tmp42 = tmp39 + tmp40;
double tmp43 = gammaBar_LL.xy * tmp22;
double tmp44 = tmp11 * tmp43;
double tmp45 = gammaBar_LL.xy * tmp2;
double tmp46 = tmp4 * tmp13;
double tmp47 = gammaBar_LL.xz * tmp46;
double tmp48 = U->beta_U.z * tmp47;
double tmp49 = gammaBar_LL.yy * partial_beta_Ul[0].y;
double tmp50 = gammaBar_LL.yz * partial_beta_Ul[0].z;
double tmp51 = gammaBar_LL.xy * partial_beta_Ul[0].x;
double tmp52 = tmp49 + tmp50;
double tmp53 = ABar_LL.xy * U->alpha;
double tmp54 = tmp51 + tmp52;
double tmp55 = -2. * tmp53;
double tmp56 = -1. * tmp48;
double tmp57 = tmp54 + tmp55;
double tmp58 = U->beta_U.x * tmp45;
double tmp59 = tmp56 + tmp57;
double tmp60 = -2. * tmp44;
double tmp61 = tmp58 + tmp59;
double tmp62 = tmp41 + tmp42;
double tmp63 = tmp60 + tmp61;
double tmp64 = -1. * tmp35;
double tmp65 = tmp62 + tmp63;
double tmp66 = -2. * tmp31;
double tmp67 = tmp64 + tmp65;
double tmp68 = tmp28 + tmp29;
double tmp69 = tmp66 + tmp67;
double tmp70 = partial_gammaBar_LLl[2].xz * tmp4;
double tmp71 = partial_gammaBar_LLl[0].xz * r;
double tmp72 = U->beta_U.y * partial_gammaBar_LLl[1].xz;
double tmp73 = U->beta_U.x * tmp71;
double tmp74 = tmp72 + tmp73;
double tmp75 = U->beta_U.z * tmp70;
double tmp76 = tmp2 * tmp74;
double tmp77 = partial_beta_Ul[2].x * tmp4;
double tmp78 = partial_beta_Ul[2].y * tmp4;
double tmp79 = partial_beta_Ul[2].z * tmp4;
double tmp80 = gammaBar_LL.xy * tmp78;
double tmp81 = gammaBar_LL.xz * tmp79;
double tmp82 = gammaBar_LL.xx * tmp77;
double tmp83 = tmp80 + tmp81;
double tmp84 = gammaBar_LL.xz * tmp10;
double tmp85 = tmp11 * tmp84;
double tmp86 = tmp14 + tmp15;
double tmp87 = tmp4 * tmp86;
double tmp88 = U->beta_U.y * gammaBar_LL.yz;
double tmp89 = U->beta_U.z * gammaBar_LL.zz;
double tmp90 = tmp88 + tmp89;
double tmp91 = tmp2 * tmp90;
double tmp92 = gammaBar_LL.xz * tmp22;
double tmp93 = tmp11 * tmp92;
double tmp94 = gammaBar_LL.yz * partial_beta_Ul[0].y;
double tmp95 = gammaBar_LL.zz * partial_beta_Ul[0].z;
double tmp96 = gammaBar_LL.xz * partial_beta_Ul[0].x;
double tmp97 = tmp94 + tmp95;
double tmp98 = ABar_LL.xz * U->alpha;
double tmp99 = tmp96 + tmp97;
double tmp100 = -2. * tmp98;
double tmp101 = -2. * tmp93;
double tmp102 = tmp99 + tmp100;
double tmp103 = -1. * tmp91;
double tmp104 = tmp101 + tmp102;
double tmp105 = gammaBar_LL.xz * tmp87;
double tmp106 = tmp103 + tmp104;
double tmp107 = -2. * tmp85;
double tmp108 = tmp105 + tmp106;
double tmp109 = tmp82 + tmp83;
double tmp110 = tmp107 + tmp108;
double tmp111 = tmp75 + tmp76;
double tmp112 = tmp109 + tmp110;
double tmp113 = partial_gammaBar_LLl[2].yz * tmp4;
double tmp114 = partial_gammaBar_LLl[0].yz * r;
double tmp115 = U->beta_U.y * partial_gammaBar_LLl[1].yz;
double tmp116 = U->beta_U.x * tmp114;
double tmp117 = tmp115 + tmp116;
double tmp118 = U->beta_U.z * tmp113;
double tmp119 = tmp2 * tmp117;
double tmp120 = gammaBar_LL.yy * tmp78;
double tmp121 = gammaBar_LL.yz * tmp79;
double tmp122 = gammaBar_LL.xy * tmp77;
double tmp123 = tmp120 + tmp121;
double tmp124 = gammaBar_LL.yz * tmp10;
double tmp125 = tmp11 * tmp124;
double tmp126 = gammaBar_LL.yz * tmp37;
double tmp127 = gammaBar_LL.zz * tmp38;
double tmp128 = gammaBar_LL.xz * tmp36;
double tmp129 = tmp126 + tmp127;
double tmp130 = gammaBar_LL.yz * tmp22;
double tmp131 = tmp11 * tmp130;
double tmp132 = gammaBar_LL.yz * tmp2;
double tmp133 = gammaBar_LL.zz * tmp46;
double tmp134 = U->beta_U.z * tmp133;
double tmp135 = ABar_LL.yz * U->alpha;
double tmp136 = -1. * tmp134;
double tmp137 = -2. * tmp135;
double tmp138 = U->beta_U.x * tmp132;
double tmp139 = tmp136 + tmp137;
double tmp140 = -2. * tmp131;
double tmp141 = tmp138 + tmp139;
double tmp142 = tmp128 + tmp129;
double tmp143 = tmp140 + tmp141;
double tmp144 = gammaBar_LL.yz * tmp87;
double tmp145 = tmp142 + tmp143;
double tmp146 = -2. * tmp125;
double tmp147 = tmp144 + tmp145;
double tmp148 = tmp122 + tmp123;
double tmp149 = tmp146 + tmp147;
double tmp150 = tmp118 + tmp119;
double tmp151 = tmp148 + tmp149;
double tmp152 = tmp68 + tmp69;
double tmp153 = tmp111 + tmp112;
double tmp154 = tmp150 + tmp151;
double dt_epsilonBar_LL.xx = -2. * gammaBar_LL.xx * tmp10 * tmp11 + -2. * (U->beta_U.z * gammaBar_LL.xz + U->beta_U.y * gammaBar_LL.xy) * tmp2 + -2. * gammaBar_LL.xx * tmp11 * tmp22 + -2. * ABar_LL.xx * U->alpha + 2. * (gammaBar_LL.xx * partial_beta_Ul[0].x + gammaBar_LL.xz * partial_beta_Ul[0].z + gammaBar_LL.xy * partial_beta_Ul[0].y) + (U->beta_U.x * partial_gammaBar_LLl[0].xx * r + U->beta_U.y * partial_gammaBar_LLl[1].xx) * tmp2 + U->beta_U.z * partial_gammaBar_LLl[2].xx * tmp4;
double dt_epsilonBar_LL.xy = tmp152;
double dt_epsilonBar_LL.xz = tmp153;
double dt_epsilonBar_LL.xy = tmp152;
double dt_epsilonBar_LL.yy = -2. * gammaBar_LL.yy * tmp10 * tmp11 + 2. * (gammaBar_LL.xy * partial_beta_Ul[1].x + gammaBar_LL.yz * partial_beta_Ul[1].z + gammaBar_LL.yy * partial_beta_Ul[1].y) * tmp2 + -2. * gammaBar_LL.yy * tmp11 * tmp22 + 2. * U->beta_U.x * gammaBar_LL.yy * tmp2 + -2. * ABar_LL.yy * U->alpha + -2. * U->beta_U.z * gammaBar_LL.yz * tmp46 + (U->beta_U.x * partial_gammaBar_LLl[0].yy * r + U->beta_U.y * partial_gammaBar_LLl[1].yy) * tmp2 + U->beta_U.z * partial_gammaBar_LLl[2].yy * tmp4;
double dt_epsilonBar_LL.yz = tmp154;
double dt_epsilonBar_LL.xz = tmp153;
double dt_epsilonBar_LL.yz = tmp154;
double dt_epsilonBar_LL.zz = 2. * (gammaBar_LL.xz * partial_beta_Ul[2].x + gammaBar_LL.zz * partial_beta_Ul[2].z + gammaBar_LL.yz * partial_beta_Ul[2].y) * tmp4 + -2. * gammaBar_LL.zz * tmp10 * tmp11 + 2. * gammaBar_LL.zz * tmp87 + -2. * ABar_LL.zz * U->alpha + -2. * gammaBar_LL.zz * tmp11 * tmp22 + (U->beta_U.x * partial_gammaBar_LLl[0].zz * r + U->beta_U.y * partial_gammaBar_LLl[1].zz) * tmp2 + U->beta_U.z * partial_gammaBar_LLl[2].zz * tmp4;
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} = {{{{\frac{1}{6}}} {{\left({{{{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}}} + {{{{{ \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}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}}} + {{{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}} {{{W}^{2}}}} + {{{-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}}} + {{{-1}} {{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _J}}} + {{{-1}} {{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^j} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\end{matrix} \right]}} _a} ^A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _B} _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]}} _I} _N}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\end{matrix} \right]}} _a} ^A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _B} _j}}} + {{{-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}}}}}\right)}}} + {{{-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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _A} _a}}} + {{{-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}} {{{{ \overset{A\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]}} ^A} _a}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}}} + {{{-1}} {{{ \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} -{{\frac{1}{r}}{\left({{{gammaBar_UU.yy}} + {{gammaBar_UU.zz}}}\right)}} \\ \frac{{-{{{{gammaBar_UU.zz}}} \cdot {{\cos\left( theta\right)}}}} + {{{2}} {{{gammaBar_UU.xy}}} \cdot {{\sin\left( theta\right)}}}}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{{{2}} {{\left({{{{{gammaBar_UU.xz}}} \cdot {{\sin\left( theta\right)}}} + {{{{gammaBar_UU.yz}}} \cdot {{\cos\left( theta\right)}}}}\right)}}}{{{r}} {{\sin\left( theta\right)}}}\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} \\ {C_U.y} \\ {C_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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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_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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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_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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}}}}\right)}}} + {{{-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}{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{W}^{2}}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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{a\downarrow M\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _M}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{a\downarrow N\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _N}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^i} _I}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _j} ^N} _i}} {{{W}^{2}}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow j\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{M\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{j\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{N\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow i\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^C} _i}} {{{W}^{2}}}}}\right)}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{\frac{1}{{det_gammaBar}}}}} + {{{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}}}}}$
double tmp1 = sin(theta);
double tmp2 = cos(theta);
double tmp3 = gammaBar_UU.xz * tmp1;
double tmp4 = gammaBar_UU.yz * tmp2;
double tmp5 = W * W;
double tmp6 = tmp3 + tmp4;
double tmp7 = tmp5 * tmp6;
double tmp8 = partial_alpha_l.z * tmp7;
double tmp9 = tmp1 * tmp1;
double tmp10 = gammaBar_UU.yy + gammaBar_UU.zz;
double tmp11 = tmp9 * tmp10;
double tmp12 = tmp5 * tmp11;
double tmp13 = r * tmp12;
double tmp14 = partial_alpha_l.x * tmp13;
double tmp15 = gammaBar_UU.zz * tmp2;
double tmp16 = gammaBar_UU.xy * tmp1;
double tmp17 = -1. * tmp15;
double tmp18 = 2. * tmp16;
double tmp19 = tmp17 + tmp18;
double tmp20 = tmp1 * tmp19;
double tmp21 = tmp5 * tmp20;
double tmp22 = -1. * tmp14;
double tmp23 = partial_alpha_l.y * tmp21;
double tmp24 = 2. * tmp8;
double tmp25 = tmp22 + tmp23;
double tmp26 = tmp24 + tmp25;
double tmp27 = r * tmp5;
double tmp28 = ABar_LL.xy * gammaBar_UU.xy;
double tmp29 = ABar_LL.xz * gammaBar_UU.xz;
double tmp30 = ABar_LL.xx * gammaBar_UU.xx;
double tmp31 = tmp28 + tmp29;
double tmp32 = tmp30 + tmp31;
double tmp33 = ABar_LL.xy * gammaBar_UU.yy;
double tmp34 = ABar_LL.xz * gammaBar_UU.yz;
double tmp35 = ABar_LL.xx * gammaBar_UU.xy;
double tmp36 = tmp33 + tmp34;
double tmp37 = tmp35 + tmp36;
double tmp38 = ABar_LL.xy * gammaBar_UU.yz;
double tmp39 = ABar_LL.xz * gammaBar_UU.zz;
double tmp40 = ABar_LL.xx * gammaBar_UU.xz;
double tmp41 = tmp38 + tmp39;
double tmp42 = tmp40 + tmp41;
double tmp43 = U->alpha * tmp27;
double tmp44 = r * tmp1;
double tmp45 = U->alpha * tmp44;
double tmp46 = U->K * tmp45;
double tmp47 = tmp1 * tmp5;
double tmp48 = r * tmp47;
double tmp49 = U->alpha * tmp48;
double tmp50 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xy;
double tmp51 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xz;
double tmp52 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xx;
double tmp53 = tmp50 + tmp51;
double tmp54 = tmp52 + tmp53;
double tmp55 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xy;
double tmp56 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xz;
double tmp57 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xx;
double tmp58 = tmp55 + tmp56;
double tmp59 = tmp57 + tmp58;
double tmp60 = tmp1 * tmp59;
double tmp61 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xy;
double tmp62 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xz;
double tmp63 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xx;
double tmp64 = tmp61 + tmp62;
double tmp65 = tmp63 + tmp64;
double tmp66 = tmp1 * tmp65;
double tmp67 = r * tmp66;
double tmp68 = gammaBar_UU.xy * tmp60;
double tmp69 = gammaBar_UU.xx * tmp67;
double tmp70 = gammaBar_UU.xz * tmp54;
double tmp71 = tmp68 + tmp69;
double tmp72 = tmp70 + tmp71;
double tmp73 = gammaBar_UU.yy * partial_gammaBar_LLl[2].xy;
double tmp74 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xz;
double tmp75 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xx;
double tmp76 = tmp73 + tmp74;
double tmp77 = tmp75 + tmp76;
double tmp78 = gammaBar_UU.yy * partial_gammaBar_LLl[1].xy;
double tmp79 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xz;
double tmp80 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xx;
double tmp81 = tmp78 + tmp79;
double tmp82 = tmp80 + tmp81;
double tmp83 = tmp1 * tmp82;
double tmp84 = gammaBar_UU.yy * partial_gammaBar_LLl[0].xy;
double tmp85 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xz;
double tmp86 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xx;
double tmp87 = tmp84 + tmp85;
double tmp88 = tmp86 + tmp87;
double tmp89 = tmp1 * tmp88;
double tmp90 = r * tmp89;
double tmp91 = gammaBar_UU.xy * tmp83;
double tmp92 = gammaBar_UU.xx * tmp90;
double tmp93 = gammaBar_UU.xz * tmp77;
double tmp94 = tmp91 + tmp92;
double tmp95 = tmp93 + tmp94;
double tmp96 = gammaBar_UU.yy * tmp60;
double tmp97 = gammaBar_UU.xy * tmp67;
double tmp98 = gammaBar_UU.yz * tmp54;
double tmp99 = tmp96 + tmp97;
double tmp100 = tmp98 + tmp99;
double tmp101 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xy;
double tmp102 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xz;
double tmp103 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xx;
double tmp104 = tmp101 + tmp102;
double tmp105 = tmp103 + tmp104;
double tmp106 = gammaBar_UU.yz * partial_gammaBar_LLl[1].xy;
double tmp107 = gammaBar_UU.zz * partial_gammaBar_LLl[1].xz;
double tmp108 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xx;
double tmp109 = tmp106 + tmp107;
double tmp110 = tmp108 + tmp109;
double tmp111 = tmp1 * tmp110;
double tmp112 = gammaBar_UU.yz * partial_gammaBar_LLl[0].xy;
double tmp113 = gammaBar_UU.zz * partial_gammaBar_LLl[0].xz;
double tmp114 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xx;
double tmp115 = tmp112 + tmp113;
double tmp116 = tmp114 + tmp115;
double tmp117 = tmp1 * tmp116;
double tmp118 = r * tmp117;
double tmp119 = gammaBar_UU.xy * tmp111;
double tmp120 = gammaBar_UU.xx * tmp118;
double tmp121 = gammaBar_UU.xz * tmp105;
double tmp122 = tmp119 + tmp120;
double tmp123 = tmp121 + tmp122;
double tmp124 = gammaBar_UU.yz * tmp60;
double tmp125 = gammaBar_UU.xz * tmp67;
double tmp126 = gammaBar_UU.zz * tmp54;
double tmp127 = tmp124 + tmp125;
double tmp128 = tmp126 + tmp127;
double tmp129 = gammaBar_UU.yy * tmp83;
double tmp130 = gammaBar_UU.xy * tmp90;
double tmp131 = gammaBar_UU.yz * tmp77;
double tmp132 = tmp129 + tmp130;
double tmp133 = tmp131 + tmp132;
double tmp134 = gammaBar_UU.yy * tmp111;
double tmp135 = gammaBar_UU.xy * tmp118;
double tmp136 = gammaBar_UU.yz * tmp105;
double tmp137 = tmp134 + tmp135;
double tmp138 = tmp136 + tmp137;
double tmp139 = gammaBar_UU.yz * tmp83;
double tmp140 = gammaBar_UU.xz * tmp90;
double tmp141 = gammaBar_UU.zz * tmp77;
double tmp142 = tmp139 + tmp140;
double tmp143 = tmp141 + tmp142;
double tmp144 = gammaBar_UU.yz * tmp111;
double tmp145 = gammaBar_UU.xz * tmp118;
double tmp146 = gammaBar_UU.zz * tmp105;
double tmp147 = tmp144 + tmp145;
double tmp148 = tmp146 + tmp147;
double tmp149 = ABar_LL.yz * tmp143;
double tmp150 = ABar_LL.zz * tmp148;
double tmp151 = ABar_LL.yz * tmp138;
double tmp152 = tmp149 + tmp150;
double tmp153 = ABar_LL.yy * tmp133;
double tmp154 = tmp151 + tmp152;
double tmp155 = ABar_LL.xz * tmp128;
double tmp156 = tmp153 + tmp154;
double tmp157 = ABar_LL.xz * tmp123;
double tmp158 = tmp155 + tmp156;
double tmp159 = ABar_LL.xy * tmp100;
double tmp160 = tmp157 + tmp158;
double tmp161 = ABar_LL.xy * tmp95;
double tmp162 = tmp159 + tmp160;
double tmp163 = ABar_LL.xx * tmp72;
double tmp164 = tmp161 + tmp162;
double tmp165 = tmp163 + tmp164;
double tmp166 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yy;
double tmp167 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yz;
double tmp168 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xy;
double tmp169 = tmp166 + tmp167;
double tmp170 = tmp168 + tmp169;
double tmp171 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yy;
double tmp172 = gammaBar_UU.xz * partial_gammaBar_LLl[1].yz;
double tmp173 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xy;
double tmp174 = tmp171 + tmp172;
double tmp175 = tmp173 + tmp174;
double tmp176 = tmp1 * tmp175;
double tmp177 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yy;
double tmp178 = gammaBar_UU.xz * partial_gammaBar_LLl[0].yz;
double tmp179 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xy;
double tmp180 = tmp177 + tmp178;
double tmp181 = tmp179 + tmp180;
double tmp182 = tmp1 * tmp181;
double tmp183 = r * tmp182;
double tmp184 = gammaBar_UU.xy * tmp176;
double tmp185 = gammaBar_UU.xx * tmp183;
double tmp186 = gammaBar_UU.xz * tmp170;
double tmp187 = tmp184 + tmp185;
double tmp188 = tmp186 + tmp187;
double tmp189 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yy;
double tmp190 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yz;
double tmp191 = tmp189 + tmp190;
double tmp192 = tmp50 + tmp191;
double tmp193 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yy;
double tmp194 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yz;
double tmp195 = tmp193 + tmp194;
double tmp196 = tmp55 + tmp195;
double tmp197 = tmp1 * tmp196;
double tmp198 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yy;
double tmp199 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yz;
double tmp200 = tmp198 + tmp199;
double tmp201 = tmp61 + tmp200;
double tmp202 = tmp1 * tmp201;
double tmp203 = r * tmp202;
double tmp204 = gammaBar_UU.xy * tmp197;
double tmp205 = gammaBar_UU.xx * tmp203;
double tmp206 = gammaBar_UU.xz * tmp192;
double tmp207 = tmp204 + tmp205;
double tmp208 = tmp206 + tmp207;
double tmp209 = gammaBar_UU.yy * tmp176;
double tmp210 = gammaBar_UU.xy * tmp183;
double tmp211 = gammaBar_UU.yz * tmp170;
double tmp212 = tmp209 + tmp210;
double tmp213 = tmp211 + tmp212;
double tmp214 = gammaBar_UU.yz * partial_gammaBar_LLl[2].yy;
double tmp215 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yz;
double tmp216 = gammaBar_UU.xz * partial_gammaBar_LLl[2].xy;
double tmp217 = tmp214 + tmp215;
double tmp218 = tmp216 + tmp217;
double tmp219 = gammaBar_UU.yz * partial_gammaBar_LLl[1].yy;
double tmp220 = gammaBar_UU.zz * partial_gammaBar_LLl[1].yz;
double tmp221 = gammaBar_UU.xz * partial_gammaBar_LLl[1].xy;
double tmp222 = tmp219 + tmp220;
double tmp223 = tmp221 + tmp222;
double tmp224 = tmp1 * tmp223;
double tmp225 = gammaBar_UU.yz * partial_gammaBar_LLl[0].yy;
double tmp226 = gammaBar_UU.zz * partial_gammaBar_LLl[0].yz;
double tmp227 = gammaBar_UU.xz * partial_gammaBar_LLl[0].xy;
double tmp228 = tmp225 + tmp226;
double tmp229 = tmp227 + tmp228;
double tmp230 = tmp1 * tmp229;
double tmp231 = r * tmp230;
double tmp232 = gammaBar_UU.xy * tmp224;
double tmp233 = gammaBar_UU.xx * tmp231;
double tmp234 = gammaBar_UU.xz * tmp218;
double tmp235 = tmp232 + tmp233;
double tmp236 = tmp234 + tmp235;
double tmp237 = gammaBar_UU.yz * tmp176;
double tmp238 = gammaBar_UU.xz * tmp183;
double tmp239 = gammaBar_UU.zz * tmp170;
double tmp240 = tmp237 + tmp238;
double tmp241 = tmp239 + tmp240;
double tmp242 = gammaBar_UU.yy * tmp197;
double tmp243 = gammaBar_UU.xy * tmp203;
double tmp244 = gammaBar_UU.yz * tmp192;
double tmp245 = tmp242 + tmp243;
double tmp246 = tmp244 + tmp245;
double tmp247 = gammaBar_UU.yy * tmp224;
double tmp248 = gammaBar_UU.xy * tmp231;
double tmp249 = gammaBar_UU.yz * tmp218;
double tmp250 = tmp247 + tmp248;
double tmp251 = tmp249 + tmp250;
double tmp252 = gammaBar_UU.yz * tmp197;
double tmp253 = gammaBar_UU.xz * tmp203;
double tmp254 = gammaBar_UU.zz * tmp192;
double tmp255 = tmp252 + tmp253;
double tmp256 = tmp254 + tmp255;
double tmp257 = gammaBar_UU.yz * tmp224;
double tmp258 = gammaBar_UU.xz * tmp231;
double tmp259 = gammaBar_UU.zz * tmp218;
double tmp260 = tmp257 + tmp258;
double tmp261 = tmp259 + tmp260;
double tmp262 = ABar_LL.yz * tmp256;
double tmp263 = ABar_LL.zz * tmp261;
double tmp264 = ABar_LL.yz * tmp251;
double tmp265 = tmp262 + tmp263;
double tmp266 = ABar_LL.yy * tmp246;
double tmp267 = tmp264 + tmp265;
double tmp268 = ABar_LL.xz * tmp241;
double tmp269 = tmp266 + tmp267;
double tmp270 = ABar_LL.xz * tmp236;
double tmp271 = tmp268 + tmp269;
double tmp272 = ABar_LL.xy * tmp213;
double tmp273 = tmp270 + tmp271;
double tmp274 = ABar_LL.xy * tmp208;
double tmp275 = tmp272 + tmp273;
double tmp276 = ABar_LL.xx * tmp188;
double tmp277 = tmp274 + tmp275;
double tmp278 = tmp276 + tmp277;
double tmp279 = gammaBar_UU.xy * partial_gammaBar_LLl[2].yz;
double tmp280 = gammaBar_UU.xz * partial_gammaBar_LLl[2].zz;
double tmp281 = gammaBar_UU.xx * partial_gammaBar_LLl[2].xz;
double tmp282 = tmp279 + tmp280;
double tmp283 = tmp281 + tmp282;
double tmp284 = gammaBar_UU.xy * partial_gammaBar_LLl[1].yz;
double tmp285 = gammaBar_UU.xz * partial_gammaBar_LLl[1].zz;
double tmp286 = gammaBar_UU.xx * partial_gammaBar_LLl[1].xz;
double tmp287 = tmp284 + tmp285;
double tmp288 = tmp286 + tmp287;
double tmp289 = tmp1 * tmp288;
double tmp290 = gammaBar_UU.xy * partial_gammaBar_LLl[0].yz;
double tmp291 = gammaBar_UU.xz * partial_gammaBar_LLl[0].zz;
double tmp292 = gammaBar_UU.xx * partial_gammaBar_LLl[0].xz;
double tmp293 = tmp290 + tmp291;
double tmp294 = tmp292 + tmp293;
double tmp295 = tmp1 * tmp294;
double tmp296 = r * tmp295;
double tmp297 = gammaBar_UU.xy * tmp289;
double tmp298 = gammaBar_UU.xx * tmp296;
double tmp299 = gammaBar_UU.xz * tmp283;
double tmp300 = tmp297 + tmp298;
double tmp301 = tmp299 + tmp300;
double tmp302 = gammaBar_UU.yy * partial_gammaBar_LLl[2].yz;
double tmp303 = gammaBar_UU.yz * partial_gammaBar_LLl[2].zz;
double tmp304 = gammaBar_UU.xy * partial_gammaBar_LLl[2].xz;
double tmp305 = tmp302 + tmp303;
double tmp306 = tmp304 + tmp305;
double tmp307 = gammaBar_UU.yy * partial_gammaBar_LLl[1].yz;
double tmp308 = gammaBar_UU.yz * partial_gammaBar_LLl[1].zz;
double tmp309 = gammaBar_UU.xy * partial_gammaBar_LLl[1].xz;
double tmp310 = tmp307 + tmp308;
double tmp311 = tmp309 + tmp310;
double tmp312 = tmp1 * tmp311;
double tmp313 = gammaBar_UU.yy * partial_gammaBar_LLl[0].yz;
double tmp314 = gammaBar_UU.yz * partial_gammaBar_LLl[0].zz;
double tmp315 = gammaBar_UU.xy * partial_gammaBar_LLl[0].xz;
double tmp316 = tmp313 + tmp314;
double tmp317 = tmp315 + tmp316;
double tmp318 = tmp1 * tmp317;
double tmp319 = r * tmp318;
double tmp320 = gammaBar_UU.xy * tmp312;
double tmp321 = gammaBar_UU.xx * tmp319;
double tmp322 = gammaBar_UU.xz * tmp306;
double tmp323 = tmp320 + tmp321;
double tmp324 = tmp322 + tmp323;
double tmp325 = gammaBar_UU.yy * tmp289;
double tmp326 = gammaBar_UU.xy * tmp296;
double tmp327 = gammaBar_UU.yz * tmp283;
double tmp328 = tmp325 + tmp326;
double tmp329 = tmp327 + tmp328;
double tmp330 = gammaBar_UU.zz * partial_gammaBar_LLl[2].zz;
double tmp331 = tmp190 + tmp330;
double tmp332 = tmp51 + tmp331;
double tmp333 = gammaBar_UU.zz * partial_gammaBar_LLl[1].zz;
double tmp334 = tmp194 + tmp333;
double tmp335 = tmp56 + tmp334;
double tmp336 = tmp1 * tmp335;
double tmp337 = gammaBar_UU.zz * partial_gammaBar_LLl[0].zz;
double tmp338 = tmp199 + tmp337;
double tmp339 = tmp62 + tmp338;
double tmp340 = tmp1 * tmp339;
double tmp341 = r * tmp340;
double tmp342 = gammaBar_UU.xy * tmp336;
double tmp343 = gammaBar_UU.xx * tmp341;
double tmp344 = gammaBar_UU.xz * tmp332;
double tmp345 = tmp342 + tmp343;
double tmp346 = tmp344 + tmp345;
double tmp347 = gammaBar_UU.yz * tmp289;
double tmp348 = gammaBar_UU.xz * tmp296;
double tmp349 = gammaBar_UU.zz * tmp283;
double tmp350 = tmp347 + tmp348;
double tmp351 = tmp349 + tmp350;
double tmp352 = gammaBar_UU.yy * tmp312;
double tmp353 = gammaBar_UU.xy * tmp319;
double tmp354 = gammaBar_UU.yz * tmp306;
double tmp355 = tmp352 + tmp353;
double tmp356 = tmp354 + tmp355;
double tmp357 = gammaBar_UU.yy * tmp336;
double tmp358 = gammaBar_UU.xy * tmp341;
double tmp359 = gammaBar_UU.yz * tmp332;
double tmp360 = tmp357 + tmp358;
double tmp361 = tmp359 + tmp360;
double tmp362 = gammaBar_UU.yz * tmp312;
double tmp363 = gammaBar_UU.xz * tmp319;
double tmp364 = gammaBar_UU.zz * tmp306;
double tmp365 = tmp362 + tmp363;
double tmp366 = tmp364 + tmp365;
double tmp367 = gammaBar_UU.yz * tmp336;
double tmp368 = gammaBar_UU.xz * tmp341;
double tmp369 = gammaBar_UU.zz * tmp332;
double tmp370 = tmp367 + tmp368;
double tmp371 = tmp369 + tmp370;
double tmp372 = ABar_LL.yz * tmp366;
double tmp373 = ABar_LL.zz * tmp371;
double tmp374 = ABar_LL.yz * tmp361;
double tmp375 = tmp372 + tmp373;
double tmp376 = ABar_LL.yy * tmp356;
double tmp377 = tmp374 + tmp375;
double tmp378 = ABar_LL.xz * tmp351;
double tmp379 = tmp376 + tmp377;
double tmp380 = ABar_LL.xz * tmp346;
double tmp381 = tmp378 + tmp379;
double tmp382 = ABar_LL.xy * tmp329;
double tmp383 = tmp380 + tmp381;
double tmp384 = ABar_LL.xy * tmp324;
double tmp385 = tmp382 + tmp383;
double tmp386 = ABar_LL.xx * tmp301;
double tmp387 = tmp384 + tmp385;
double tmp388 = tmp386 + tmp387;
double tmp389 = U->beta_U.y * tmp278;
double tmp390 = U->beta_U.z * tmp388;
double tmp391 = U->beta_U.x * tmp165;
double tmp392 = tmp389 + tmp390;
double tmp393 = tmp391 + tmp392;
double tmp394 = gammaBar_UU.xy * partial_ABar_LLl[2].xy;
double tmp395 = gammaBar_UU.xz * partial_ABar_LLl[2].xz;
double tmp396 = gammaBar_UU.yz * partial_ABar_LLl[2].yz;
double tmp397 = 2. * tmp395;
double tmp398 = 2. * tmp396;
double tmp399 = 2. * tmp394;
double tmp400 = tmp397 + tmp398;
double tmp401 = gammaBar_UU.zz * partial_ABar_LLl[2].zz;
double tmp402 = tmp399 + tmp400;
double tmp403 = gammaBar_UU.yy * partial_ABar_LLl[2].yy;
double tmp404 = tmp401 + tmp402;
double tmp405 = gammaBar_UU.xx * partial_ABar_LLl[2].xx;
double tmp406 = tmp403 + tmp404;
double tmp407 = tmp405 + tmp406;
double tmp408 = gammaBar_UU.xy * partial_ABar_LLl[1].xy;
double tmp409 = gammaBar_UU.xz * partial_ABar_LLl[1].xz;
double tmp410 = gammaBar_UU.yz * partial_ABar_LLl[1].yz;
double tmp411 = 2. * tmp409;
double tmp412 = 2. * tmp410;
double tmp413 = 2. * tmp408;
double tmp414 = tmp411 + tmp412;
double tmp415 = gammaBar_UU.zz * partial_ABar_LLl[1].zz;
double tmp416 = tmp413 + tmp414;
double tmp417 = gammaBar_UU.yy * partial_ABar_LLl[1].yy;
double tmp418 = tmp415 + tmp416;
double tmp419 = gammaBar_UU.xx * partial_ABar_LLl[1].xx;
double tmp420 = tmp417 + tmp418;
double tmp421 = tmp419 + tmp420;
double tmp422 = tmp1 * tmp421;
double tmp423 = gammaBar_UU.xy * partial_ABar_LLl[0].xy;
double tmp424 = gammaBar_UU.xz * partial_ABar_LLl[0].xz;
double tmp425 = gammaBar_UU.yz * partial_ABar_LLl[0].yz;
double tmp426 = 2. * tmp424;
double tmp427 = 2. * tmp425;
double tmp428 = 2. * tmp423;
double tmp429 = tmp426 + tmp427;
double tmp430 = gammaBar_UU.zz * partial_ABar_LLl[0].zz;
double tmp431 = tmp428 + tmp429;
double tmp432 = gammaBar_UU.yy * partial_ABar_LLl[0].yy;
double tmp433 = tmp430 + tmp431;
double tmp434 = gammaBar_UU.xx * partial_ABar_LLl[0].xx;
double tmp435 = tmp432 + tmp433;
double tmp436 = tmp434 + tmp435;
double tmp437 = tmp1 * tmp436;
double tmp438 = r * tmp437;
double tmp439 = U->beta_U.y * tmp422;
double tmp440 = U->beta_U.x * tmp438;
double tmp441 = U->beta_U.z * tmp407;
double tmp442 = tmp439 + tmp440;
double tmp443 = tmp441 + tmp442;
double tmp444 = partial_gammaBar_LLl[1].xx * tmp1;
double tmp445 = partial_gammaBar_LLl[0].xx * tmp44;
double tmp446 = gammaBar_UU.xy * tmp444;
double tmp447 = gammaBar_UU.xx * tmp445;
double tmp448 = tmp446 + tmp447;
double tmp449 = tmp103 + tmp448;
double tmp450 = partial_gammaBar_LLl[1].xy * tmp1;
double tmp451 = partial_gammaBar_LLl[0].xy * tmp44;
double tmp452 = gammaBar_UU.xy * tmp450;
double tmp453 = gammaBar_UU.xx * tmp451;
double tmp454 = tmp452 + tmp453;
double tmp455 = tmp216 + tmp454;
double tmp456 = partial_gammaBar_LLl[1].xz * tmp1;
double tmp457 = partial_gammaBar_LLl[0].xz * tmp44;
double tmp458 = gammaBar_UU.xy * tmp456;
double tmp459 = gammaBar_UU.xx * tmp457;
double tmp460 = tmp458 + tmp459;
double tmp461 = tmp51 + tmp460;
double tmp462 = gammaBar_UU.xy * tmp455;
double tmp463 = gammaBar_UU.xz * tmp461;
double tmp464 = gammaBar_UU.xx * tmp449;
double tmp465 = tmp462 + tmp463;
double tmp466 = tmp464 + tmp465;
double tmp467 = gammaBar_UU.yy * tmp444;
double tmp468 = gammaBar_UU.xy * tmp445;
double tmp469 = gammaBar_UU.yz * partial_gammaBar_LLl[2].xx;
double tmp470 = tmp467 + tmp468;
double tmp471 = tmp469 + tmp470;
double tmp472 = gammaBar_UU.yy * tmp450;
double tmp473 = gammaBar_UU.xy * tmp451;
double tmp474 = tmp472 + tmp473;
double tmp475 = tmp101 + tmp474;
double tmp476 = gammaBar_UU.yy * tmp456;
double tmp477 = gammaBar_UU.xy * tmp457;
double tmp478 = tmp476 + tmp477;
double tmp479 = tmp74 + tmp478;
double tmp480 = gammaBar_UU.xy * tmp475;
double tmp481 = gammaBar_UU.xz * tmp479;
double tmp482 = gammaBar_UU.xx * tmp471;
double tmp483 = tmp480 + tmp481;
double tmp484 = tmp482 + tmp483;
double tmp485 = gammaBar_UU.yy * tmp455;
double tmp486 = gammaBar_UU.yz * tmp461;
double tmp487 = gammaBar_UU.xy * tmp449;
double tmp488 = tmp485 + tmp486;
double tmp489 = tmp487 + tmp488;
double tmp490 = gammaBar_UU.yz * tmp444;
double tmp491 = gammaBar_UU.xz * tmp445;
double tmp492 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xx;
double tmp493 = tmp490 + tmp491;
double tmp494 = tmp492 + tmp493;
double tmp495 = gammaBar_UU.yz * tmp450;
double tmp496 = gammaBar_UU.xz * tmp451;
double tmp497 = gammaBar_UU.zz * partial_gammaBar_LLl[2].xy;
double tmp498 = tmp495 + tmp496;
double tmp499 = tmp497 + tmp498;
double tmp500 = gammaBar_UU.yz * tmp456;
double tmp501 = gammaBar_UU.xz * tmp457;
double tmp502 = tmp500 + tmp501;
double tmp503 = tmp102 + tmp502;
double tmp504 = gammaBar_UU.xy * tmp499;
double tmp505 = gammaBar_UU.xz * tmp503;
double tmp506 = gammaBar_UU.xx * tmp494;
double tmp507 = tmp504 + tmp505;
double tmp508 = tmp506 + tmp507;
double tmp509 = gammaBar_UU.yz * tmp455;
double tmp510 = gammaBar_UU.zz * tmp461;
double tmp511 = gammaBar_UU.xz * tmp449;
double tmp512 = tmp509 + tmp510;
double tmp513 = tmp511 + tmp512;
double tmp514 = gammaBar_UU.yy * tmp475;
double tmp515 = gammaBar_UU.yz * tmp479;
double tmp516 = gammaBar_UU.xy * tmp471;
double tmp517 = tmp514 + tmp515;
double tmp518 = tmp516 + tmp517;
double tmp519 = gammaBar_UU.yy * tmp499;
double tmp520 = gammaBar_UU.yz * tmp503;
double tmp521 = gammaBar_UU.xy * tmp494;
double tmp522 = tmp519 + tmp520;
double tmp523 = tmp521 + tmp522;
double tmp524 = gammaBar_UU.yz * tmp475;
double tmp525 = gammaBar_UU.zz * tmp479;
double tmp526 = gammaBar_UU.xz * tmp471;
double tmp527 = tmp524 + tmp525;
double tmp528 = tmp526 + tmp527;
double tmp529 = gammaBar_UU.yz * tmp499;
double tmp530 = gammaBar_UU.zz * tmp503;
double tmp531 = gammaBar_UU.xz * tmp494;
double tmp532 = tmp529 + tmp530;
double tmp533 = tmp531 + tmp532;
double tmp534 = ABar_LL.yz * tmp528;
double tmp535 = ABar_LL.zz * tmp533;
double tmp536 = ABar_LL.yz * tmp523;
double tmp537 = tmp534 + tmp535;
double tmp538 = ABar_LL.yy * tmp518;
double tmp539 = tmp536 + tmp537;
double tmp540 = ABar_LL.xz * tmp513;
double tmp541 = tmp538 + tmp539;
double tmp542 = ABar_LL.xz * tmp508;
double tmp543 = tmp540 + tmp541;
double tmp544 = ABar_LL.xy * tmp489;
double tmp545 = tmp542 + tmp543;
double tmp546 = ABar_LL.xy * tmp484;
double tmp547 = tmp544 + tmp545;
double tmp548 = ABar_LL.xx * tmp466;
double tmp549 = tmp546 + tmp547;
double tmp550 = tmp548 + tmp549;
double tmp551 = partial_gammaBar_LLl[1].yy * tmp1;
double tmp552 = partial_gammaBar_LLl[0].yy * tmp44;
double tmp553 = gammaBar_UU.xy * tmp551;
double tmp554 = gammaBar_UU.xx * tmp552;
double tmp555 = gammaBar_UU.xz * partial_gammaBar_LLl[2].yy;
double tmp556 = tmp553 + tmp554;
double tmp557 = tmp555 + tmp556;
double tmp558 = partial_gammaBar_LLl[1].yz * tmp1;
double tmp559 = partial_gammaBar_LLl[0].yz * tmp44;
double tmp560 = gammaBar_UU.xy * tmp558;
double tmp561 = gammaBar_UU.xx * tmp559;
double tmp562 = tmp560 + tmp561;
double tmp563 = tmp167 + tmp562;
double tmp564 = gammaBar_UU.xy * tmp557;
double tmp565 = gammaBar_UU.xz * tmp563;
double tmp566 = gammaBar_UU.xx * tmp455;
double tmp567 = tmp564 + tmp565;
double tmp568 = tmp566 + tmp567;
double tmp569 = gammaBar_UU.yy * tmp551;
double tmp570 = gammaBar_UU.xy * tmp552;
double tmp571 = tmp569 + tmp570;
double tmp572 = tmp214 + tmp571;
double tmp573 = gammaBar_UU.yy * tmp558;
double tmp574 = gammaBar_UU.xy * tmp559;
double tmp575 = tmp573 + tmp574;
double tmp576 = tmp190 + tmp575;
double tmp577 = gammaBar_UU.xy * tmp572;
double tmp578 = gammaBar_UU.xz * tmp576;
double tmp579 = gammaBar_UU.xx * tmp475;
double tmp580 = tmp577 + tmp578;
double tmp581 = tmp579 + tmp580;
double tmp582 = gammaBar_UU.yy * tmp557;
double tmp583 = gammaBar_UU.yz * tmp563;
double tmp584 = tmp582 + tmp583;
double tmp585 = tmp462 + tmp584;
double tmp586 = gammaBar_UU.yz * tmp551;
double tmp587 = gammaBar_UU.xz * tmp552;
double tmp588 = gammaBar_UU.zz * partial_gammaBar_LLl[2].yy;
double tmp589 = tmp586 + tmp587;
double tmp590 = tmp588 + tmp589;
double tmp591 = gammaBar_UU.yz * tmp558;
double tmp592 = gammaBar_UU.xz * tmp559;
double tmp593 = tmp591 + tmp592;
double tmp594 = tmp215 + tmp593;
double tmp595 = gammaBar_UU.xy * tmp590;
double tmp596 = gammaBar_UU.xz * tmp594;
double tmp597 = gammaBar_UU.xx * tmp499;
double tmp598 = tmp595 + tmp596;
double tmp599 = tmp597 + tmp598;
double tmp600 = gammaBar_UU.yz * tmp557;
double tmp601 = gammaBar_UU.zz * tmp563;
double tmp602 = gammaBar_UU.xz * tmp455;
double tmp603 = tmp600 + tmp601;
double tmp604 = tmp602 + tmp603;
double tmp605 = gammaBar_UU.yy * tmp572;
double tmp606 = gammaBar_UU.yz * tmp576;
double tmp607 = tmp605 + tmp606;
double tmp608 = tmp480 + tmp607;
double tmp609 = gammaBar_UU.yy * tmp590;
double tmp610 = gammaBar_UU.yz * tmp594;
double tmp611 = tmp609 + tmp610;
double tmp612 = tmp504 + tmp611;
double tmp613 = gammaBar_UU.yz * tmp572;
double tmp614 = gammaBar_UU.zz * tmp576;
double tmp615 = gammaBar_UU.xz * tmp475;
double tmp616 = tmp613 + tmp614;
double tmp617 = tmp615 + tmp616;
double tmp618 = gammaBar_UU.yz * tmp590;
double tmp619 = gammaBar_UU.zz * tmp594;
double tmp620 = gammaBar_UU.xz * tmp499;
double tmp621 = tmp618 + tmp619;
double tmp622 = tmp620 + tmp621;
double tmp623 = ABar_LL.yz * tmp617;
double tmp624 = ABar_LL.zz * tmp622;
double tmp625 = ABar_LL.yz * tmp612;
double tmp626 = tmp623 + tmp624;
double tmp627 = ABar_LL.yy * tmp608;
double tmp628 = tmp625 + tmp626;
double tmp629 = ABar_LL.xz * tmp604;
double tmp630 = tmp627 + tmp628;
double tmp631 = ABar_LL.xz * tmp599;
double tmp632 = tmp629 + tmp630;
double tmp633 = ABar_LL.xy * tmp585;
double tmp634 = tmp631 + tmp632;
double tmp635 = ABar_LL.xy * tmp581;
double tmp636 = tmp633 + tmp634;
double tmp637 = ABar_LL.xx * tmp568;
double tmp638 = tmp635 + tmp636;
double tmp639 = tmp637 + tmp638;
double tmp640 = gammaBar_UU.xy * tmp170;
double tmp641 = gammaBar_UU.xx * tmp54;
double tmp642 = tmp299 + tmp640;
double tmp643 = tmp641 + tmp642;
double tmp644 = gammaBar_UU.xy * tmp192;
double tmp645 = gammaBar_UU.xx * tmp77;
double tmp646 = tmp322 + tmp644;
double tmp647 = tmp645 + tmp646;
double tmp648 = gammaBar_UU.yy * tmp170;
double tmp649 = gammaBar_UU.xy * tmp54;
double tmp650 = tmp327 + tmp648;
double tmp651 = tmp649 + tmp650;
double tmp652 = gammaBar_UU.xy * tmp218;
double tmp653 = gammaBar_UU.xx * tmp105;
double tmp654 = tmp344 + tmp652;
double tmp655 = tmp653 + tmp654;
double tmp656 = tmp211 + tmp349;
double tmp657 = tmp70 + tmp656;
double tmp658 = gammaBar_UU.yy * tmp192;
double tmp659 = gammaBar_UU.xy * tmp77;
double tmp660 = tmp354 + tmp658;
double tmp661 = tmp659 + tmp660;
double tmp662 = gammaBar_UU.yy * tmp218;
double tmp663 = gammaBar_UU.xy * tmp105;
double tmp664 = tmp359 + tmp662;
double tmp665 = tmp663 + tmp664;
double tmp666 = tmp244 + tmp364;
double tmp667 = tmp93 + tmp666;
double tmp668 = tmp249 + tmp369;
double tmp669 = tmp121 + tmp668;
double tmp670 = ABar_LL.yz * tmp667;
double tmp671 = ABar_LL.zz * tmp669;
double tmp672 = ABar_LL.yz * tmp665;
double tmp673 = tmp670 + tmp671;
double tmp674 = ABar_LL.yy * tmp661;
double tmp675 = tmp672 + tmp673;
double tmp676 = ABar_LL.xz * tmp657;
double tmp677 = tmp674 + tmp675;
double tmp678 = ABar_LL.xz * tmp655;
double tmp679 = tmp676 + tmp677;
double tmp680 = ABar_LL.xy * tmp651;
double tmp681 = tmp678 + tmp679;
double tmp682 = ABar_LL.xy * tmp647;
double tmp683 = tmp680 + tmp681;
double tmp684 = ABar_LL.xx * tmp643;
double tmp685 = tmp682 + tmp683;
double tmp686 = tmp684 + tmp685;
double tmp687 = partial_gammaBar_LLl[1].zz * tmp1;
double tmp688 = partial_gammaBar_LLl[0].zz * tmp44;
double tmp689 = gammaBar_UU.xy * tmp687;
double tmp690 = gammaBar_UU.xx * tmp688;
double tmp691 = tmp689 + tmp690;
double tmp692 = tmp280 + tmp691;
double tmp693 = gammaBar_UU.xy * tmp563;
double tmp694 = gammaBar_UU.xz * tmp692;
double tmp695 = gammaBar_UU.xx * tmp461;
double tmp696 = tmp693 + tmp694;
double tmp697 = tmp695 + tmp696;
double tmp698 = gammaBar_UU.yy * tmp687;
double tmp699 = gammaBar_UU.xy * tmp688;
double tmp700 = tmp698 + tmp699;
double tmp701 = tmp303 + tmp700;
double tmp702 = gammaBar_UU.xy * tmp576;
double tmp703 = gammaBar_UU.xz * tmp701;
double tmp704 = gammaBar_UU.xx * tmp479;
double tmp705 = tmp702 + tmp703;
double tmp706 = tmp704 + tmp705;
double tmp707 = gammaBar_UU.yy * tmp563;
double tmp708 = gammaBar_UU.yz * tmp692;
double tmp709 = gammaBar_UU.xy * tmp461;
double tmp710 = tmp707 + tmp708;
double tmp711 = tmp709 + tmp710;
double tmp712 = gammaBar_UU.yz * tmp687;
double tmp713 = gammaBar_UU.xz * tmp688;
double tmp714 = tmp712 + tmp713;
double tmp715 = tmp330 + tmp714;
double tmp716 = gammaBar_UU.xy * tmp594;
double tmp717 = gammaBar_UU.xz * tmp715;
double tmp718 = gammaBar_UU.xx * tmp503;
double tmp719 = tmp716 + tmp717;
double tmp720 = tmp718 + tmp719;
double tmp721 = gammaBar_UU.zz * tmp692;
double tmp722 = tmp583 + tmp721;
double tmp723 = tmp463 + tmp722;
double tmp724 = gammaBar_UU.yy * tmp576;
double tmp725 = gammaBar_UU.yz * tmp701;
double tmp726 = gammaBar_UU.xy * tmp479;
double tmp727 = tmp724 + tmp725;
double tmp728 = tmp726 + tmp727;
double tmp729 = gammaBar_UU.yy * tmp594;
double tmp730 = gammaBar_UU.yz * tmp715;
double tmp731 = gammaBar_UU.xy * tmp503;
double tmp732 = tmp729 + tmp730;
double tmp733 = tmp731 + tmp732;
double tmp734 = gammaBar_UU.zz * tmp701;
double tmp735 = tmp606 + tmp734;
double tmp736 = tmp481 + tmp735;
double tmp737 = gammaBar_UU.zz * tmp715;
double tmp738 = tmp610 + tmp737;
double tmp739 = tmp505 + tmp738;
double tmp740 = ABar_LL.yz * tmp736;
double tmp741 = ABar_LL.zz * tmp739;
double tmp742 = ABar_LL.yz * tmp733;
double tmp743 = tmp740 + tmp741;
double tmp744 = ABar_LL.yy * tmp728;
double tmp745 = tmp742 + tmp743;
double tmp746 = ABar_LL.xz * tmp723;
double tmp747 = tmp744 + tmp745;
double tmp748 = ABar_LL.xz * tmp720;
double tmp749 = tmp746 + tmp747;
double tmp750 = ABar_LL.xy * tmp711;
double tmp751 = tmp748 + tmp749;
double tmp752 = ABar_LL.xy * tmp706;
double tmp753 = tmp750 + tmp751;
double tmp754 = ABar_LL.xx * tmp697;
double tmp755 = tmp752 + tmp753;
double tmp756 = tmp754 + tmp755;
double tmp757 = partial_alpha_l.y * tmp1;
double tmp758 = partial_alpha_l.x * tmp44;
double tmp759 = C_U.y * tmp757;
double tmp760 = C_U.x * tmp758;
double tmp761 = C_U.z * partial_alpha_l.z;
double tmp762 = tmp759 + tmp760;
double tmp763 = tmp761 + tmp762;
double tmp764 = gammaBar_UU.xy * tmp175;
double tmp765 = gammaBar_UU.xz * tmp288;
double tmp766 = gammaBar_UU.xx * tmp59;
double tmp767 = tmp764 + tmp765;
double tmp768 = tmp766 + tmp767;
double tmp769 = gammaBar_UU.xy * tmp196;
double tmp770 = gammaBar_UU.xz * tmp311;
double tmp771 = gammaBar_UU.xx * tmp82;
double tmp772 = tmp769 + tmp770;
double tmp773 = tmp771 + tmp772;
double tmp774 = gammaBar_UU.yy * tmp175;
double tmp775 = gammaBar_UU.yz * tmp288;
double tmp776 = gammaBar_UU.xy * tmp59;
double tmp777 = tmp774 + tmp775;
double tmp778 = tmp776 + tmp777;
double tmp779 = gammaBar_UU.xy * tmp223;
double tmp780 = gammaBar_UU.xz * tmp335;
double tmp781 = gammaBar_UU.xx * tmp110;
double tmp782 = tmp779 + tmp780;
double tmp783 = tmp781 + tmp782;
double tmp784 = gammaBar_UU.yz * tmp175;
double tmp785 = gammaBar_UU.zz * tmp288;
double tmp786 = gammaBar_UU.xz * tmp59;
double tmp787 = tmp784 + tmp785;
double tmp788 = tmp786 + tmp787;
double tmp789 = gammaBar_UU.yy * tmp196;
double tmp790 = gammaBar_UU.yz * tmp311;
double tmp791 = gammaBar_UU.xy * tmp82;
double tmp792 = tmp789 + tmp790;
double tmp793 = tmp791 + tmp792;
double tmp794 = gammaBar_UU.yy * tmp223;
double tmp795 = gammaBar_UU.yz * tmp335;
double tmp796 = gammaBar_UU.xy * tmp110;
double tmp797 = tmp794 + tmp795;
double tmp798 = tmp796 + tmp797;
double tmp799 = gammaBar_UU.yz * tmp196;
double tmp800 = gammaBar_UU.zz * tmp311;
double tmp801 = gammaBar_UU.xz * tmp82;
double tmp802 = tmp799 + tmp800;
double tmp803 = tmp801 + tmp802;
double tmp804 = gammaBar_UU.yz * tmp223;
double tmp805 = gammaBar_UU.zz * tmp335;
double tmp806 = gammaBar_UU.xz * tmp110;
double tmp807 = tmp804 + tmp805;
double tmp808 = tmp806 + tmp807;
double tmp809 = ABar_LL.yz * tmp803;
double tmp810 = ABar_LL.zz * tmp808;
double tmp811 = ABar_LL.yz * tmp798;
double tmp812 = tmp809 + tmp810;
double tmp813 = ABar_LL.yy * tmp793;
double tmp814 = tmp811 + tmp812;
double tmp815 = ABar_LL.xz * tmp788;
double tmp816 = tmp813 + tmp814;
double tmp817 = ABar_LL.xz * tmp783;
double tmp818 = tmp815 + tmp816;
double tmp819 = ABar_LL.xy * tmp778;
double tmp820 = tmp817 + tmp818;
double tmp821 = ABar_LL.xy * tmp773;
double tmp822 = tmp819 + tmp820;
double tmp823 = ABar_LL.xx * tmp768;
double tmp824 = tmp821 + tmp822;
double tmp825 = tmp823 + tmp824;
double tmp826 = tmp1 * tmp825;
double tmp827 = gammaBar_UU.xy * tmp181;
double tmp828 = gammaBar_UU.xz * tmp294;
double tmp829 = gammaBar_UU.xx * tmp65;
double tmp830 = tmp827 + tmp828;
double tmp831 = tmp829 + tmp830;
double tmp832 = gammaBar_UU.xy * tmp201;
double tmp833 = gammaBar_UU.xz * tmp317;
double tmp834 = gammaBar_UU.xx * tmp88;
double tmp835 = tmp832 + tmp833;
double tmp836 = tmp834 + tmp835;
double tmp837 = gammaBar_UU.yy * tmp181;
double tmp838 = gammaBar_UU.yz * tmp294;
double tmp839 = gammaBar_UU.xy * tmp65;
double tmp840 = tmp837 + tmp838;
double tmp841 = tmp839 + tmp840;
double tmp842 = gammaBar_UU.xy * tmp229;
double tmp843 = gammaBar_UU.xz * tmp339;
double tmp844 = gammaBar_UU.xx * tmp116;
double tmp845 = tmp842 + tmp843;
double tmp846 = tmp844 + tmp845;
double tmp847 = gammaBar_UU.yz * tmp181;
double tmp848 = gammaBar_UU.zz * tmp294;
double tmp849 = gammaBar_UU.xz * tmp65;
double tmp850 = tmp847 + tmp848;
double tmp851 = tmp849 + tmp850;
double tmp852 = gammaBar_UU.yy * tmp201;
double tmp853 = gammaBar_UU.yz * tmp317;
double tmp854 = gammaBar_UU.xy * tmp88;
double tmp855 = tmp852 + tmp853;
double tmp856 = tmp854 + tmp855;
double tmp857 = gammaBar_UU.yy * tmp229;
double tmp858 = gammaBar_UU.yz * tmp339;
double tmp859 = gammaBar_UU.xy * tmp116;
double tmp860 = tmp857 + tmp858;
double tmp861 = tmp859 + tmp860;
double tmp862 = gammaBar_UU.yz * tmp201;
double tmp863 = gammaBar_UU.zz * tmp317;
double tmp864 = gammaBar_UU.xz * tmp88;
double tmp865 = tmp862 + tmp863;
double tmp866 = tmp864 + tmp865;
double tmp867 = gammaBar_UU.yz * tmp229;
double tmp868 = gammaBar_UU.zz * tmp339;
double tmp869 = gammaBar_UU.xz * tmp116;
double tmp870 = tmp867 + tmp868;
double tmp871 = tmp869 + tmp870;
double tmp872 = ABar_LL.yz * tmp866;
double tmp873 = ABar_LL.zz * tmp871;
double tmp874 = ABar_LL.yz * tmp861;
double tmp875 = tmp872 + tmp873;
double tmp876 = ABar_LL.yy * tmp856;
double tmp877 = tmp874 + tmp875;
double tmp878 = ABar_LL.xz * tmp851;
double tmp879 = tmp876 + tmp877;
double tmp880 = ABar_LL.xz * tmp846;
double tmp881 = tmp878 + tmp879;
double tmp882 = ABar_LL.xy * tmp841;
double tmp883 = tmp880 + tmp881;
double tmp884 = ABar_LL.xy * tmp836;
double tmp885 = tmp882 + tmp883;
double tmp886 = ABar_LL.xx * tmp831;
double tmp887 = tmp884 + tmp885;
double tmp888 = tmp886 + tmp887;
double tmp889 = tmp1 * tmp888;
double tmp890 = r * tmp889;
double tmp891 = U->beta_U.y * tmp826;
double tmp892 = U->beta_U.x * tmp890;
double tmp893 = tmp5 * tmp763;
double tmp894 = tmp891 + tmp892;
double tmp895 = U->beta_U.z * tmp756;
double tmp896 = tmp893 + tmp894;
double tmp897 = U->beta_U.z * tmp686;
double tmp898 = tmp895 + tmp896;
double tmp899 = U->beta_U.y * tmp639;
double tmp900 = tmp897 + tmp898;
double tmp901 = U->beta_U.x * tmp550;
double tmp902 = tmp899 + tmp900;
double tmp903 = -1. * tmp443;
double tmp904 = tmp901 + tmp902;
double tmp905 = -1. * tmp393;
double tmp906 = tmp903 + tmp904;
double tmp907 = tmp905 + tmp906;
double tmp908 = partial_beta_Ul[1].y * tmp1;
double tmp909 = partial_beta_Ul[0].x * tmp44;
double tmp910 = tmp908 + tmp909;
double tmp911 = partial_beta_Ul[2].z + tmp910;
double tmp912 = r * r;
double tmp913 = 1. / tmp912;
double tmp914 = 1. / tmp9;
double tmp915 = tmp913 * tmp914;
double tmp916 = 1. / 3.;
double tmp917 = gammaBar_UU.yz * tmp757;
double tmp918 = gammaBar_UU.xz * tmp758;
double tmp919 = gammaBar_UU.zz * partial_alpha_l.z;
double tmp920 = tmp917 + tmp918;
double tmp921 = tmp919 + tmp920;
double tmp922 = gammaBar_UU.yy * tmp757;
double tmp923 = gammaBar_UU.xy * tmp758;
double tmp924 = gammaBar_UU.yz * partial_alpha_l.z;
double tmp925 = tmp922 + tmp923;
double tmp926 = tmp924 + tmp925;
double tmp927 = tmp1 * tmp926;
double tmp928 = gammaBar_UU.xy * tmp757;
double tmp929 = gammaBar_UU.xx * tmp758;
double tmp930 = gammaBar_UU.xz * partial_alpha_l.z;
double tmp931 = tmp928 + tmp929;
double tmp932 = tmp930 + tmp931;
double tmp933 = tmp1 * tmp932;
double tmp934 = r * tmp933;
double tmp935 = partial_W_l.y * tmp927;
double tmp936 = partial_W_l.x * tmp934;
double tmp937 = partial_W_l.z * tmp921;
double tmp938 = tmp935 + tmp936;
double tmp939 = tmp937 + tmp938;
double tmp940 = U->LambdaBar_U.y * tmp757;
double tmp941 = U->LambdaBar_U.x * tmp758;
double tmp942 = U->LambdaBar_U.z * partial_alpha_l.z;
double tmp943 = R_LL.xy * gammaBar_UU.xy;
double tmp944 = R_LL.xz * gammaBar_UU.xz;
double tmp945 = R_LL.yz * gammaBar_UU.yz;
double tmp946 = 2. * tmp944;
double tmp947 = 2. * tmp945;
double tmp948 = 2. * tmp943;
double tmp949 = tmp946 + tmp947;
double tmp950 = R_LL.zz * gammaBar_UU.zz;
double tmp951 = tmp948 + tmp949;
double tmp952 = R_LL.yy * gammaBar_UU.yy;
double tmp953 = tmp950 + tmp951;
double tmp954 = R_LL.xx * gammaBar_UU.xx;
double tmp955 = tmp952 + tmp953;
double tmp956 = tmp954 + tmp955;
double tmp957 = tmp1 * tmp956;
double tmp958 = r * tmp957;
double tmp959 = tmp5 * tmp9;
double tmp960 = partial2_alpha_ll.yy * tmp959;
double tmp961 = partial2_alpha_ll.zz * tmp5;
double tmp962 = tmp9 * tmp912;
double tmp963 = tmp5 * tmp962;
double tmp964 = partial2_alpha_ll.xx * tmp963;
double tmp965 = r * tmp959;
double tmp966 = partial2_alpha_ll.xy * tmp965;
double tmp967 = gammaBar_UU.xy * tmp966;
double tmp968 = partial2_alpha_ll.yz * tmp47;
double tmp969 = gammaBar_UU.yz * tmp968;
double tmp970 = partial2_alpha_ll.xz * tmp48;
double tmp971 = gammaBar_UU.xz * tmp970;
double tmp972 = 2. * tmp969;
double tmp973 = 2. * tmp971;
double tmp974 = 2. * tmp967;
double tmp975 = tmp972 + tmp973;
double tmp976 = gammaBar_UU.xx * tmp964;
double tmp977 = tmp974 + tmp975;
double tmp978 = gammaBar_UU.zz * tmp961;
double tmp979 = tmp976 + tmp977;
double tmp980 = gammaBar_UU.yy * tmp960;
double tmp981 = tmp978 + tmp979;
double tmp982 = tmp980 + tmp981;
double tmp983 = tmp915 * tmp982;
double tmp984 = 1. / 2.;
double tmp985 = U->beta_U.x * tmp1;
double tmp986 = U->beta_U.y * tmp2;
double tmp987 = 2. * tmp985;
double tmp988 = tmp986 + tmp987;
double tmp989 = r * tmp912;
double tmp990 = tmp1 * tmp988;
double tmp991 = tmp989 * tmp990;
double tmp992 = 1. / det_gammaBar;
double tmp993 = gammaBar_LL.xy * tmp26;
double tmp994 = gammaBar_UU.xy * gammaBar_UU.xy;
double tmp995 = gammaBar_LL.xy * gammaBar_LL.xy;
double tmp996 = tmp1 * tmp994;
double tmp997 = gammaBar_UU.yy * tmp2;
double tmp998 = tmp16 + tmp997;
double tmp999 = gammaBar_UU.xz * tmp998;
double tmp1000 = gammaBar_LL.xz * tmp999;
double tmp1001 = tmp995 * tmp996;
double tmp1002 = gammaBar_LL.xy * tmp1000;
double tmp1003 = tmp1001 + tmp1002;
double tmp1004 = gammaBar_UU.xx * tmp1;
double tmp1005 = gammaBar_UU.xy * tmp2;
double tmp1006 = tmp1004 + tmp1005;
double tmp1007 = gammaBar_UU.xz * tmp1006;
double tmp1008 = gammaBar_UU.xx * tmp16;
double tmp1009 = gammaBar_LL.xz * tmp1007;
double tmp1010 = gammaBar_LL.xy * tmp1008;
double tmp1011 = tmp1009 + tmp1010;
double tmp1012 = gammaBar_LL.xy * tmp1011;
double tmp1013 = gammaBar_UU.yz * tmp1006;
double tmp1014 = gammaBar_UU.yy * tmp1;
double tmp1015 = gammaBar_UU.xx * tmp1014;
double tmp1016 = gammaBar_LL.xz * tmp1013;
double tmp1017 = gammaBar_LL.xy * tmp1015;
double tmp1018 = tmp1016 + tmp1017;
double tmp1019 = gammaBar_LL.xy * tmp1018;
double tmp1020 = gammaBar_UU.zz * tmp1006;
double tmp1021 = gammaBar_UU.yz * tmp1;
double tmp1022 = gammaBar_UU.xx * tmp1021;
double tmp1023 = gammaBar_LL.xz * tmp1020;
double tmp1024 = gammaBar_LL.xy * tmp1022;
double tmp1025 = tmp1023 + tmp1024;
double tmp1026 = gammaBar_LL.xy * tmp1025;
double tmp1027 = gammaBar_UU.yz * tmp998;
double tmp1028 = gammaBar_UU.xy * tmp1014;
double tmp1029 = gammaBar_LL.xz * tmp1027;
double tmp1030 = gammaBar_LL.xy * tmp1028;
double tmp1031 = tmp1029 + tmp1030;
double tmp1032 = gammaBar_LL.xy * tmp1031;
double tmp1033 = gammaBar_UU.yz * tmp6;
double tmp1034 = gammaBar_UU.xz * tmp1014;
double tmp1035 = gammaBar_LL.xz * tmp1033;
double tmp1036 = gammaBar_LL.xy * tmp1034;
double tmp1037 = tmp1035 + tmp1036;
double tmp1038 = gammaBar_LL.xy * tmp1037;
double tmp1039 = gammaBar_UU.zz * tmp998;
double tmp1040 = gammaBar_UU.xy * tmp1021;
double tmp1041 = gammaBar_LL.xz * tmp1039;
double tmp1042 = gammaBar_LL.xy * tmp1040;
double tmp1043 = tmp1041 + tmp1042;
double tmp1044 = gammaBar_LL.xy * tmp1043;
double tmp1045 = gammaBar_UU.zz * tmp6;
double tmp1046 = gammaBar_UU.xz * tmp1021;
double tmp1047 = gammaBar_LL.xz * tmp1045;
double tmp1048 = gammaBar_LL.xy * tmp1046;
double tmp1049 = tmp1047 + tmp1048;
double tmp1050 = gammaBar_LL.xy * tmp1049;
double tmp1051 = gammaBar_LL.xz * tmp6;
double tmp1052 = gammaBar_LL.xy * tmp16;
double tmp1053 = tmp1051 + tmp1052;
double tmp1054 = gammaBar_UU.xz * tmp1053;
double tmp1055 = gammaBar_LL.xy * tmp1054;
double tmp1056 = ABar_LL.zz * tmp1050;
double tmp1057 = ABar_LL.xz * tmp1055;
double tmp1058 = ABar_LL.yz * tmp1044;
double tmp1059 = tmp1056 + tmp1057;
double tmp1060 = ABar_LL.yz * tmp1038;
double tmp1061 = tmp1058 + tmp1059;
double tmp1062 = ABar_LL.yy * tmp1032;
double tmp1063 = tmp1060 + tmp1061;
double tmp1064 = ABar_LL.xz * tmp1026;
double tmp1065 = tmp1062 + tmp1063;
double tmp1066 = ABar_LL.xy * tmp1019;
double tmp1067 = tmp1064 + tmp1065;
double tmp1068 = ABar_LL.xx * tmp1012;
double tmp1069 = tmp1066 + tmp1067;
double tmp1070 = ABar_LL.xy * tmp1003;
double tmp1071 = tmp1068 + tmp1069;
double tmp1072 = tmp1070 + tmp1071;
double tmp1073 = gammaBar_LL.yz * tmp1007;
double tmp1074 = gammaBar_LL.yy * tmp1008;
double tmp1075 = tmp1073 + tmp1074;
double tmp1076 = gammaBar_LL.yy * tmp996;
double tmp1077 = gammaBar_LL.yz * tmp999;
double tmp1078 = tmp1076 + tmp1077;
double tmp1079 = gammaBar_LL.yz * tmp1013;
double tmp1080 = gammaBar_LL.yy * tmp1015;
double tmp1081 = tmp1079 + tmp1080;
double tmp1082 = gammaBar_LL.yz * tmp1020;
double tmp1083 = gammaBar_LL.yy * tmp1022;
double tmp1084 = tmp1082 + tmp1083;
double tmp1085 = gammaBar_LL.yz * tmp1027;
double tmp1086 = gammaBar_LL.yy * tmp1028;
double tmp1087 = tmp1085 + tmp1086;
double tmp1088 = gammaBar_LL.yz * tmp1033;
double tmp1089 = gammaBar_LL.yy * tmp1034;
double tmp1090 = tmp1088 + tmp1089;
double tmp1091 = gammaBar_LL.yz * tmp1039;
double tmp1092 = gammaBar_LL.yy * tmp1040;
double tmp1093 = tmp1091 + tmp1092;
double tmp1094 = gammaBar_LL.yz * tmp1045;
double tmp1095 = gammaBar_LL.yy * tmp1046;
double tmp1096 = tmp1094 + tmp1095;
double tmp1097 = gammaBar_LL.yz * tmp6;
double tmp1098 = gammaBar_LL.yy * tmp16;
double tmp1099 = tmp1097 + tmp1098;
double tmp1100 = gammaBar_UU.xz * tmp1099;
double tmp1101 = ABar_LL.zz * tmp1096;
double tmp1102 = ABar_LL.xz * tmp1100;
double tmp1103 = ABar_LL.yz * tmp1093;
double tmp1104 = tmp1101 + tmp1102;
double tmp1105 = ABar_LL.yz * tmp1090;
double tmp1106 = tmp1103 + tmp1104;
double tmp1107 = ABar_LL.yy * tmp1087;
double tmp1108 = tmp1105 + tmp1106;
double tmp1109 = ABar_LL.xz * tmp1084;
double tmp1110 = tmp1107 + tmp1108;
double tmp1111 = ABar_LL.xy * tmp1081;
double tmp1112 = tmp1109 + tmp1110;
double tmp1113 = ABar_LL.xy * tmp1078;
double tmp1114 = tmp1111 + tmp1112;
double tmp1115 = ABar_LL.xx * tmp1075;
double tmp1116 = tmp1113 + tmp1114;
double tmp1117 = tmp1115 + tmp1116;
double tmp1118 = gammaBar_LL.xy * tmp1117;
double tmp1119 = gammaBar_LL.zz * tmp1007;
double tmp1120 = gammaBar_LL.yz * tmp1008;
double tmp1121 = tmp1119 + tmp1120;
double tmp1122 = gammaBar_LL.yz * tmp996;
double tmp1123 = gammaBar_LL.zz * tmp999;
double tmp1124 = tmp1122 + tmp1123;
double tmp1125 = gammaBar_LL.zz * tmp1013;
double tmp1126 = gammaBar_LL.yz * tmp1015;
double tmp1127 = tmp1125 + tmp1126;
double tmp1128 = gammaBar_LL.zz * tmp1020;
double tmp1129 = gammaBar_LL.yz * tmp1022;
double tmp1130 = tmp1128 + tmp1129;
double tmp1131 = gammaBar_LL.zz * tmp1027;
double tmp1132 = gammaBar_LL.yz * tmp1028;
double tmp1133 = tmp1131 + tmp1132;
double tmp1134 = gammaBar_LL.zz * tmp1033;
double tmp1135 = gammaBar_LL.yz * tmp1034;
double tmp1136 = tmp1134 + tmp1135;
double tmp1137 = gammaBar_LL.zz * tmp1039;
double tmp1138 = gammaBar_LL.yz * tmp1040;
double tmp1139 = tmp1137 + tmp1138;
double tmp1140 = gammaBar_LL.zz * tmp1045;
double tmp1141 = gammaBar_LL.yz * tmp1046;
double tmp1142 = tmp1140 + tmp1141;
double tmp1143 = gammaBar_LL.zz * tmp6;
double tmp1144 = gammaBar_LL.yz * tmp16;
double tmp1145 = tmp1143 + tmp1144;
double tmp1146 = gammaBar_UU.xz * tmp1145;
double tmp1147 = ABar_LL.zz * tmp1142;
double tmp1148 = ABar_LL.xz * tmp1146;
double tmp1149 = ABar_LL.yz * tmp1139;
double tmp1150 = tmp1147 + tmp1148;
double tmp1151 = ABar_LL.yz * tmp1136;
double tmp1152 = tmp1149 + tmp1150;
double tmp1153 = ABar_LL.yy * tmp1133;
double tmp1154 = tmp1151 + tmp1152;
double tmp1155 = ABar_LL.xz * tmp1130;
double tmp1156 = tmp1153 + tmp1154;
double tmp1157 = ABar_LL.xy * tmp1127;
double tmp1158 = tmp1155 + tmp1156;
double tmp1159 = ABar_LL.xy * tmp1124;
double tmp1160 = tmp1157 + tmp1158;
double tmp1161 = ABar_LL.xx * tmp1121;
double tmp1162 = tmp1159 + tmp1160;
double tmp1163 = tmp1161 + tmp1162;
double tmp1164 = gammaBar_LL.xy * tmp1163;
double tmp1165 = U->beta_U.y * tmp1118;
double tmp1166 = U->beta_U.z * tmp1164;
double tmp1167 = U->beta_U.x * tmp1072;
double tmp1168 = tmp1165 + tmp1166;
double tmp1169 = tmp1167 + tmp1168;
double tmp1170 = ABar_LL.xy * partial_beta_Ul[1].y;
double tmp1171 = ABar_LL.xz * partial_beta_Ul[1].z;
double tmp1172 = ABar_LL.xx * partial_beta_Ul[1].x;
double tmp1173 = tmp1170 + tmp1171;
double tmp1174 = tmp1172 + tmp1173;
double tmp1175 = ABar_LL.yy * U->beta_U.y;
double tmp1176 = ABar_LL.yz * U->beta_U.z;
double tmp1177 = U->beta_U.z * tmp2;
double tmp1178 = ABar_LL.xz * tmp1177;
double tmp1179 = partial_ABar_LLl[1].xy * tmp1;
double tmp1180 = partial2_alpha_ll.xy * tmp47;
double tmp1181 = ABar_LL.yy * partial_beta_Ul[0].y;
double tmp1182 = ABar_LL.yz * partial_beta_Ul[0].z;
double tmp1183 = ABar_LL.xy * partial_beta_Ul[0].x;
double tmp1184 = tmp1181 + tmp1182;
double tmp1185 = tmp1183 + tmp1184;
double tmp1186 = tmp1 * tmp1185;
double tmp1187 = partial_ABar_LLl[0].xy * tmp44;
double tmp1188 = partial_W_l.x * tmp757;
double tmp1189 = W * tmp1188;
double tmp1190 = partial_alpha_l.x * tmp1;
double tmp1191 = partial_W_l.y * tmp1190;
double tmp1192 = W * tmp1191;
double tmp1193 = R_LL.xy * tmp49;
double tmp1194 = ABar_LL.xy * tmp46;
double tmp1195 = -1. * tmp1192;
double tmp1196 = -1. * tmp1189;
double tmp1197 = U->beta_U.x * tmp1187;
double tmp1198 = r * tmp1186;
double tmp1199 = -1. * tmp1180;
double tmp1200 = U->beta_U.y * tmp1179;
double tmp1201 = -1. * tmp1178;
double tmp1202 = ABar_LL.xy * tmp985;
double tmp1203 = tmp1 * tmp1174;
double tmp1204 = U->beta_U.z * partial_ABar_LLl[2].xy;
double tmp1205 = tmp895 + tmp899;
double tmp1206 = tmp901 + tmp1205;
double tmp1207 = gammaBar_LL.xy * tmp393;
double tmp1208 = gammaBar_LL.xy * tmp443;
double tmp1209 = tmp894 + tmp897;
double tmp1210 = ABar_LL.xy * tmp911;
double tmp1211 = gammaBar_LL.xy * tmp893;
double tmp1212 = tmp1166 + tmp1211;
double tmp1213 = -2. * tmp1210;
double tmp1214 = tmp1165 + tmp1212;
double tmp1215 = gammaBar_LL.xy * tmp1209;
double tmp1216 = tmp1213 + tmp1214;
double tmp1217 = -1. * tmp1208;
double tmp1218 = tmp1215 + tmp1216;
double tmp1219 = -1. * tmp1207;
double tmp1220 = tmp1217 + tmp1218;
double tmp1221 = gammaBar_LL.xy * tmp1206;
double tmp1222 = tmp1219 + tmp1220;
double tmp1223 = tmp1221 + tmp1222;
double tmp1224 = tmp1167 + tmp1223;
double tmp1225 = -1. * tmp1169;
double tmp1226 = -1. * tmp993;
double tmp1227 = gammaBar_LL.xy * tmp983;
double tmp1228 = tmp5 * tmp913;
double tmp1229 = partial_alpha_l.y * tmp1228;
double tmp1230 = tmp1 * tmp475;
double tmp1231 = tmp1 * tmp455;
double tmp1232 = r * tmp1231;
double tmp1233 = partial_alpha_l.y * tmp1230;
double tmp1234 = partial_alpha_l.x * tmp1232;
double tmp1235 = partial_alpha_l.z * tmp499;
double tmp1236 = tmp1233 + tmp1234;
double tmp1237 = tmp1235 + tmp1236;
double tmp1238 = tmp915 * tmp1237;
double tmp1239 = tmp5 * tmp1238;
double tmp1240 = tmp984 * tmp1239;
double tmp1241 = r * tmp60;
double tmp1242 = partial_alpha_l.y * tmp83;
double tmp1243 = partial_alpha_l.x * tmp1241;
double tmp1244 = partial_alpha_l.z * tmp110;
double tmp1245 = tmp1242 + tmp1243;
double tmp1246 = 1. / tmp1;
double tmp1247 = tmp1244 + tmp1245;
double tmp1248 = tmp913 * tmp1246;
double tmp1249 = tmp1247 * tmp1248;
double tmp1250 = tmp5 * tmp1249;
double tmp1251 = gammaBar_LL.yy * gammaBar_UU.yz;
double tmp1252 = gammaBar_LL.yz * gammaBar_UU.zz;
double tmp1253 = tmp1251 + tmp1252;
double tmp1254 = gammaBar_LL.yy * gammaBar_UU.yy;
double tmp1255 = gammaBar_LL.yz * gammaBar_UU.yz;
double tmp1256 = tmp1254 + tmp1255;
double tmp1257 = tmp1 * tmp1256;
double tmp1258 = gammaBar_LL.yy * gammaBar_UU.xy;
double tmp1259 = gammaBar_LL.yz * gammaBar_UU.xz;
double tmp1260 = tmp1258 + tmp1259;
double tmp1261 = tmp1 * tmp1260;
double tmp1262 = r * tmp1261;
double tmp1263 = partial_alpha_l.y * tmp1257;
double tmp1264 = partial_alpha_l.x * tmp1262;
double tmp1265 = partial_alpha_l.z * tmp1253;
double tmp1266 = tmp1263 + tmp1264;
double tmp1267 = tmp1265 + tmp1266;
double tmp1268 = partial_alpha_l.y * tmp202;
double tmp1269 = partial_alpha_l.x * tmp183;
double tmp1270 = partial_alpha_l.z * tmp229;
double tmp1271 = tmp1268 + tmp1269;
double tmp1272 = tmp1270 + tmp1271;
double tmp1273 = U->alpha * tmp958;
double tmp1274 = tmp941 + tmp1273;
double tmp1275 = tmp940 + tmp1274;
double tmp1276 = tmp942 + tmp1275;
double tmp1277 = gammaBar_LL.xy * tmp1276;
double tmp1278 = 3. * tmp1272;
double tmp1279 = -2. * tmp1277;
double tmp1280 = 1. / r;
double tmp1281 = tmp1278 + tmp1279;
double tmp1282 = tmp1246 * tmp1280;
double tmp1283 = tmp1281 * tmp1282;
double tmp1284 = 1. / 6.;
double tmp1285 = tmp5 * tmp1283;
double tmp1286 = tmp915 * tmp939;
double tmp1287 = gammaBar_LL.xy * tmp1286;
double tmp1288 = W * tmp1287;
double tmp1289 = tmp916 * tmp1288;
double tmp1290 = tmp2 * tmp915;
double tmp1291 = tmp921 * tmp1290;
double tmp1292 = tmp5 * tmp1291;
double tmp1293 = gammaBar_LL.xz * tmp1292;
double tmp1294 = 2. * tmp1289;
double tmp1295 = tmp984 * tmp1293;
double tmp1296 = tmp1284 * tmp1285;
double tmp1297 = tmp984 * tmp1250;
double tmp1298 = -1. * tmp1240;
double tmp1299 = tmp984 * tmp1229;
double tmp1300 = tmp916 * tmp1227;
double tmp1301 = ABar_LL.xy * tmp991;
double tmp1302 = det_gammaBar * gammaBar_LL.xy;
double tmp1303 = U->alpha * tmp1302;
double tmp1304 = S * tmp1303;
double tmp1305 = M_PI * tmp1304;
double tmp1306 = -1. * tmp1301;
double tmp1307 = 4. * tmp1305;
double tmp1308 = tmp1306 + tmp1307;
double tmp1309 = tmp992 * tmp1308;
double tmp1310 = tmp916 * tmp1309;
double tmp1311 = 2. * tmp1310;
double tmp1312 = gammaBar_LL.xz * tmp26;
double tmp1313 = tmp985 + tmp986;
double tmp1314 = partial2_alpha_ll.xz * tmp5;
double tmp1315 = ABar_LL.yz * U->beta_U.y;
double tmp1316 = ABar_LL.zz * U->beta_U.z;
double tmp1317 = partial_ABar_LLl[1].xz * tmp1;
double tmp1318 = partial_W_l.x * partial_alpha_l.z;
double tmp1319 = W * tmp1318;
double tmp1320 = partial_W_l.z * partial_alpha_l.x;
double tmp1321 = W * tmp1320;
double tmp1322 = ABar_LL.yz * partial_beta_Ul[0].y;
double tmp1323 = ABar_LL.zz * partial_beta_Ul[0].z;
double tmp1324 = ABar_LL.xz * partial_beta_Ul[0].x;
double tmp1325 = tmp1322 + tmp1323;
double tmp1326 = tmp1324 + tmp1325;
double tmp1327 = tmp1 * tmp1326;
double tmp1328 = partial_ABar_LLl[0].xz * tmp44;
double tmp1329 = R_LL.xz * tmp49;
double tmp1330 = ABar_LL.xz * tmp46;
double tmp1331 = U->beta_U.x * tmp1328;
double tmp1332 = r * tmp1327;
double tmp1333 = -1. * tmp1321;
double tmp1334 = -1. * tmp1319;
double tmp1335 = U->beta_U.y * tmp1317;
double tmp1336 = -1. * tmp1314;
double tmp1337 = U->beta_U.z * partial_ABar_LLl[2].xz;
double tmp1338 = ABar_LL.xz * tmp1313;
double tmp1339 = ABar_LL.xz * partial_beta_Ul[2].z;
double tmp1340 = ABar_LL.xy * partial_beta_Ul[2].y;
double tmp1341 = ABar_LL.xx * partial_beta_Ul[2].x;
double tmp1342 = ABar_LL.xz * tmp911;
double tmp1343 = gammaBar_LL.xz * tmp907;
double tmp1344 = -2. * tmp1342;
double tmp1345 = tmp1343 + tmp1344;
double tmp1346 = -1. * tmp1312;
double tmp1347 = gammaBar_LL.xz * tmp983;
double tmp1348 = tmp1 * tmp77;
double tmp1349 = tmp1 * tmp54;
double tmp1350 = r * tmp1349;
double tmp1351 = partial_alpha_l.y * tmp1348;
double tmp1352 = partial_alpha_l.x * tmp1350;
double tmp1353 = partial_alpha_l.z * tmp105;
double tmp1354 = tmp1351 + tmp1352;
double tmp1355 = tmp1353 + tmp1354;
double tmp1356 = tmp915 * tmp1355;
double tmp1357 = tmp5 * tmp1356;
double tmp1358 = tmp1 * tmp479;
double tmp1359 = tmp1 * tmp461;
double tmp1360 = r * tmp1359;
double tmp1361 = partial_alpha_l.y * tmp1358;
double tmp1362 = partial_alpha_l.x * tmp1360;
double tmp1363 = partial_alpha_l.z * tmp503;
double tmp1364 = tmp1361 + tmp1362;
double tmp1365 = tmp1363 + tmp1364;
double tmp1366 = tmp915 * tmp1365;
double tmp1367 = tmp5 * tmp1366;
double tmp1368 = tmp984 * tmp1367;
double tmp1369 = tmp1 * tmp998;
double tmp1370 = tmp1 * tmp1006;
double tmp1371 = r * tmp1370;
double tmp1372 = partial_alpha_l.y * tmp1369;
double tmp1373 = partial_alpha_l.x * tmp1371;
double tmp1374 = partial_alpha_l.z * tmp6;
double tmp1375 = tmp1372 + tmp1373;
double tmp1376 = tmp1374 + tmp1375;
double tmp1377 = tmp915 * tmp1376;
double tmp1378 = tmp5 * tmp1377;
double tmp1379 = gammaBar_LL.xz * tmp1378;
double tmp1380 = tmp984 * tmp1379;
double tmp1381 = tmp5 * tmp1248;
double tmp1382 = partial_alpha_l.z * tmp1381;
double tmp1383 = gammaBar_LL.zz * gammaBar_UU.zz;
double tmp1384 = tmp1255 + tmp1383;
double tmp1385 = gammaBar_LL.yz * gammaBar_UU.yy;
double tmp1386 = gammaBar_LL.zz * gammaBar_UU.yz;
double tmp1387 = tmp1385 + tmp1386;
double tmp1388 = tmp1 * tmp1387;
double tmp1389 = gammaBar_LL.yz * gammaBar_UU.xy;
double tmp1390 = gammaBar_LL.zz * gammaBar_UU.xz;
double tmp1391 = tmp1389 + tmp1390;
double tmp1392 = tmp1 * tmp1391;
double tmp1393 = r * tmp1392;
double tmp1394 = partial_alpha_l.y * tmp1388;
double tmp1395 = partial_alpha_l.x * tmp1393;
double tmp1396 = partial_alpha_l.z * tmp1384;
double tmp1397 = tmp1394 + tmp1395;
double tmp1398 = tmp1396 + tmp1397;
double tmp1399 = tmp1248 * tmp1398;
double tmp1400 = tmp5 * tmp1399;
double tmp1401 = partial_alpha_l.y * tmp318;
double tmp1402 = partial_alpha_l.x * tmp296;
double tmp1403 = partial_alpha_l.z * tmp339;
double tmp1404 = tmp1401 + tmp1402;
double tmp1405 = tmp1403 + tmp1404;
double tmp1406 = gammaBar_LL.xz * tmp1276;
double tmp1407 = 3. * tmp1405;
double tmp1408 = -2. * tmp1406;
double tmp1409 = tmp1407 + tmp1408;
double tmp1410 = tmp1282 * tmp1409;
double tmp1411 = tmp5 * tmp1410;
double tmp1412 = gammaBar_LL.xz * tmp1286;
double tmp1413 = W * tmp1412;
double tmp1414 = tmp916 * tmp1413;
double tmp1415 = tmp1284 * tmp1411;
double tmp1416 = 2. * tmp1414;
double tmp1417 = tmp984 * tmp1400;
double tmp1418 = tmp1415 + tmp1416;
double tmp1419 = tmp984 * tmp1382;
double tmp1420 = tmp1417 + tmp1418;
double tmp1421 = -1. * tmp1380;
double tmp1422 = tmp1419 + tmp1420;
double tmp1423 = -1. * tmp1368;
double tmp1424 = tmp1421 + tmp1422;
double tmp1425 = tmp984 * tmp1357;
double tmp1426 = tmp1423 + tmp1424;
double tmp1427 = tmp916 * tmp1347;
double tmp1428 = tmp1425 + tmp1426;
double tmp1429 = tmp1427 + tmp1428;
double tmp1430 = ABar_LL.xz * tmp991;
double tmp1431 = det_gammaBar * gammaBar_LL.xz;
double tmp1432 = U->alpha * tmp1431;
double tmp1433 = S * tmp1432;
double tmp1434 = M_PI * tmp1433;
double tmp1435 = -1. * tmp1430;
double tmp1436 = 4. * tmp1434;
double tmp1437 = tmp1435 + tmp1436;
double tmp1438 = tmp992 * tmp1437;
double tmp1439 = tmp916 * tmp1438;
double tmp1440 = 2. * tmp1439;
double tmp1441 = ABar_LL.yy * gammaBar_UU.xy;
double tmp1442 = ABar_LL.yz * gammaBar_UU.xz;
double tmp1443 = ABar_LL.xy * gammaBar_UU.xx;
double tmp1444 = tmp1441 + tmp1442;
double tmp1445 = tmp1443 + tmp1444;
double tmp1446 = ABar_LL.yy * gammaBar_UU.yy;
double tmp1447 = ABar_LL.yz * gammaBar_UU.yz;
double tmp1448 = tmp1446 + tmp1447;
double tmp1449 = tmp28 + tmp1448;
double tmp1450 = ABar_LL.yy * gammaBar_UU.yz;
double tmp1451 = ABar_LL.yz * gammaBar_UU.zz;
double tmp1452 = ABar_LL.xy * gammaBar_UU.xz;
double tmp1453 = tmp1450 + tmp1451;
double tmp1454 = tmp1452 + tmp1453;
double tmp1455 = tmp932 * tmp1248;
double tmp1456 = tmp5 * tmp1455;
double tmp1457 = tmp1 * tmp912;
double tmp1458 = tmp5 * tmp1457;
double tmp1459 = U->alpha * tmp1458;
double tmp1460 = U->alpha * tmp1457;
double tmp1461 = U->K * tmp1460;
double tmp1462 = gammaBar_LL.yy * gammaBar_LL.yy;
double tmp1463 = tmp996 * tmp1462;
double tmp1464 = gammaBar_LL.yy * tmp1077;
double tmp1465 = tmp1463 + tmp1464;
double tmp1466 = gammaBar_LL.yy * tmp1075;
double tmp1467 = gammaBar_LL.yy * tmp1081;
double tmp1468 = gammaBar_LL.yy * tmp1084;
double tmp1469 = gammaBar_LL.yy * tmp1087;
double tmp1470 = gammaBar_LL.yy * tmp1090;
double tmp1471 = gammaBar_LL.yy * tmp1093;
double tmp1472 = gammaBar_LL.yy * tmp1096;
double tmp1473 = gammaBar_LL.yy * tmp1100;
double tmp1474 = ABar_LL.zz * tmp1472;
double tmp1475 = ABar_LL.xz * tmp1473;
double tmp1476 = ABar_LL.yz * tmp1471;
double tmp1477 = tmp1474 + tmp1475;
double tmp1478 = ABar_LL.yz * tmp1470;
double tmp1479 = tmp1476 + tmp1477;
double tmp1480 = ABar_LL.yy * tmp1469;
double tmp1481 = tmp1478 + tmp1479;
double tmp1482 = ABar_LL.xz * tmp1468;
double tmp1483 = tmp1480 + tmp1481;
double tmp1484 = ABar_LL.xy * tmp1467;
double tmp1485 = tmp1482 + tmp1483;
double tmp1486 = ABar_LL.xx * tmp1466;
double tmp1487 = tmp1484 + tmp1485;
double tmp1488 = ABar_LL.xy * tmp1465;
double tmp1489 = tmp1486 + tmp1487;
double tmp1490 = tmp1488 + tmp1489;
double tmp1491 = gammaBar_LL.xy * tmp996;
double tmp1492 = tmp1000 + tmp1491;
double tmp1493 = ABar_LL.zz * tmp1049;
double tmp1494 = ABar_LL.xz * tmp1054;
double tmp1495 = ABar_LL.yz * tmp1043;
double tmp1496 = tmp1493 + tmp1494;
double tmp1497 = ABar_LL.yz * tmp1037;
double tmp1498 = tmp1495 + tmp1496;
double tmp1499 = ABar_LL.yy * tmp1031;
double tmp1500 = tmp1497 + tmp1498;
double tmp1501 = ABar_LL.xz * tmp1025;
double tmp1502 = tmp1499 + tmp1500;
double tmp1503 = ABar_LL.xy * tmp1018;
double tmp1504 = tmp1501 + tmp1502;
double tmp1505 = ABar_LL.xy * tmp1492;
double tmp1506 = tmp1503 + tmp1504;
double tmp1507 = ABar_LL.xx * tmp1011;
double tmp1508 = tmp1505 + tmp1506;
double tmp1509 = tmp1507 + tmp1508;
double tmp1510 = gammaBar_LL.yy * tmp1509;
double tmp1511 = gammaBar_LL.yy * tmp1163;
double tmp1512 = U->beta_U.x * tmp1510;
double tmp1513 = U->beta_U.z * tmp1511;
double tmp1514 = U->beta_U.y * tmp1490;
double tmp1515 = tmp1 * tmp1276;
double tmp1516 = r * tmp1515;
double tmp1517 = gammaBar_LL.yz * tmp26;
double tmp1518 = partial2_alpha_ll.yz * tmp5;
double tmp1519 = ABar_LL.yy * partial_beta_Ul[2].y;
double tmp1520 = ABar_LL.yz * partial_beta_Ul[2].z;
double tmp1521 = ABar_LL.xy * partial_beta_Ul[2].x;
double tmp1522 = tmp1519 + tmp1520;
double tmp1523 = tmp1521 + tmp1522;
double tmp1524 = partial_ABar_LLl[1].yz * tmp1;
double tmp1525 = partial_ABar_LLl[0].yz * tmp44;
double tmp1526 = U->beta_U.y * tmp1524;
double tmp1527 = U->beta_U.x * tmp1525;
double tmp1528 = U->beta_U.z * partial_ABar_LLl[2].yz;
double tmp1529 = tmp1526 + tmp1527;
double tmp1530 = tmp1528 + tmp1529;
double tmp1531 = ABar_LL.zz * tmp1177;
double tmp1532 = S_LL.yz * tmp49;
double tmp1533 = M_PI * tmp1532;
double tmp1534 = -1. * tmp1531;
double tmp1535 = -8. * tmp1533;
double tmp1536 = ABar_LL.yz * tmp985;
double tmp1537 = tmp1534 + tmp1535;
double tmp1538 = ABar_LL.yz * tmp1313;
double tmp1539 = tmp1536 + tmp1537;
double tmp1540 = tmp1538 + tmp1539;
double tmp1541 = partial_W_l.y * partial_alpha_l.z;
double tmp1542 = W * tmp1541;
double tmp1543 = partial_W_l.z * partial_alpha_l.y;
double tmp1544 = W * tmp1543;
double tmp1545 = ABar_LL.yz * partial_beta_Ul[1].y;
double tmp1546 = ABar_LL.zz * partial_beta_Ul[1].z;
double tmp1547 = ABar_LL.xz * partial_beta_Ul[1].x;
double tmp1548 = tmp1545 + tmp1546;
double tmp1549 = tmp1547 + tmp1548;
double tmp1550 = tmp1 * tmp1549;
double tmp1551 = ABar_LL.yz * tmp1461;
double tmp1552 = R_LL.yz * tmp1459;
double tmp1553 = r * tmp1550;
double tmp1554 = -1. * tmp1544;
double tmp1555 = -1. * tmp1542;
double tmp1556 = r * tmp1540;
double tmp1557 = r * tmp1530;
double tmp1558 = r * tmp1523;
double tmp1559 = -1. * tmp1518;
double tmp1560 = gammaBar_LL.yz * gammaBar_LL.yz;
double tmp1561 = tmp996 * tmp1560;
double tmp1562 = gammaBar_LL.yz * tmp1123;
double tmp1563 = tmp1561 + tmp1562;
double tmp1564 = gammaBar_LL.yz * tmp1121;
double tmp1565 = gammaBar_LL.yz * tmp1127;
double tmp1566 = gammaBar_LL.yz * tmp1130;
double tmp1567 = gammaBar_LL.yz * tmp1133;
double tmp1568 = gammaBar_LL.yz * tmp1136;
double tmp1569 = gammaBar_LL.yz * tmp1139;
double tmp1570 = gammaBar_LL.yz * tmp1142;
double tmp1571 = gammaBar_LL.yz * tmp1146;
double tmp1572 = ABar_LL.zz * tmp1570;
double tmp1573 = ABar_LL.xz * tmp1571;
double tmp1574 = ABar_LL.yz * tmp1569;
double tmp1575 = tmp1572 + tmp1573;
double tmp1576 = ABar_LL.yz * tmp1568;
double tmp1577 = tmp1574 + tmp1575;
double tmp1578 = ABar_LL.yy * tmp1567;
double tmp1579 = tmp1576 + tmp1577;
double tmp1580 = ABar_LL.xz * tmp1566;
double tmp1581 = tmp1578 + tmp1579;
double tmp1582 = ABar_LL.xy * tmp1565;
double tmp1583 = tmp1580 + tmp1581;
double tmp1584 = ABar_LL.xx * tmp1564;
double tmp1585 = tmp1582 + tmp1583;
double tmp1586 = ABar_LL.xy * tmp1563;
double tmp1587 = tmp1584 + tmp1585;
double tmp1588 = tmp1586 + tmp1587;
double tmp1589 = gammaBar_LL.yz * tmp1509;
double tmp1590 = gammaBar_LL.yz * tmp1117;
double tmp1591 = U->beta_U.x * tmp1589;
double tmp1592 = U->beta_U.y * tmp1590;
double tmp1593 = U->beta_U.z * tmp1588;
double tmp1594 = tmp1591 + tmp1592;
double tmp1595 = tmp1593 + tmp1594;
double tmp1596 = gammaBar_LL.yz * tmp393;
double tmp1597 = gammaBar_LL.yz * tmp443;
double tmp1598 = ABar_LL.yz * tmp911;
double tmp1599 = gammaBar_LL.yz * tmp893;
double tmp1600 = tmp1592 + tmp1599;
double tmp1601 = -2. * tmp1598;
double tmp1602 = tmp1591 + tmp1600;
double tmp1603 = gammaBar_LL.yz * tmp1209;
double tmp1604 = tmp1601 + tmp1602;
double tmp1605 = -1. * tmp1597;
double tmp1606 = tmp1603 + tmp1604;
double tmp1607 = -1. * tmp1596;
double tmp1608 = tmp1605 + tmp1606;
double tmp1609 = gammaBar_LL.yz * tmp1206;
double tmp1610 = tmp1607 + tmp1608;
double tmp1611 = tmp1609 + tmp1610;
double tmp1612 = -1. * tmp1595;
double tmp1613 = tmp1593 + tmp1611;
double tmp1614 = tmp1612 + tmp1613;
double tmp1615 = r * tmp1614;
double tmp1616 = -1. * tmp1517;
double tmp1617 = gammaBar_LL.yz * tmp983;
double tmp1618 = tmp1 * tmp192;
double tmp1619 = tmp1 * tmp170;
double tmp1620 = r * tmp1619;
double tmp1621 = partial_alpha_l.y * tmp1618;
double tmp1622 = partial_alpha_l.x * tmp1620;
double tmp1623 = partial_alpha_l.z * tmp218;
double tmp1624 = tmp1621 + tmp1622;
double tmp1625 = tmp1623 + tmp1624;
double tmp1626 = tmp915 * tmp1625;
double tmp1627 = tmp5 * tmp1626;
double tmp1628 = tmp1 * tmp576;
double tmp1629 = tmp1 * tmp563;
double tmp1630 = r * tmp1629;
double tmp1631 = partial_alpha_l.y * tmp1628;
double tmp1632 = partial_alpha_l.x * tmp1630;
double tmp1633 = partial_alpha_l.z * tmp594;
double tmp1634 = tmp1631 + tmp1632;
double tmp1635 = tmp1633 + tmp1634;
double tmp1636 = tmp915 * tmp1635;
double tmp1637 = tmp5 * tmp1636;
double tmp1638 = tmp984 * tmp1637;
double tmp1639 = gammaBar_LL.yz * tmp1378;
double tmp1640 = tmp984 * tmp1639;
double tmp1641 = tmp5 * tmp1290;
double tmp1642 = partial_alpha_l.z * tmp1641;
double tmp1643 = r * tmp289;
double tmp1644 = partial_alpha_l.y * tmp312;
double tmp1645 = partial_alpha_l.x * tmp1643;
double tmp1646 = partial_alpha_l.z * tmp335;
double tmp1647 = tmp1644 + tmp1645;
double tmp1648 = tmp1646 + tmp1647;
double tmp1649 = tmp1248 * tmp1648;
double tmp1650 = tmp5 * tmp1649;
double tmp1651 = gammaBar_LL.yz * tmp1286;
double tmp1652 = W * tmp1651;
double tmp1653 = tmp916 * tmp1652;
double tmp1654 = gammaBar_LL.yz * tmp1456;
double tmp1655 = tmp984 * tmp1654;
double tmp1656 = tmp915 * tmp921;
double tmp1657 = tmp2 * tmp1656;
double tmp1658 = tmp5 * tmp1657;
double tmp1659 = gammaBar_LL.zz * tmp1658;
double tmp1660 = tmp1276 * tmp1282;
double tmp1661 = tmp5 * tmp1660;
double tmp1662 = gammaBar_LL.yz * tmp1661;
double tmp1663 = tmp916 * tmp1662;
double tmp1664 = tmp984 * tmp1659;
double tmp1665 = -1. * tmp1663;
double tmp1666 = -1. * tmp1655;
double tmp1667 = tmp1664 + tmp1665;
double tmp1668 = 2. * tmp1653;
double tmp1669 = tmp1666 + tmp1667;
double tmp1670 = tmp984 * tmp1650;
double tmp1671 = tmp1668 + tmp1669;
double tmp1672 = tmp984 * tmp1642;
double tmp1673 = tmp1670 + tmp1671;
double tmp1674 = -1. * tmp1640;
double tmp1675 = tmp1672 + tmp1673;
double tmp1676 = -1. * tmp1638;
double tmp1677 = tmp1674 + tmp1675;
double tmp1678 = tmp984 * tmp1627;
double tmp1679 = tmp1676 + tmp1677;
double tmp1680 = tmp916 * tmp1617;
double tmp1681 = tmp1678 + tmp1679;
double tmp1682 = tmp1680 + tmp1681;
double tmp1683 = ABar_LL.yz * tmp991;
double tmp1684 = det_gammaBar * gammaBar_LL.yz;
double tmp1685 = U->alpha * tmp1684;
double tmp1686 = S * tmp1685;
double tmp1687 = M_PI * tmp1686;
double tmp1688 = -1. * tmp1683;
double tmp1689 = 4. * tmp1687;
double tmp1690 = tmp1688 + tmp1689;
double tmp1691 = tmp992 * tmp1690;
double tmp1692 = tmp916 * tmp1691;
double tmp1693 = 2. * tmp1692;
double tmp1694 = ABar_LL.yz * gammaBar_UU.xy;
double tmp1695 = ABar_LL.zz * gammaBar_UU.xz;
double tmp1696 = ABar_LL.xz * gammaBar_UU.xx;
double tmp1697 = tmp1694 + tmp1695;
double tmp1698 = tmp1696 + tmp1697;
double tmp1699 = ABar_LL.yz * gammaBar_UU.yy;
double tmp1700 = ABar_LL.zz * gammaBar_UU.yz;
double tmp1701 = ABar_LL.xz * gammaBar_UU.xy;
double tmp1702 = tmp1699 + tmp1700;
double tmp1703 = tmp1701 + tmp1702;
double tmp1704 = ABar_LL.zz * gammaBar_UU.zz;
double tmp1705 = tmp1447 + tmp1704;
double tmp1706 = tmp29 + tmp1705;
double dt_ABar_LL.xx = 2. * (4. * M_PI * S * U->alpha * det_gammaBar * gammaBar_LL.xx + -1. * ABar_LL.xx * tmp991) * tmp916 * tmp992 + (r * (3. * (U->beta_U.z * partial_ABar_LLl[2].xx + (-2. * (ABar_LL.xz * U->beta_U.z + ABar_LL.xy * U->beta_U.y) + 2. * r * (ABar_LL.xx * partial_beta_Ul[0].x + ABar_LL.xz * partial_beta_Ul[0].z + ABar_LL.xy * partial_beta_Ul[0].y) + -1. * partial2_alpha_ll.xx * tmp27 + -2. * U->alpha * r * (ABar_LL.xx * tmp32 + ABar_LL.xz * tmp42 + ABar_LL.xy * tmp37) + -8. * M_PI * S_LL.xx * tmp43 + -2. * W * partial_W_l.x * partial_alpha_l.x * r) * tmp1 + U->beta_U.y * partial_ABar_LLl[1].xx * tmp1 + U->beta_U.x * partial_ABar_LLl[0].xx * tmp44 + R_LL.xx * tmp49 + ABar_LL.xx * tmp46) + -2. * ABar_LL.xx * tmp911 + gammaBar_LL.xx * tmp907) * tmp1 + -1. * gammaBar_LL.xx * tmp26) * tmp915 * tmp916 + W * (W * (r * (3. * (partial_alpha_l.z * tmp116 + partial_alpha_l.x * tmp67 + partial_alpha_l.y * tmp89) + -1. * U->alpha * gammaBar_LL.xx * tmp958 + -1. * gammaBar_LL.xx * (tmp940 + tmp941 + tmp942)) + 3. * (partial_alpha_l.z * (gammaBar_LL.xz * gammaBar_UU.zz + gammaBar_LL.xy * gammaBar_UU.yz) + partial_alpha_l.x * r * (gammaBar_LL.xz * gammaBar_UU.xz + gammaBar_LL.xy * gammaBar_UU.xy) * tmp1 + partial_alpha_l.y * (gammaBar_LL.xz * gammaBar_UU.yz + gammaBar_LL.xy * gammaBar_UU.yy) * tmp1)) * tmp1 + 2. * gammaBar_LL.xx * tmp939) * tmp915 * tmp916 + -1. * (partial_alpha_l.z * tmp494 + partial_alpha_l.x * r * tmp1 * tmp449 + partial_alpha_l.y * tmp1 * tmp471) * tmp5 * tmp915 * tmp984 + gammaBar_LL.xx * tmp916 * tmp983;
double dt_ABar_LL.xy = (r * (3. * (-1. * (tmp1175 + tmp1176) * tmp1 + -2. * U->alpha * r * (ABar_LL.xy * tmp32 + ABar_LL.yz * tmp42 + ABar_LL.yy * tmp37) * tmp1 + -8. * M_PI * S_LL.xy * tmp49 + tmp1193 + tmp1194 + tmp1195 + tmp1196 + tmp1197 + tmp1198 + tmp1199 + tmp1200 + tmp1201 + tmp1202 + tmp1203 + tmp1204) + tmp1224 + tmp1225) * tmp1 + tmp1226) * tmp915 * tmp916 + (-1. * gammaBar_LL.xy * tmp932 + tmp1267) * tmp5 * tmp984 * tmp1248 + tmp1294 + tmp1295 + tmp1296 + tmp1297 + tmp1298 + tmp1299 + tmp1300 + tmp1311;
double dt_ABar_LL.xz = (r * (3. * (-1. * (tmp1315 + tmp1316) * tmp1 + -2. * U->alpha * r * (ABar_LL.xz * tmp32 + ABar_LL.zz * tmp42 + ABar_LL.yz * tmp37) * tmp1 + -8. * M_PI * S_LL.xz * tmp49 + tmp1329 + tmp1330 + tmp1331 + tmp1332 + tmp1333 + tmp1334 + tmp1335 + tmp1336 + tmp1337 + tmp1338 + tmp1339 + tmp1340 + tmp1341) + tmp1345) * tmp1 + tmp1346) * tmp915 * tmp916 + tmp1429 + tmp1440;
double dt_ABar_LL.xy = (r * (3. * (-1. * (8. * M_PI * S_LL.xy * tmp43 + tmp1175 + tmp1176) * tmp1 + -2. * U->alpha * r * (ABar_LL.xx * tmp1445 + ABar_LL.xz * tmp1454 + ABar_LL.xy * tmp1449) * tmp1 + tmp1193 + tmp1194 + tmp1195 + tmp1196 + tmp1197 + tmp1198 + tmp1199 + tmp1200 + tmp1201 + tmp1202 + tmp1203 + tmp1204) + tmp1224 + tmp1225) * tmp1 + tmp1226) * tmp915 * tmp916 + tmp5 * tmp984 * tmp1248 * tmp1267 + -1. * gammaBar_LL.xy * tmp984 * tmp1456 + tmp1294 + tmp1295 + tmp1296 + tmp1297 + tmp1298 + tmp1299 + tmp1300 + tmp1311;
double dt_ABar_LL.yy = 2. * (4. * M_PI * S * U->alpha * det_gammaBar * gammaBar_LL.yy + -1. * ABar_LL.yy * tmp991) * tmp916 * tmp992 + ((r * (-1. * (tmp1512 + tmp1513 + tmp1514) + gammaBar_LL.yy * tmp1206 + -1. * gammaBar_LL.yy * tmp393 + -1. * gammaBar_LL.yy * tmp443 + gammaBar_LL.yy * tmp1209 + -2. * ABar_LL.yy * tmp911 + gammaBar_LL.yy * tmp893 + tmp1512 + tmp1513 + tmp1514) + 3. * (r * (U->beta_U.z * partial_ABar_LLl[2].yy + U->beta_U.x * partial_ABar_LLl[0].yy * tmp44 + U->beta_U.y * partial_ABar_LLl[1].yy * tmp1) + 2. * r * (ABar_LL.yy * tmp985 + -4. * M_PI * S_LL.yy * tmp49 + -1. * ABar_LL.yz * tmp1177) + -1. * partial2_alpha_ll.yy * tmp47 + 2. * r * (ABar_LL.xy * partial_beta_Ul[1].x + ABar_LL.yz * partial_beta_Ul[1].z + ABar_LL.yy * partial_beta_Ul[1].y) * tmp1 + R_LL.yy * tmp1459 + -2. * U->alpha * (ABar_LL.xy * tmp1445 + ABar_LL.yz * tmp1454 + ABar_LL.yy * tmp1449) * tmp1 * tmp912 + ABar_LL.yy * tmp1461 + -2. * W * partial_W_l.y * tmp757)) * tmp1 + -1. * gammaBar_LL.yy * tmp26) * tmp915 * tmp916 + W * (2. * gammaBar_LL.yy * tmp939 + 3. * W * (partial_alpha_l.z * tmp223 + partial_alpha_l.x * r * tmp176 + partial_alpha_l.y * tmp197) * tmp1 + -3. * W * gammaBar_LL.yy * tmp933 + -1. * W * gammaBar_LL.yy * tmp1516 + 3. * W * gammaBar_LL.yz * tmp2 * tmp921) * tmp915 * tmp916 + -1. * (partial_alpha_l.z * tmp590 + partial_alpha_l.x * r * tmp1 * tmp557 + partial_alpha_l.y * tmp1 * tmp572) * tmp5 * tmp915 * tmp984 + gammaBar_LL.yy * tmp916 * tmp983;
double dt_ABar_LL.yz = ((3. * (-2. * U->alpha * (ABar_LL.xz * tmp1445 + ABar_LL.zz * tmp1454 + ABar_LL.yz * tmp1449) * tmp1 * tmp912 + tmp1551 + tmp1552 + tmp1553 + tmp1554 + tmp1555 + tmp1556 + tmp1557 + tmp1558 + tmp1559) + tmp1615) * tmp1 + tmp1616) * tmp915 * tmp916 + tmp1682 + tmp1693;
double dt_ABar_LL.xz = (r * (3. * (-1. * (8. * M_PI * S_LL.xz * tmp43 + tmp1315 + tmp1316) * tmp1 + -2. * U->alpha * r * (ABar_LL.xx * tmp1698 + ABar_LL.xz * tmp1706 + ABar_LL.xy * tmp1703) * tmp1 + tmp1329 + tmp1330 + tmp1331 + tmp1332 + tmp1333 + tmp1334 + tmp1335 + tmp1336 + tmp1337 + tmp1338 + tmp1339 + tmp1340 + tmp1341) + tmp1345) * tmp1 + tmp1346) * tmp915 * tmp916 + tmp1429 + tmp1440;
double dt_ABar_LL.yz = ((3. * (-2. * U->alpha * (ABar_LL.xy * tmp1698 + ABar_LL.yz * tmp1706 + ABar_LL.yy * tmp1703) * tmp1 * tmp912 + tmp1551 + tmp1552 + tmp1553 + tmp1554 + tmp1555 + tmp1556 + tmp1557 + tmp1558 + tmp1559) + tmp1615) * tmp1 + tmp1616) * tmp915 * tmp916 + tmp1682 + tmp1693;
double dt_ABar_LL.zz = 2. * (4. * M_PI * S * U->alpha * det_gammaBar * gammaBar_LL.zz + -1. * ABar_LL.zz * tmp991) * tmp916 * tmp992 + (3. * (-1. * tmp961 + r * (U->beta_U.z * partial_ABar_LLl[2].zz + U->beta_U.x * partial_ABar_LLl[0].zz * tmp44 + U->beta_U.y * partial_ABar_LLl[1].zz * tmp1) * tmp1 + -2. * U->alpha * (ABar_LL.xz * tmp1698 + ABar_LL.zz * tmp1706 + ABar_LL.yz * tmp1703) * tmp9 * tmp912 + -2. * W * partial_W_l.z * partial_alpha_l.z + 2. * r * (-4. * M_PI * S_LL.zz * tmp49 + ABar_LL.zz * tmp1313) * tmp1 + 2. * r * (ABar_LL.xz * partial_beta_Ul[2].x + ABar_LL.zz * partial_beta_Ul[2].z + ABar_LL.yz * partial_beta_Ul[2].y) * tmp1 + R_LL.zz * U->alpha * tmp963 + ABar_LL.zz * U->K * U->alpha * tmp962) + r * (-2. * ABar_LL.zz * tmp911 + gammaBar_LL.zz * tmp907) * tmp1 + -1. * gammaBar_LL.zz * tmp26) * tmp915 * tmp916 + W * (2. * gammaBar_LL.zz * tmp939 + 3. * W * (partial_alpha_l.z * tmp332 + partial_alpha_l.x * r * tmp1 * tmp283 + partial_alpha_l.y * tmp1 * tmp306) + -1. * W * gammaBar_LL.zz * tmp1516 + -3. * W * gammaBar_LL.zz * tmp1376) * tmp915 * tmp916 + -1. * (partial_alpha_l.z * tmp715 + partial_alpha_l.x * r * tmp1 * tmp692 + partial_alpha_l.y * tmp1 * tmp701) * tmp5 * tmp915 * tmp984 + gammaBar_LL.zz * tmp916 * tmp983;
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} = {{{{\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}}}}} + {{{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} {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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{C\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{C\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _C} _D}} {{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^B} ^C}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{C\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{G\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{G\downarrow E\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \cos\left( theta\right) & 0 \\ \cos\left( theta\right) & -{{{r}} {{\sin\left( theta\right)}}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \cos\left( theta\right) & 0 \\ \cos\left( theta\right) & -{{{r}} {{\sin\left( theta\right)}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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} \frac{2}{{r}^{3}} & 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} \frac{2}{{{{r}^{3}}} {{\sin\left( theta\right)}}} & \frac{\cos\left( theta\right)}{{{{r}^{2}}} {{{\sin\left( theta\right)}^{2}}}} & 0 \\ \frac{\cos\left( theta\right)}{{{{r}^{2}}} {{{\sin\left( theta\right)}^{2}}}} & \frac{{{\sin\left( theta\right)}^{2}} + {{{2}} {{{\cos\left( theta\right)}^{2}}}}}{{{r}} {{{\sin\left( theta\right)}^{3}}}} & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _a} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _d}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _c}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^B} _d}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^C} _b}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{B\downarrow D\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^c} _C} _a}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^G} _e}} {{U->alpha}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^B} _e}} {{U->alpha}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^E} _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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^D} _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} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _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]}} ^I} ^B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow e\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _c}} {{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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]}} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^D} _c}} {{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^G} _d}} {{U->alpha}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _a}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{f\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^H} _f}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _a}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^K} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow J\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow f\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _f}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _c}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _c}}} + {{{-1}} {{{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^E} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _H}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _D}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _e} ^H} _c}}} + {{{-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} {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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{G\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^H} _a}}} + {{{-1}} {{{ \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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _a}}} + {{{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} \frac{2}{{r}^{3}} & 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} \frac{2}{{{{r}^{3}}} {{\sin\left( theta\right)}}} & \frac{\cos\left( theta\right)}{{{{r}^{2}}} {{{\sin\left( theta\right)}^{2}}}} & 0 \\ \frac{\cos\left( theta\right)}{{{{r}^{2}}} {{{\sin\left( theta\right)}^{2}}}} & \frac{{{\sin\left( theta\right)}^{2}} + {{{2}} {{{\cos\left( theta\right)}^{2}}}}}{{{r}} {{{\sin\left( theta\right)}^{3}}}} & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} ^b} _B} _a} _b}}} + {{{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{A\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^a} _A} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 0\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{{det_gammaBar}}^{2}}}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 0\end{matrix} \right]}} _a}} {{{ \overset{b\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{{det_gammaBar}}^{2}}}}} + {{{-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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{C\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^c} _C} _c}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{A\downarrow B\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^I} _A} _B}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^b} _B} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & -{\frac{1}{r}} & 0 \\ 0 & 0 & -{\frac{1}{r}}\end{matrix} \right]} \\ \overset{B\downarrow C\rightarrow}{\left[ \begin{matrix} 0 & \frac{1}{r} & 0 \\ \frac{1}{r} & 0 & 0 \\ 0 & 0 & -{\frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}}}\end{matrix} \right]} \\ \overset{B\downarrow C\rightarrow}{\left[ \begin{matrix} 0 & 0 & \frac{1}{r} \\ 0 & 0 & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} \\ \frac{1}{r} & \frac{\cos\left( theta\right)}{{{r}} {{\sin\left( theta\right)}}} & 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} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{\frac{1}{{det_gammaBar}}}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \cos\left( theta\right) & 0 \\ \cos\left( theta\right) & -{{{r}} {{\sin\left( theta\right)}}} & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 & \cos\left( theta\right) & 0 \\ \cos\left( theta\right) & -{{{r}} {{\sin\left( theta\right)}}} & 0 \\ 0 & 0 & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^C} _a} _b}}} + {{{-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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _a}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow d\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _d}}} + {{{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _F}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _a} ^I} _b}}} + {{{-1}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{\frac{1}{{det_gammaBar}}}} {{U->alpha}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^I} _c}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{3}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _F}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _c}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _F}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^F} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^I} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\frac{1}{2}}} {{{ \overset{a\downarrow}{\left[ \begin{matrix} {{4}} {{{r}^{3}}} {{{\sin\left( theta\right)}^{2}}} \\ {{2}} {{{r}^{4}}} {{\cos\left( theta\right)}} {{\sin\left( theta\right)}} \\ 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{i\downarrow I\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{J\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^i} _J} _b}} {{\frac{1}{{det_gammaBar}}}}} + {{{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{B\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow D\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _d} ^I} _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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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} ^E}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{d\downarrow H\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^d} _H}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{H\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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}}} + {{{\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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _K}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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]}} ^E} ^F}} {{{{ \overset{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _K}} {{{{ \overset{e\downarrow E\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^e} _E}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{I\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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{a\downarrow A\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow K\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _K}} {{{{ \overset{f\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{F\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{K\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _f} ^K} _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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _c} ^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{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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 0\end{matrix} \right]}\end{matrix} \right]}} _b} ^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]}} ^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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow c\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 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 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^a} _A}} {{{{ \overset{b\downarrow B\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^b} _B}} {{{{ \overset{c\downarrow C\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{r} & 0 \\ 0 & 0 & \frac{1}{{{r}} {{\sin\left( theta\right)}}}\end{matrix} \right]}} ^c} _C}} {{{{ \overset{d\downarrow F\rightarrow}{\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & {{r}} {{\sin\left( theta\right)}}\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 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{E\downarrow a\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \sin\left( theta\right) & {{r}} {{\cos\left( theta\right)}} & 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 \\ -{\frac{1}{{r}^{2}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix} \right]} \\ \overset{D\downarrow b\rightarrow}{\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ -{\frac{1}{{{{r}^{2}}} {{\sin\left( theta\right)}}}} & -{\frac{\cos\left( theta\right)}{{{r}} {{{\sin\left( theta\right)}^{2}}}}} & 0\end{matrix} \right]}\end{matrix} \right]}} ^d} _D} _b}}}}$