Z4 formulation
For more background, see my derivation from the Einstein Field Equations (with Z4 Killing vectors) to initial value problems
here.
${{ \gamma} _i} _j$ = spatial metric
${{{{ d} _k} _i} _j} = {{{\frac{1}{2}}} {{{{{ \gamma} _i} _j} _{,k}}}}$ = spatial metric derivative
${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
${{ d} _i} = {{{{ d} _i} _k} ^k}$
${{ e} _i} = {{{{ d} ^k} _k} _i}$
${{{ b} ^i} _j} = {{{ \beta} ^i} _{,j}}$
${{{ \beta} ^i} _{,j}} = {{{ b} ^i} _j}$
connections:
${{{{ \Gamma} _i} _j} _k} = {{{\frac{1}{2}}} {{\left({{{{{ \gamma} _i} _j} _{,k}} + {{{{ \gamma} _i} _k} _{,j}}{-{{{{ \gamma} _j} _k} _{,i}}}}\right)}}}$
${{{{ \gamma} _i} _j} _{,k}} = {{{{{ \Gamma} _i} _k} _j} + {{{{ \Gamma} _j} _k} _i}}$
${{{{ \Gamma} ^i} _j} _k} = {{\frac{1}{2}} {{{{{ \gamma} ^i} ^m}} {{\left({{-{{{{ \gamma} _j} _k} _{,m}}} + {{{{ \gamma} _m} _k} _{,j}} + {{{{ \gamma} _m} _j} _{,k}}}\right)}}}}$
using ${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
${{{{ \Gamma} ^i} _j} _k} = {{{{{ \gamma} ^i} ^m}} {{\left({{-{{{{ d} _m} _j} _k}} + {{{{ d} _j} _m} _k} + {{{{ d} _k} _m} _j}}\right)}}}$
simplifying metrics:
${{{{ \Gamma} ^i} _j} _k} = {{{{-1}} {{{{{ d} ^i} _j} _k}}} + {{{{ d} _j} _k} ^i} + {{{{ d} _k} _j} ^i}}$
${{\left( \log\left( {\sqrt{\gamma}}\right)\right)} _{,i}} = {{{{ \Gamma} ^k} _k} _i}$ definition:
${{{{ \Gamma} ^k} _k} _i} = {{{{-1}} {{{{{ d} ^k} _k} _i}}} + {{{{ d} _k} _i} ^k} + {{{{ d} _i} _k} ^k}}$
${{ d} _i} = {{{{ \Gamma} ^k} _k} _i}$
${{ \Gamma} ^i} = {{{{{{ \Gamma} ^i} _j} _k}} {{{{ \gamma} ^j} ^k}}}$
using ${{{{ \Gamma} ^i} _j} _k} = {{{{-1}} {{{{{ d} ^i} _j} _k}}} + {{{{ d} _j} _k} ^i} + {{{{ d} _k} _j} ^i}}$
${{ \Gamma} ^i} = {{{\left({{{{-1}} {{{{{ d} ^i} _j} _k}}} + {{{{ d} _j} _k} ^i} + {{{{ d} _k} _j} ^i}}\right)}} {{{{ \gamma} ^j} ^k}}}$
simplifying metrics and simplifying traces:
${{ \Gamma} ^i} = {{-{{ d} ^i}} + {{{2}} {{{ e} ^i}}}}$
metric inverse partial:
${{\left( {{{{ \gamma} _l} _i}} {{{{ \gamma} ^i} ^j}}\right)} _{,k}} = {0}$
${{{{{{ \gamma} _l} _i}} {{{{{ \gamma} ^i} ^j} _{,k}}}} + {{{{{ \gamma} ^i} ^j}} {{{{{ \gamma} _l} _i} _{,k}}}}} = {0}$
${{{{{{ \gamma} ^l} ^m}} {{{{ \gamma} _l} _i}} {{{{{ \gamma} ^i} ^j} _{,k}}}} + {{{{{ \gamma} ^l} ^m}} {{{{ \gamma} ^i} ^j}} {{{{{ \gamma} _l} _i} _{,k}}}}} = {0}$
${{{{ \gamma} ^i} ^j} _{,k}} = {-{{{{{ \gamma} ^l} ^i}} {{{{ \gamma} ^m} ^j}} {{{{{ \gamma} _l} _m} _{,k}}}}}$
using ${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
${{{{ \gamma} ^i} ^j} _{,k}} = {-{{{2}} {{{{ \gamma} ^l} ^i}} {{{{ \gamma} ^m} ^j}} {{{{{ d} _k} _l} _m}}}}$
$\alpha$ = lapse
lapse derivative:
${{ a} _i} = {{\left( \log\left( \alpha\right)\right)} _{,i}}$
${{ a} _i} = {{\frac{1}{\alpha}} {{ \alpha} _{,i}}}$
${{ \alpha} _{,i}} = {{{\alpha}} \cdot {{{ a} _i}}}$
lapse evolution:
${{ \alpha} _{,t}} = {{{{{ \alpha} _{,i}}} {{{ \beta} ^i}}}{-{{{{\alpha}^{2}}} {{f}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}}}$
using ${{ \alpha} _{,i}} = {{{\alpha}} \cdot {{{ a} _i}}}$
${{ \alpha} _{,t}} = {{{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}}$
${{ \alpha} _{,t}} = {{{{f}} {{{\alpha}^{2}}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}}} + {{\left( {{\alpha}} \cdot {{{ \beta} ^r}}\right)} _{,r}}{-{{{\alpha}} \cdot {{tr(b)}}}}}$
${ \alpha} _{,t}$ flux term $-{{\left( {{\alpha}} \cdot {{{ \beta} ^r}}\right)} _{,r}}$
${ \alpha} _{,t}$ source term ${{{f}} {{{\alpha}^{2}}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}}}{-{{{\alpha}} \cdot {{tr(b)}}}}$
lapse partial evolution
${{ { \alpha} _{,t}} _{,k}} = {{\left( {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}\right)} _{,k}}$
using ${{{ \alpha} _{,t}} _{,k}} = {{ { \alpha} _{,k}} _{,t}}$ ; ${{ \alpha} _{,i}} = {{{\alpha}} \cdot {{{ a} _i}}}$
${{{{\alpha}} \cdot {{{{ a} _k} _{,t}}}} + {{{{ \alpha} _{,t}}} {{{ a} _k}}}} = {{\left( {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}\right)} _{,k}}$
using on lhs only ${{ a} _k} = {{\frac{1}{\alpha}} {{ \alpha} _{,k}}}$
${{{{\alpha}} \cdot {{{{ a} _k} _{,t}}}} + {{{{ \alpha} _{,t}}} {{{\frac{1}{\alpha}} {{ \alpha} _{,k}}}}}} = {{\left( {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}\right)} _{,k}}$
subtracting ${{{ \alpha} _{,t}}} {{{ \alpha} _{,k}}} {{\frac{1}{\alpha}}}$ from both sides
${{{\alpha}} \cdot {{{{ a} _k} _{,t}}}} = {{{\left( {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}\right)} _{,k}}{-{{{{ \alpha} _{,t}}} {{{ \alpha} _{,k}}} {{\frac{1}{\alpha}}}}}}$
using ${{ \alpha} _{,t}} = {{{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}}$
${{{\alpha}} \cdot {{{{ a} _k} _{,t}}}} = {{{\left( {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}\right)} _{,k}}{-{{{{ \alpha} _{,k}}} {{\frac{1}{\alpha}}} {{\alpha}} \cdot {{\left({{{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}}\right)}}}}}$
${{{ a} _k} _{,t}} = {{\left( {{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}\right)} _{,k}}$
${{{ a} _k} _{,t}} = {{{\left( {{{{ \beta} ^i}} {{{ a} _i}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}\right)} _{,k}} + {{\left( {{{ \beta} ^m}} {{{ a} _k}}\right)} _{,m}}{-{\left({{{{{ \beta} ^m}} {{{{ a} _k} _{,m}}}} + {{{{ a} _k}} {{tr(b)}}}}\right)}}{-{{\left( {{{ \beta} ^m}} {{{ a} _m}}\right)} _{,k}}} + {{{{ \beta} ^m}} {{{{ a} _m} _{,k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}}$
${{{ a} _k} _{,t}} = {{-{{\left( {{{ \beta} ^m}} {{{ a} _m}}\right)} _{,k}}} + {{\left( {{{ \beta} ^m}} {{{ a} _k}}\right)} _{,m}} + {{\left( {{{{ \beta} ^m}} {{{ a} _m}}}{-{{{\alpha}} \cdot {{f}} {{tr(K)}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}}}\right)} _{,k}}{-{{{tr(b)}} \cdot {{{ a} _k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}}$
${{{ a} _k} _{,t}} = {{{\left( {{{ \beta} ^m}} {{{ a} _k}}\right)} _{,m}} + {{\left( {{\alpha}} \cdot {{f}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}}\right)} _{,k}}{-{{{tr(b)}} \cdot {{{ a} _k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}}$
${{{ a} _k} _{,t}} = {{{\left( {{{\alpha}} \cdot {{f}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}} {{{{ δ} ^r} _k}}} + {{{{ \beta} ^r}} {{{ a} _k}}}\right)} _{,r}}{-{{{tr(b)}} \cdot {{{ a} _k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}}$
${{ a} _k} _{,t}$ flux term: $-{{\left( {{{\alpha}} \cdot {{f}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}} {{{{ δ} ^r} _k}}} + {{{{ \beta} ^r}} {{{ a} _k}}}\right)} _{,r}}$
${{ a} _k} _{,t}$ source term: ${-{{{tr(b)}} \cdot {{{ a} _k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}$
metric evolution:
${{{{ \gamma} _i} _j} _{,t}} = {{{{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{ \beta} _i} _{,j}} + {{{ \beta} _j} _{,i}}}{-{{{2}} {{{ \beta} ^k}} {{{{{ \Gamma} _k} _i} _j}}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{{ \gamma} _i} _k} _{,j}}}} + {{{{ \beta} ^k}} {{{{{ \gamma} _j} _k} _{,i}}}} + {{{{{ \beta} ^k} _{,j}}} {{{{ \gamma} _i} _k}}} + {{{{{ \beta} ^k} _{,i}}} {{{{ \gamma} _j} _k}}} + {{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{-2}} {{{ \beta} ^k}} {{{{{ \Gamma} _k} _i} _j}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{{ \gamma} _i} _k} _{,j}}}} + {{{{ \beta} ^k}} {{{{{ \gamma} _j} _k} _{,i}}}} + {{{{{ \beta} ^k} _{,i}}} {{{{ \gamma} _j} _k}}} + {{{{{ \beta} ^k} _{,j}}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}{-{{{2}} {{{ \beta} ^k}} {{{{{ \Gamma} _k} _i} _j}}}}}$
using ${{{{ \Gamma} _i} _j} _k} = {{{\frac{1}{2}}} {{\left({{{{{ \gamma} _i} _j} _{,k}} + {{{{ \gamma} _i} _k} _{,j}}{-{{{{ \gamma} _j} _k} _{,i}}}}\right)}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{{ \gamma} _i} _k} _{,j}}}} + {{{{ \beta} ^k}} {{{{{ \gamma} _j} _k} _{,i}}}}{-{{{{ \beta} ^k}} {{{{{ \gamma} _k} _j} _{,i}}}}} + {{{{ \beta} ^k}} {{{{{ \gamma} _i} _j} _{,k}}}}{-{{{{ \beta} ^k}} {{{{{ \gamma} _k} _i} _{,j}}}}} + {{{{{ \beta} ^k} _{,j}}} {{{{ \gamma} _i} _k}}} + {{{{{ \beta} ^k} _{,i}}} {{{{ \gamma} _j} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}$
symmetrizing ${{ \gamma} _i} _j$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{{ \gamma} _i} _j} _{,k}}}} + {{{{{ \beta} ^k} _{,i}}} {{{{ \gamma} _j} _k}}} + {{{{{ \beta} ^k} _{,j}}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}$
using ${{{ \beta} ^i} _{,j}} = {{{ b} ^i} _j}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{{ \gamma} _i} _j} _{,k}}}} + {{{{{ b} ^k} _i}} {{{{ \gamma} _j} _k}}} + {{{{{ b} ^k} _j}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}$
using ${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^k}} {{{{2}} {{{{{ d} _k} _i} _j}}}}} + {{{{{ b} ^k} _i}} {{{{ \gamma} _j} _k}}} + {{{{{ b} ^k} _j}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{{ b} ^k} _i}} {{{{ \gamma} _j} _k}}} + {{{{{ b} ^k} _j}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}} + {{\left( {{{{ \gamma} _i} _j}} {{{ \beta} ^r}}\right)} _{,r}}{-{{{{{ \gamma} _i} _j}} {{tr(b)}}}}}$
${{{ \gamma} _i} _j} _{,t}$ flux term $-{{\left( {{{{ \gamma} _i} _j}} {{{ \beta} ^r}}\right)} _{,r}}$
${{{ \gamma} _i} _j} _{,t}$ source term ${{{{{ b} ^k} _i}} {{{{ \gamma} _j} _k}}} + {{{{{ b} ^k} _j}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}{-{{{{{ \gamma} _i} _j}} {{tr(b)}}}}$
metric partial evolution:
${{\frac{1}{2}} {{{{{ \gamma} _i} _j} _{,t}} _{,k}}} = {{\left( {\frac{1}{2}}{\left({{{{{ \beta} ^l}} {{{{2}} {{{{{ d} _l} _i} _j}}}}} + {{{{{ b} ^l} _i}} {{{{ \gamma} _j} _l}}} + {{{{{ b} ^l} _j}} {{{{ \gamma} _i} _l}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}\right)} _{,k}}$
using ${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
${{\frac{1}{2}} {{\left( {{2}} {{{{{ d} _k} _i} _j}}\right)} _{,t}}} = {{\left( {\frac{1}{2}}{\left({{{{{ \beta} ^l}} {{2}} {{{{{ d} _l} _i} _j}}} + {{{{{ b} ^l} _i}} {{{{ \gamma} _j} _l}}} + {{{{{ b} ^l} _j}} {{{{ \gamma} _i} _l}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}\right)} _{,k}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\left( {\frac{1}{2}}{\left({{{{{ \beta} ^l}} {{2}} {{{{{ d} _l} _i} _j}}} + {{{{{ b} ^l} _i}} {{{{ \gamma} _j} _l}}} + {{{{{ b} ^l} _j}} {{{{ \gamma} _i} _l}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}\right)} _{,k}}$
inserting flux shift terms...
${{{{{ d} _k} _i} _j} _{,t}} = {{{\left( {\frac{1}{2}}{\left({{{{{ \beta} ^l}} {{2}} {{{{{ d} _l} _i} _j}}} + {{{{{ b} ^l} _i}} {{{{ \gamma} _j} _l}}} + {{{{{ b} ^l} _j}} {{{{ \gamma} _i} _l}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}\right)} _{,k}} + {{\left( {{{ \beta} ^l}} {{{{{ d} _k} _i} _j}}\right)} _{,l}}{-{\left({{{{{ \beta} ^l}} {{{{{{ d} _k} _i} _j} _{,l}}}} + {{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}}\right)}}{-{{\left( {{{ \beta} ^l}} {{{{{ d} _l} _i} _j}}\right)} _{,k}}} + {{{{ \beta} ^l}} {{{{{{ d} _k} _i} _j} _{,l}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}}$
simplifying without distributing flux derivative
${{{{{ d} _k} _i} _j} _{,t}} = {{-{{\left( {{{ \beta} ^l}} {{{{{ d} _l} _i} _j}}\right)} _{,k}}} + {{\left( {{{ \beta} ^l}} {{{{{ d} _k} _i} _j}}\right)} _{,l}} + {{\left( {\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}} + {{{2}} {{{ \beta} ^l}} {{{{{ d} _l} _i} _j}}}}\right)}\right)} _{,k}}{-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}}$
combining derivatives
${{{{{ d} _k} _i} _j} _{,t}} = {{{\left( {-{{{{ \beta} ^l}} {{{{{ d} _l} _i} _j}}}} + {{\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}} + {{{2}} {{{ \beta} ^l}} {{{{{ d} _l} _i} _j}}}}\right)}}\right)} _{,k}} + {{\left( {{{ \beta} ^l}} {{{{{ d} _k} _i} _j}}\right)} _{,l}} + {{-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}}}$
simplifying without distributing flux derivative
${{{{{ d} _k} _i} _j} _{,t}} = {{{\left( {{{ \beta} ^l}} {{{{{ d} _k} _i} _j}}\right)} _{,l}} + {{\left( {\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}\right)} _{,k}}{-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{{\left( {{{{\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}}} {{{{ δ} ^r} _k}}} + {{{{ \beta} ^r}} {{{{{ d} _k} _i} _j}}}\right)} _{,r}}{-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}}$
${{{{ d} _k} _i} _j} _{,t}$ flux term: $-{{\left( {{{{\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}}} {{{{ δ} ^r} _k}}} + {{{{ \beta} ^r}} {{{{{ d} _k} _i} _j}}}\right)} _{,r}}$
${{{{ d} _k} _i} _j} _{,t}$ source term: ${-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}$
Riemann curvature
${{{{{ R} ^i} _j} _k} _l} = {{{{{{{ \Gamma} ^i} _j} _l} _{,k}}{-{{{{{ \Gamma} ^i} _j} _k} _{,l}}} + {{{{{{ \Gamma} ^i} _m} _k}} {{{{{ \Gamma} ^m} _j} _l}}}}{-{{{{{{ \Gamma} ^i} _m} _l}} {{{{{ \Gamma} ^m} _j} _k}}}}}$
Ricci curvature
${{{ R} _i} _j} = {{{{{ R} ^k} _i} _k} _j}$
using ${{{{{ R} ^k} _i} _k} _j} = {{{{{{{ \Gamma} ^k} _i} _j} _{,k}}{-{{{{{ \Gamma} ^k} _i} _k} _{,j}}} + {{{{{{ \Gamma} ^k} _m} _k}} {{{{{ \Gamma} ^m} _i} _j}}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}$
${{{ R} _i} _j} = {{{{{{ \Gamma} ^k} _i} _j} _{,k}}{-{{{{{ \Gamma} ^k} _i} _k} _{,j}}} + {{{{{{ \Gamma} ^k} _m} _k}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}$
using ${{{{ \Gamma} ^k} _i} _k} = {{ d} _i}$
${{{ R} _i} _j} = {{-{{{ d} _i} _{,j}}} + {{{{{ \Gamma} ^k} _i} _j} _{,k}} + {{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}$
${{{ R} _i} _j} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{ {{{ \Gamma} ^k} _i} _j} _{,k}} + {{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}$
combining derivatives
${{{ R} _i} _j} = {{{\left( {-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}\right)} _{,k}} + {{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}$
Ricci_ll_negflux ${\left( {-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}\right)} _{,k}$
Ricci_ll_rhs ${{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}$
extrinsic curvature evolution:
${{{{ K} _i} _j} _{,t}} = {{-{{{ \alpha} _{,i}} _{,j}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}}}$
using ${{{ \alpha} _{,i}} _{,j}} = {{{\frac{1}{2}}} {{\left({{{{{{ \alpha} _{,i}} _{,k}}} {{{{ δ} ^k} _j}}} + {{{{{ \alpha} _{,j}} _{,k}}} {{{{ δ} ^k} _i}}}}\right)}}}$
using ${{{ \alpha} _{,i}} _{,j}} = {{{\frac{1}{2}}} {{{\left( {{{{ \alpha} _{,i}}} {{{{ δ} ^k} _j}}} + {{{{ \alpha} _{,j}}} {{{{ δ} ^k} _i}}}\right)} _{,k}}}}$
using ${{{ \alpha} _{,i}} _{,j}} = {{{\frac{1}{2}}} {{{\left( {{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}\right)} _{,k}}}}$
using ${{{ \alpha} _{,i}} _{,j}} = {{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}}}$
using ${{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} = {{{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}}$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}}$
using ${{{ \beta} ^i} _{,j}} = {{{ b} ^i} _j}$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}} + {{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}}$
using ${{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} = {{{\alpha}} \cdot {{\left({{{{{{ Z} _i} _{,k}}} {{{{ δ} ^k} _j}}} + {{{{{ Z} _j} _{,k}}} {{{{ δ} ^k} _i}}}}\right)}}}$
using ${{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} = {{{\alpha}} \cdot {{{\left( {{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}\right)} _{,k}}}}$
using ${{{\alpha}} \cdot {{\left({{{{ Z} _i} _{,j}} + {{{ Z} _j} _{,i}}}\right)}}} = {{{\left( {{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}{-{{{{ \alpha} _{,k}}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}}}$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}} + {{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}} + {{\left( {{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}{-{{{{ \alpha} _{,k}}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}}}$
using ${{ \alpha} _{,i}} = {{{\alpha}} \cdot {{{ a} _i}}}$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{{\alpha}} \cdot {{{ a} _k}}}}} + {{{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}} + {{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}} + {{\left( {{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}{-{{{{{\alpha}} \cdot {{{ a} _k}}}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}}}$
using the definition of ${{ R} _i} _j$
${{{{ K} _i} _j} _{,t}} = {{-{{\left( {{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{\alpha}} \cdot {{{ a} _k}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}} + {{\left( {{{{ K} _i} _j}} {{{ \beta} ^k}}\right)} _{,k}}{-{{{{{ K} _i} _j}} {{tr(b)}}}} + {{\left( {{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}\right)} _{,k}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{\alpha}} \cdot {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}} + {{\left( {{\alpha}} \cdot {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}\right)} _{,k}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}}}$
combining derivatives into flux:
${{{{ K} _i} _j} _{,t}} = {{{\left( {-{{{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^k} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{{ K} _i} _j}} {{{ \beta} ^k}}} + {{{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}} + {{{\alpha}} \cdot {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}\right)} _{,k}} + {{{{{{{ \Gamma} ^k} _i} _j}} {{\alpha}} \cdot {{{ a} _k}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{\alpha}} \cdot {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}}}}$
${{{ K} _i} _j} _{,t}$ flux term: $-{{\left( {-{{{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^r} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^r} _i}}}}\right)}}}} + {{{{{ K} _i} _j}} {{{ \beta} ^r}}} + {{{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^r} _j}}} + {{{{ Z} _j}} {{{{ δ} ^r} _i}}}}\right)}}} + {{{\alpha}} \cdot {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^r} _j}}} + {{{{ d} _j}} {{{{ δ} ^r} _i}}}}\right)}}}} + {{{{ \Gamma} ^r} _i} _j}}\right)}}}\right)} _{,r}}$
${{{ K} _i} _j} _{,t}$ source term: ${{{{{{ \Gamma} ^k} _i} _j}} {{\alpha}} \cdot {{{ a} _k}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{\alpha}} \cdot {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}}$
Gaussian curvature
${R} = {{{{{ \gamma} ^i} ^j}} {{{{ R} _i} _j}}}$
using Ricci definition
${R} = {{{{{ \gamma} ^i} ^j}} {{\left({{{\left( {-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}\right)} _{,k}} + {{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}}$
${R} = {{{\left( {{{{ \gamma} ^i} ^j}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}\right)} _{,k}}{-{{{{{{ \gamma} ^i} ^j} _{,k}}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}} + {{{{{ \gamma} ^i} ^j}} {{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}} + {{{{{ \gamma} ^i} ^j}} \cdot {-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}}$
using ${{{{ \gamma} ^i} ^j} _{,k}} = {-{{{2}} {{{{ \gamma} ^l} ^i}} {{{{ \gamma} ^m} ^j}} {{{{{ d} _k} _l} _m}}}}$
${R} = {{{\left( {{{{ \gamma} ^i} ^j}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}\right)} _{,k}}{-{ {-{{{2}} {{{{ \gamma} ^a} ^i}} {{{{ \gamma} ^b} ^j}} {{{{{ d} _k} _a} _b}}}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}} + {{{{{ \gamma} ^i} ^j}} {{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}} + {{{{{ \gamma} ^i} ^j}} \cdot {-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}}$
using ${{{{ \Gamma} ^i} _j} _k} = {{{{-1}} {{{{{ d} ^i} _j} _k}}} + {{{{ d} _j} _k} ^i} + {{{{ d} _k} _j} ^i}}$
${R} = {{{\left( {{{{ \gamma} ^i} ^j}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{-1}} {{{{{ d} ^k} _i} _j}}} + {{{{ d} _i} _j} ^k} + {{{{ d} _j} _i} ^k}}}\right)}}\right)} _{,k}}{-{ {-{{{2}} {{{{ \gamma} ^a} ^i}} {{{{ \gamma} ^b} ^j}} {{{{{ d} _k} _a} _b}}}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{-1}} {{{{{ d} ^k} _i} _j}}} + {{{{ d} _i} _j} ^k} + {{{{ d} _j} _i} ^k}}}\right)}}}} + {{{{{ \gamma} ^i} ^j}} {{{ d} _m}} {{\left({{{{-1}} {{{{{ d} ^m} _i} _j}}} + {{{{ d} _i} _j} ^m} + {{{{ d} _j} _i} ^m}}\right)}}} + {{{{{ \gamma} ^i} ^j}} \cdot {-{{{\left({{{{-1}} {{{{{ d} ^k} _m} _j}}} + {{{{ d} _m} _j} ^k} + {{{{ d} _j} _m} ^k}}\right)}} {{\left({{{{-1}} {{{{{ d} ^m} _i} _k}}} + {{{{ d} _i} _k} ^m} + {{{{ d} _k} _i} ^m}}\right)}}}}}}$
Gaussian_negflux ${\left( {{{{ \gamma} ^i} ^j}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{-1}} {{{{{ d} ^k} _i} _j}}} + {{{{ d} _i} _j} ^k} + {{{{ d} _j} _i} ^k}}\right)}}\right)} _{,k}$
Gaussian_rhs ${-{ {-{{{2}} {{{{ \gamma} ^a} ^i}} {{{{ \gamma} ^b} ^j}} {{{{{ d} _k} _a} _b}}}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{-1}} {{{{{ d} ^k} _i} _j}}} + {{{{ d} _i} _j} ^k} + {{{{ d} _j} _i} ^k}}\right)}}}} + {{{{{ \gamma} ^i} ^j}} {{{ d} _m}} {{\left({{{{-1}} {{{{{ d} ^m} _i} _j}}} + {{{{ d} _i} _j} ^m} + {{{{ d} _j} _i} ^m}}\right)}}} + {{{{{ \gamma} ^i} ^j}} \cdot {-{{{\left({{{{-1}} {{{{{ d} ^k} _m} _j}}} + {{{{ d} _m} _j} ^k} + {{{{ d} _j} _m} ^k}}\right)}} {{\left({{{{-1}} {{{{{ d} ^m} _i} _k}}} + {{{{ d} _i} _k} ^m} + {{{{ d} _k} _i} ^m}}\right)}}}}}$
Gaussian_negflux ${\left( {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}\right)} _{,k}$
Gaussian_rhs ${-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}$
${R} = {{{\left( {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}\right)} _{,k}}{-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}}$
Z4 $\Theta$ definition
${{ \Theta} _{,t}} = {{{{{\left( {{\Theta}} \cdot {{{ \beta} ^k}}\right)} _{,k}} + {{\left( {{\alpha}} \cdot {{{ Z} ^k}}\right)} _{,k}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{R}}} + {{{\alpha}} \cdot {{\left({{{ d} ^k}{-{{{2}} {{{ a} ^k}}}}}\right)}} {{{ Z} _k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{{{tr(K)}} \cdot {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{{{ K} ^m} _n}} {{{{ K} ^n} _m}}}}{-{{{16}} {{π}} \cdot {{\rho}}}}}\right)}}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{{\kappa_2}} + {2}}\right)}} {{\Theta}}}}}{-{{{\Theta}} \cdot {{tr(b)}}}}}$
using the definition of R
${{ \Theta} _{,t}} = {{{\left( {{\Theta}} \cdot {{{ \beta} ^k}}\right)} _{,k}} + {{\left( {{\alpha}} \cdot {{{ Z} ^k}}\right)} _{,k}} + {{{\alpha}} \cdot {{\left({{{ d} ^k}{-{{{2}} {{{ a} ^k}}}}}\right)}} {{{ Z} _k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{{{tr(K)}} \cdot {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{{{ K} ^m} _n}} {{{{ K} ^n} _m}}}}{-{{{16}} {{π}} \cdot {{\rho}}}}}\right)}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}}\right)}}} + {{\left( {{\frac{1}{2}}} {{\alpha}} \cdot {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}\right)} _{,k}}{-{{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _k}} {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{{\kappa_2}} + {2}}\right)}} {{\Theta}}}}{-{{{\Theta}} \cdot {{tr(b)}}}}}$
combining derivatives into flux:
${{ \Theta} _{,t}} = {{{\left( {{{\Theta}} \cdot {{{ \beta} ^k}}} + {{{\alpha}} \cdot {{{ Z} ^k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}}\right)} _{,k}} + {{{{\alpha}} \cdot {{\left({{{ d} ^k}{-{{{2}} {{{ a} ^k}}}}}\right)}} {{{ Z} _k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{{{tr(K)}} \cdot {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{{{ K} ^m} _n}} {{{{ K} ^n} _m}}}}{-{{{16}} {{π}} \cdot {{\rho}}}}}\right)}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}}\right)}}}{-{{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _k}} {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{{\kappa_2}} + {2}}\right)}} {{\Theta}}}}{-{{{\Theta}} \cdot {{tr(b)}}}}}}$
${ \Theta} _{,t}$ flux term: $-{{\left( {{{\Theta}} \cdot {{{ \beta} ^r}}} + {{{\alpha}} \cdot {{{ Z} ^r}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{2}} {{\left({{-{{ d} ^r}} + {{ e} ^r}}\right)}}}\right)} _{,r}}$
${ \Theta} _{,t}$ source term: ${{{\alpha}} \cdot {{\left({{{ d} ^k}{-{{{2}} {{{ a} ^k}}}}}\right)}} {{{ Z} _k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{{{tr(K)}} \cdot {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{{{ K} ^m} _n}} {{{{ K} ^n} _m}}}}{-{{{16}} {{π}} \cdot {{\rho}}}}}\right)}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}}\right)}}}{-{{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _k}} {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{{\kappa_2}} + {2}}\right)}} {{\Theta}}}}{-{{{\Theta}} \cdot {{tr(b)}}}}$
Z4 $Z_k$ definition
${{{ Z} _k} _{,t}} = {{{-{{\left( { {-{{ \beta} ^r}} {{{ Z} _k}}} + {{{\alpha}} \cdot {{\left({{-{{{ K} ^r} _k}} + {{{{{ δ} ^r} _k}} {{\left({{tr(K)}{-{\Theta}}}\right)}}}}\right)}}}\right)} _{,r}}} + {{{\alpha}} \cdot {{\left({{{{{ a} _k}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}} + {{{{{ K} _k} _l}} {{\left({{-{{ a} ^l}} + {{ d} ^l}{-{{{2}} {{{ Z} ^l}}}}}\right)}}}{-{{{{{{ d} _k} _p} _q}} {{{{ K} ^p} ^q}}}}{-{{{{\kappa_1}}} \cdot {{{ Z} _k}}}}{-{{{8}} {{π}} \cdot {{{ S} _k}}}}}\right)}}} + {{{{ Z} _l}} {{{{ b} ^l} _k}}}}{-{{{{ Z} _k}} {{tr(b)}}}}}$
${{{ Z} _k} _{,t}} = {{{\left( -{\left({{ {-{{ \beta} ^r}} {{{ Z} _k}}} + {{{\alpha}} \cdot {{\left({{-{{{ K} ^r} _k}} + {{{{{ δ} ^r} _k}} {{\left({{tr(K)}{-{\Theta}}}\right)}}}}\right)}}}}\right)}\right)} _{,r}} + {{{{\alpha}} \cdot {{\left({{{{{ a} _k}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}} + {{{{{ K} _k} _l}} {{\left({{-{{ a} ^l}} + {{ d} ^l}{-{{{2}} {{{ Z} ^l}}}}}\right)}}}{-{{{{{{ d} _k} _p} _q}} {{{{ K} ^p} ^q}}}}{-{{{{\kappa_1}}} \cdot {{{ Z} _k}}}}{-{{{8}} {{π}} \cdot {{{ S} _k}}}}}\right)}}} + {{{{ Z} _l}} {{{{ b} ^l} _k}}}{-{{{{ Z} _k}} {{tr(b)}}}}}}$
${{ Z} _k} _{,t}$ flux term: $-{{\left( -{\left({{ {-{{ \beta} ^r}} {{{ Z} _k}}} + {{{\alpha}} \cdot {{\left({{-{{{ K} ^r} _k}} + {{{{{ δ} ^r} _k}} {{\left({{tr(K)}{-{\Theta}}}\right)}}}}\right)}}}}\right)}\right)} _{,r}}$
${{ Z} _k} _{,t}$ source term: ${{{\alpha}} \cdot {{\left({{{{{ a} _k}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}} + {{{{{ K} _k} _l}} {{\left({{-{{ a} ^l}} + {{ d} ^l}{-{{{2}} {{{ Z} ^l}}}}}\right)}}}{-{{{{{{ d} _k} _p} _q}} {{{{ K} ^p} ^q}}}}{-{{{{\kappa_1}}} \cdot {{{ Z} _k}}}}{-{{{8}} {{π}} \cdot {{{ S} _k}}}}}\right)}}} + {{{{ Z} _l}} {{{{ b} ^l} _k}}}{-{{{{ Z} _k}} {{tr(b)}}}}$
shift evolution:
harmonic shift evolution:
${{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}$
shift: HarmonicParabolic
${{{ \beta} ^l} _{,t}} = {{{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{\left( {{{ \beta} ^k}} {{{ \beta} ^l}}\right)} _{,k}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}$
${{ \beta} ^l} _{,t}$ flux term: $-{{\left( {{{ \beta} ^r}} {{{ \beta} ^l}}\right)} _{,r}}$
${{ \beta} ^l} _{,t}$ source term: ${{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}$
${{ {{ b} ^l} _k} _{,t}} = {{\left( {{{{ δ} ^r} _k}} {{\left({{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{\left( {{{ \beta} ^i}} {{{ \beta} ^l}}\right)} _{,i}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}\right)}}\right)} _{,r}}$
${{ {{ b} ^l} _k} _{,t}} = {{{\left( {{{{ δ} ^r} _k}} {{\left({{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}\right)} _{,r}}{-{{\left( {{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}\right)} _{,r}}} + {{\left( {{{ \beta} ^r}} {{{{ b} ^l} _k}}\right)} _{,r}}}$
${{{ b} ^l} _k} _{,t}$ flux term: $-{{\left( {{{{{ δ} ^r} _k}} {{\left({{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}{-{{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}} + {{{{ \beta} ^r}} {{{{ b} ^l} _k}}}\right)} _{,r}}$
${{{ b} ^l} _k} _{,t}$ source term: $0$
shift: HarmonicHyperbolic
${{{ \beta} ^l} _{,t}} = {{{{ B} ^l} + {{\left( {{{ \beta} ^k}} {{{ \beta} ^l}}\right)} _{,k}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}$
${{{ B} ^l} _{,t}} = {{{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{\left( {{{ \beta} ^k}} {{{ B} ^l}}\right)} _{,k}}}{-{{{{ B} ^l}} {{tr(b)}}}}}$
${{ \beta} ^l} _{,t}$ flux term: $-{{\left( {{{ \beta} ^r}} {{{ \beta} ^l}}\right)} _{,r}}$
${{ \beta} ^l} _{,t}$ source term: ${{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}$
${{ B} ^l} _{,t}$ flux term: $-{{\left( {{{ \beta} ^r}} {{{ B} ^l}}\right)} _{,r}}$
${{ B} ^l} _{,t}$ source term: ${{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}}{-{{{{ B} ^l}} {{tr(b)}}}}$
${{ {{ b} ^l} _k} _{,t}} = {{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{\left( {{{ \beta} ^i}} {{{ \beta} ^l}}\right)} _{,i}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}\right)}}\right)} _{,r}}$
${{ {{ b} ^l} _k} _{,t}} = {{{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}\right)} _{,r}}{-{{\left( {{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}\right)} _{,r}}} + {{\left( {{{ \beta} ^r}} {{{{ b} ^l} _k}}\right)} _{,r}}}$
${{{ b} ^l} _k} _{,t}$ flux term: $-{{\left( {{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}{-{{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}} + {{{{ \beta} ^r}} {{{{ b} ^l} _k}}}\right)} _{,r}}$
${{{ b} ^l} _k} _{,t}$ source term: $0$
minimal distortion shift evolution:
shift: MinimalDistortionHyperbolic
${{{ \beta} ^l} _{,t}} = {{{{ B} ^l} + {{\left( {{{ \beta} ^k}} {{{ \beta} ^l}}\right)} _{,k}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}$
${{{ B} ^l} _{,t}} = {{{{\left( {{{\epsilon_{mde}}}} \cdot {{\left({{{{ (\nabla\beta)} ^l} ^k} + {{{\frac{1}{3}}} {{{{ \gamma} ^k} ^l}} {{(\nabla \cdot \beta)}}} + {{{{{ \gamma} ^l} ^i}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}} {{{ \beta} ^j}}}{-{{{2}} {{\alpha}} \cdot {{{{ A} ^l} ^k}}}}}\right)}}\right)} _{,k}} + {{{{\epsilon_{mde}}}} \cdot {{\left({{{{{{ (\nabla\beta)} ^l} ^j}} {{{ d} _j}}} + {{{{{ (\nabla\beta)} ^n} ^k}} {{{{{ \Gamma} ^l} _n} _k}}} + {{{\frac{2}{3}}} {{(\nabla \cdot \beta)}} \cdot {{{ e} ^l}}} + {{{{{ \gamma} ^l} ^i}} {{{ \beta} ^j}} {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}} + {{{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}} {{\left({{{{-2}} {{{{{ d} _k} ^l} ^i}} {{{ \beta} ^j}}} + {{{{{ \gamma} ^l} ^i}} {{{{ b} ^j} _k}}}}\right)}}}{-{{{2}} {{\alpha}} \cdot {{\left({{{{{{ A} ^m} ^n}} {{{{{ \Gamma} ^l} _n} _m}}} + {{{{{ A} ^l} ^m}} {{{{{ \Gamma} ^n} _n} _m}}}}\right)}}}}}\right)}}} + {{\left( {{{ \beta} ^k}} {{{ B} ^l}}\right)} _{,k}}}{-{{{{ B} ^l}} {{tr(b)}}}}}$
${{ \beta} ^l} _{,t}$ flux term: $-{{\left( {{{ \beta} ^r}} {{{ \beta} ^l}}\right)} _{,r}}$
${{ \beta} ^l} _{,t}$ source term: ${{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}$
${{ B} ^l} _{,t}$ flux term: $-{{\left( {{{{\epsilon_{mde}}}} \cdot {{\left({{{{ (\nabla\beta)} ^l} ^r} + {{{\frac{1}{3}}} {{{{ \gamma} ^r} ^l}} {{(\nabla \cdot \beta)}}} + {{{{{ \gamma} ^l} ^i}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^r} _j}}} + {{{{ d} _j}} {{{{ δ} ^r} _i}}}}\right)}}}} + {{{{ \Gamma} ^r} _i} _j}}\right)}} {{{ \beta} ^j}}}{-{{{2}} {{\alpha}} \cdot {{{{ A} ^l} ^r}}}}}\right)}}} + {{{{ \beta} ^r}} {{{ B} ^l}}}\right)} _{,r}}$
${{ B} ^l} _{,t}$ source term: ${{{{\epsilon_{mde}}}} \cdot {{\left({{{{{{ (\nabla\beta)} ^l} ^j}} {{{ d} _j}}} + {{{{{ (\nabla\beta)} ^n} ^k}} {{{{{ \Gamma} ^l} _n} _k}}} + {{{\frac{2}{3}}} {{(\nabla \cdot \beta)}} \cdot {{{ e} ^l}}} + {{{{{ \gamma} ^l} ^i}} {{{ \beta} ^j}} {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}} + {{{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}} {{\left({{{{-2}} {{{{{ d} _k} ^l} ^i}} {{{ \beta} ^j}}} + {{{{{ \gamma} ^l} ^i}} {{{{ b} ^j} _k}}}}\right)}}}{-{{{2}} {{\alpha}} \cdot {{\left({{{{{{ A} ^m} ^n}} {{{{{ \Gamma} ^l} _n} _m}}} + {{{{{ A} ^l} ^m}} {{{{{ \Gamma} ^n} _n} _m}}}}\right)}}}}}\right)}}}{-{{{{ B} ^l}} {{tr(b)}}}}$
${{ {{ b} ^l} _k} _{,t}} = {{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{\left( {{{ \beta} ^i}} {{{ \beta} ^l}}\right)} _{,i}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}\right)}}\right)} _{,r}}$
${{ {{ b} ^l} _k} _{,t}} = {{{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}\right)} _{,r}}{-{{\left( {{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}\right)} _{,r}}} + {{\left( {{{ \beta} ^r}} {{{{ b} ^l} _k}}\right)} _{,r}}}$
${{{ b} ^l} _k} _{,t}$ flux term: $-{{\left( {{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}{-{{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}} + {{{{ \beta} ^r}} {{{{ b} ^l} _k}}}\right)} _{,r}}$
${{{ b} ^l} _k} _{,t}$ source term: $0$
gamma driver shift evolution:
gamma driver shift, hyperbolic:
${{{{\left( {{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{{{ \gamma} ^r} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{{ \gamma} ^l} ^r}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}\right)} _{,r}} + {{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{2}} {{{ e} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{{{ \gamma} ^j} ^k}} {{\left({{{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{ b} ^m} _k}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{ b} ^l} _m}}}} + {{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{{ \hat{\Gamma}} ^m} _n} _k}} {{{ \beta} ^n}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{{ \hat{\Gamma}} ^l} _n} _m}} {{{ \beta} ^n}}}}}\right)}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{{ \Delta\Gamma} ^l} _m} _n}} {{{{ \gamma} ^m} ^n}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ e} ^l}}}{-{{{2}} {{{{ A} ^l} ^j}} {{\left({{{{\alpha}} \cdot {{{ a} _j}}}{-{{ \overset{\Delta}{G}} _j}}}\right)}}}} + {{{2}} {{{{ A} ^j} ^k}} {{{{{ \Delta\Gamma} ^l} _j} _k}}} + {{{\frac{4}{3}}} {{\alpha}} \cdot {{tr(K)}} \cdot {{\left({{{ a} ^l}{-{{{2}} {{{ e} ^l}}}}}\right)}}}{-{{{\frac{2}{3}}} {{\left({{{{{ \overset{\Delta}{G}} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{ \overset{\Delta}{G}} ^l}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}}}}\right)}}}}{-{{{\frac{3}{4}}} {{{ \bar{\Lambda}} ^j}} {{{{ b} ^l} _j}}}}}{-{{{\eta}} \cdot {{{ B} ^l}}}}$
shift: GammaDriverHyperbolic
${{{ \beta} ^l} _{,t}} = {{{{ B} ^l} + {{\left( {{{ \beta} ^k}} {{{ \beta} ^l}}\right)} _{,k}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}$
${{{ B} ^l} _{,t}} = {{{{\left( {{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{{{ \gamma} ^r} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{{ \gamma} ^l} ^r}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}\right)} _{,r}} + {{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{2}} {{{ e} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{{{ \gamma} ^j} ^k}} {{\left({{{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{ b} ^m} _k}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{ b} ^l} _m}}}} + {{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{{ \hat{\Gamma}} ^m} _n} _k}} {{{ \beta} ^n}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{{ \hat{\Gamma}} ^l} _n} _m}} {{{ \beta} ^n}}}}}\right)}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{{ \Delta\Gamma} ^l} _m} _n}} {{{{ \gamma} ^m} ^n}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ e} ^l}}}{-{{{2}} {{{{ A} ^l} ^j}} {{\left({{{{\alpha}} \cdot {{{ a} _j}}}{-{{ \overset{\Delta}{G}} _j}}}\right)}}}} + {{{2}} {{{{ A} ^j} ^k}} {{{{{ \Delta\Gamma} ^l} _j} _k}}} + {{{\frac{4}{3}}} {{\alpha}} \cdot {{tr(K)}} \cdot {{\left({{{ a} ^l}{-{{{2}} {{{ e} ^l}}}}}\right)}}}{-{{{\frac{2}{3}}} {{\left({{{{{ \overset{\Delta}{G}} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{ \overset{\Delta}{G}} ^l}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}}}}\right)}}}{-{{{\frac{3}{4}}} {{{ \bar{\Lambda}} ^j}} {{{{ b} ^l} _j}}}}{-{{{\eta}} \cdot {{{ B} ^l}}}} + {{\left( {{{ \beta} ^k}} {{{ B} ^l}}\right)} _{,k}}}{-{{{{ B} ^l}} {{tr(b)}}}}}$
${{ \beta} ^l} _{,t}$ flux term: $-{{\left( {{{ \beta} ^r}} {{{ \beta} ^l}}\right)} _{,r}}$
${{ \beta} ^l} _{,t}$ source term: ${{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}$
${{ B} ^l} _{,t}$ flux term: $-{{\left( {{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{{{ \gamma} ^r} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{{ \gamma} ^l} ^r}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}} + {{{{ \beta} ^r}} {{{ B} ^l}}}\right)} _{,r}}$
${{ B} ^l} _{,t}$ source term: ${{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{2}} {{{ e} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{{{ \gamma} ^j} ^k}} {{\left({{{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{ b} ^m} _k}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{ b} ^l} _m}}}} + {{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{{ \hat{\Gamma}} ^m} _n} _k}} {{{ \beta} ^n}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{{ \hat{\Gamma}} ^l} _n} _m}} {{{ \beta} ^n}}}}}\right)}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{{ \Delta\Gamma} ^l} _m} _n}} {{{{ \gamma} ^m} ^n}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ e} ^l}}}{-{{{2}} {{{{ A} ^l} ^j}} {{\left({{{{\alpha}} \cdot {{{ a} _j}}}{-{{ \overset{\Delta}{G}} _j}}}\right)}}}} + {{{2}} {{{{ A} ^j} ^k}} {{{{{ \Delta\Gamma} ^l} _j} _k}}} + {{{\frac{4}{3}}} {{\alpha}} \cdot {{tr(K)}} \cdot {{\left({{{ a} ^l}{-{{{2}} {{{ e} ^l}}}}}\right)}}}{-{{{\frac{2}{3}}} {{\left({{{{{ \overset{\Delta}{G}} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{ \overset{\Delta}{G}} ^l}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}}}}\right)}}}{-{{{\frac{3}{4}}} {{{ \bar{\Lambda}} ^j}} {{{{ b} ^l} _j}}}}{-{{{\eta}} \cdot {{{ B} ^l}}}}{-{{{{ B} ^l}} {{tr(b)}}}}$
${{ {{ b} ^l} _k} _{,t}} = {{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{\left( {{{ \beta} ^i}} {{{ \beta} ^l}}\right)} _{,i}}{-{{{{ \beta} ^l}} {{tr(b)}}}}}\right)}}\right)} _{,r}}$
${{ {{ b} ^l} _k} _{,t}} = {{{\left( {{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}\right)} _{,r}}{-{{\left( {{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}\right)} _{,r}}} + {{\left( {{{ \beta} ^r}} {{{{ b} ^l} _k}}\right)} _{,r}}}$
${{{ b} ^l} _k} _{,t}$ flux term: $-{{\left( {{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}{-{{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}} + {{{{ \beta} ^r}} {{{{ b} ^l} _k}}}\right)} _{,r}}$
${{{ b} ^l} _k} _{,t}$ source term: $0$
as a system:
flux vector in index form:
${{{ \left[\begin{array}{c} \alpha\\ {{ \gamma} _i} _j\\ { a} _k\\ {{{ d} _k} _i} _j\\ {{ K} _i} _j\\ \Theta\\ { Z} _k\\ { {(\beta_{h.p.})}} ^l\\ {{ {(b_{h.p.})}} ^l} _k\\ { {(\beta_{h.h.})}} ^l\\ {{ {(b_{h.h.})}} ^l} _k\\ { {(B_{h.h.})}} ^l\\ { {(\beta_{m.h.})}} ^l\\ {{ {(b_{m.h.})}} ^l} _k\\ { {(B_{m.h.})}} ^l\\ { {(\beta_{γ.h.})}} ^l\\ {{ {(b_{γ.h.})}} ^l} _k\\ { {(B_{γ.h.})}} ^l\end{array}\right]} _{,t}} + {{ \left[\begin{array}{c} -{{{\alpha}} \cdot {{{ \beta} ^r}}}\\ -{{{{{ \gamma} _i} _j}} {{{ \beta} ^r}}}\\ {-{{{\alpha}} \cdot {{f}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}} {{{{ δ} ^r} _k}}}}{-{{{{ \beta} ^r}} {{{ a} _k}}}}\\ {-{{{{\frac{1}{2}}{\left({{{{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}}} + {{{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}}\right)}}} {{{{ δ} ^r} _k}}}}{-{{{{ \beta} ^r}} {{{{{ d} _k} _i} _j}}}}\\ {{{\frac{1}{2}}} {{\left({{{{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^r} _j}}} + {{{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^r} _i}}}}\right)}}}{-{{{{{ K} _i} _j}} {{{ \beta} ^r}}}}{-{{{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ δ} ^r} _j}}} + {{{{ Z} _j}} {{{{ δ} ^r} _i}}}}\right)}}}}{-{{{\alpha}} \cdot {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^r} _j}}} + {{{{ d} _j}} {{{{ δ} ^r} _i}}}}\right)}}}} + {{{{ \Gamma} ^r} _i} _j}}\right)}}}}\\ {-{{{\Theta}} \cdot {{{ \beta} ^r}}}}{-{{{\alpha}} \cdot {{{ Z} ^r}}}}{-{{{\frac{1}{2}}} {{\alpha}} \cdot {{2}} {{\left({{-{{ d} ^r}} + {{ e} ^r}}\right)}}}}\\ { {-{{ \beta} ^r}} {{{ Z} _k}}} + {{{\alpha}} \cdot {{\left({{-{{{ K} ^r} _k}} + {{{{{ δ} ^r} _k}} {{\left({{tr(K)}{-{\Theta}}}\right)}}}}\right)}}}\\ -{{{{ \beta} ^r}} {{{ \beta} ^l}}}\\ {-{{{{{ δ} ^r} _k}} {{\left({{{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}} + {{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}{-{{{{ \beta} ^r}} {{{{ b} ^l} _k}}}}\\ -{{{{ \beta} ^r}} {{{ \beta} ^l}}}\\ {-{{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}} + {{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}{-{{{{ \beta} ^r}} {{{{ b} ^l} _k}}}}\\ -{{{{ \beta} ^r}} {{{ B} ^l}}}\\ -{{{{ \beta} ^r}} {{{ \beta} ^l}}}\\ {-{{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}} + {{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}{-{{{{ \beta} ^r}} {{{{ b} ^l} _k}}}}\\ {-{{{{\epsilon_{mde}}}} \cdot {{\left({{{{ (\nabla\beta)} ^l} ^r} + {{{\frac{1}{3}}} {{{{ \gamma} ^r} ^l}} {{(\nabla \cdot \beta)}}} + {{{{{ \gamma} ^l} ^i}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^r} _j}}} + {{{{ d} _j}} {{{{ δ} ^r} _i}}}}\right)}}}} + {{{{ \Gamma} ^r} _i} _j}}\right)}} {{{ \beta} ^j}}}{-{{{2}} {{\alpha}} \cdot {{{{ A} ^l} ^r}}}}}\right)}}}}{-{{{{ \beta} ^r}} {{{ B} ^l}}}}\\ -{{{{ \beta} ^r}} {{{ \beta} ^l}}}\\ {-{{{{{ δ} ^r} _k}} {{\left({{{ B} ^l} + {{{{ \beta} ^i}} {{{{ b} ^l} _i}}} + {0}}\right)}}}} + {{{{{ δ} ^r} _k}} {{{ \beta} ^i}} {{{{ b} ^l} _i}}}{-{{{{ \beta} ^r}} {{{{ b} ^l} _k}}}}\\ {-{{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{{{ \gamma} ^r} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{{ \gamma} ^l} ^r}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}}}{-{{{{ \beta} ^r}} {{{ B} ^l}}}}\end{array}\right]} _{,r}}} = {\left[\begin{array}{c} {{{f}} {{{\alpha}^{2}}} {{\left({{-{tr(K)}} + {{{2}} {{\Theta}}}}\right)}}}{-{{{\alpha}} \cdot {{tr(b)}}}}\\ {{{{{ b} ^k} _i}} {{{{ \gamma} _j} _k}}} + {{{{{ b} ^k} _j}} {{{{ \gamma} _i} _k}}}{-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}}{-{{{{{ \gamma} _i} _j}} {{tr(b)}}}}\\ {-{{{tr(b)}} \cdot {{{ a} _k}}}} + {{{{ a} _m}} {{{{ b} ^m} _k}}}\\ {-{{{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}}} + {{{{{ b} ^l} _k}} {{{{{ d} _l} _i} _j}}}\\ {{{{{{ \Gamma} ^k} _i} _j}} {{\alpha}} \cdot {{{ a} _k}}} + {{{\alpha}} \cdot {{\left({{{{-2}} {{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}} + {{{{{ K} _i} _j}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _j}}}}}\right)}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{1} + {{\kappa_2}}}\right)}} {{{{ \gamma} _i} _j}} {{\Theta}}}} + {{{4}} {{π}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S}{-{\rho}}}\right)}}}{-{{{2}} {{{{ S} _i} _j}}}}}\right)}}} + {{{{{ K} _k} _i}} {{{{ b} ^k} _j}}} + {{{{{ K} _k} _j}} {{{{ b} ^k} _i}}}{-{{{{{ K} _i} _j}} {{tr(b)}}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{{{{ Z} _i}} {{{{ δ} ^k} _j}}} + {{{{ Z} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{\alpha}} \cdot {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}}{-{{{\alpha}} \cdot {{{ a} _k}} {{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}}}}\\ {{{\alpha}} \cdot {{\left({{{ d} ^k}{-{{{2}} {{{ a} ^k}}}}}\right)}} {{{ Z} _k}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{{{tr(K)}} \cdot {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}}{-{{{{{ K} ^m} _n}} {{{{ K} ^n} _m}}}}{-{{{16}} {{π}} \cdot {{\rho}}}}}\right)}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{\left({{-{{{{ d} _l}} {{{ d} ^l}}}}{-{{{{{{ d} _l} _m} _n}} {{{{{ d} ^l} ^m} ^n}}}} + {{{2}} {{{{{ d} _l} _m} _n}} {{{{{ d} ^m} ^l} ^n}}}}\right)}}}{-{{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _k}} {{2}} {{\left({{-{{ d} ^k}} + {{ e} ^k}}\right)}}}}{-{{{\alpha}} \cdot {{{\kappa_1}}} \cdot {{\left({{{\kappa_2}} + {2}}\right)}} {{\Theta}}}}{-{{{\Theta}} \cdot {{tr(b)}}}}\\ {{{\alpha}} \cdot {{\left({{{{{ a} _k}} {{\left({{tr(K)}{-{{{2}} {{\Theta}}}}}\right)}}} + {{{{{ K} _k} _l}} {{\left({{-{{ a} ^l}} + {{ d} ^l}{-{{{2}} {{{ Z} ^l}}}}}\right)}}}{-{{{{{{ d} _k} _p} _q}} {{{{ K} ^p} ^q}}}}{-{{{{\kappa_1}}} \cdot {{{ Z} _k}}}}{-{{{8}} {{π}} \cdot {{{ S} _k}}}}}\right)}}} + {{{{ Z} _l}} {{{{ b} ^l} _k}}}{-{{{{ Z} _k}} {{tr(b)}}}}\\ {{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}}{-{{{{ \beta} ^l}} {{tr(b)}}}}\\ 0\\ {{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}\\ 0\\ {{{{\alpha}^{2}}} {{\left({{{{2}} {{{ e} ^l}}}{-{{ d} ^l}}{-{{ a} ^l}}}\right)}}}{-{{{{ B} ^l}} {{tr(b)}}}}\\ {{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}\\ 0\\ {{{{\epsilon_{mde}}}} \cdot {{\left({{{{{{ (\nabla\beta)} ^l} ^j}} {{{ d} _j}}} + {{{{{ (\nabla\beta)} ^n} ^k}} {{{{{ \Gamma} ^l} _n} _k}}} + {{{\frac{2}{3}}} {{(\nabla \cdot \beta)}} \cdot {{{ e} ^l}}} + {{{{{ \gamma} ^l} ^i}} {{{ \beta} ^j}} {{\left({{{{{ d} _m}} {{{{{ \Gamma} ^m} _i} _j}}}{-{{{{{{ \Gamma} ^k} _m} _j}} {{{{{ \Gamma} ^m} _i} _k}}}}}\right)}}} + {{{\left({{-{{{\frac{1}{2}}} {{\left({{{{{ d} _i}} {{{{ δ} ^k} _j}}} + {{{{ d} _j}} {{{{ δ} ^k} _i}}}}\right)}}}} + {{{{ \Gamma} ^k} _i} _j}}\right)}} {{\left({{{{-2}} {{{{{ d} _k} ^l} ^i}} {{{ \beta} ^j}}} + {{{{{ \gamma} ^l} ^i}} {{{{ b} ^j} _k}}}}\right)}}}{-{{{2}} {{\alpha}} \cdot {{\left({{{{{{ A} ^m} ^n}} {{{{{ \Gamma} ^l} _n} _m}}} + {{{{{ A} ^l} ^m}} {{{{{ \Gamma} ^n} _n} _m}}}}\right)}}}}}\right)}}}{-{{{{ B} ^l}} {{tr(b)}}}}\\ {{ B} ^l}{-{{{{ \beta} ^l}} {{tr(b)}}}}\\ 0\\ {{{\frac{3}{4}}} {{{(1/W)}^{2}}} {{\left({{{{2}} {{{ e} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{{{ \gamma} ^j} ^k}} {{\left({{{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{ b} ^m} _k}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{ b} ^l} _m}}}} + {{{{{{ \hat{\Gamma}} ^l} _j} _m}} {{{{{ \hat{\Gamma}} ^m} _n} _k}} {{{ \beta} ^n}}}{-{{{{{{ \hat{\Gamma}} ^m} _j} _k}} {{{{{ \hat{\Gamma}} ^l} _n} _m}} {{{ \beta} ^n}}}}}\right)}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{{ \Delta\Gamma} ^l} _m} _n}} {{{{ \gamma} ^m} ^n}}} + {{{\frac{2}{3}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ e} ^l}}}{-{{{2}} {{{{ A} ^l} ^j}} {{\left({{{{\alpha}} \cdot {{{ a} _j}}}{-{{ \overset{\Delta}{G}} _j}}}\right)}}}} + {{{2}} {{{{ A} ^j} ^k}} {{{{{ \Delta\Gamma} ^l} _j} _k}}} + {{{\frac{4}{3}}} {{\alpha}} \cdot {{tr(K)}} \cdot {{\left({{{ a} ^l}{-{{{2}} {{{ e} ^l}}}}}\right)}}}{-{{{\frac{2}{3}}} {{\left({{{{{ \overset{\Delta}{G}} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}}} + {{{\frac{1}{3}}} {{{ \overset{\Delta}{G}} ^l}} {{\left({{{(\hat{\nabla}\cdot\beta)}}{-{{{4}} {{\alpha}} \cdot {{tr(K)}}}}}\right)}}}}\right)}}}}}\right)}}}{-{{{\frac{3}{4}}} {{{ \bar{\Lambda}} ^j}} {{{{ b} ^l} _j}}}}{-{{{\eta}} \cdot {{{ B} ^l}}}}{-{{{{ B} ^l}} {{tr(b)}}}}\end{array}\right]}$
${{{ \left[\begin{array}{c} \alpha\\ {{ \gamma} _i} _j\\ { a} _k\\ {{{ d} _k} _i} _j\\ {{ K} _i} _j\\ \Theta\\ { Z} _k\\ { {(\beta_{h.p.})}} ^l\\ {{ {(b_{h.p.})}} ^l} _k\\ { {(\beta_{h.h.})}} ^l\\ {{ {(b_{h.h.})}} ^l} _k\\ { {(B_{h.h.})}} ^l\\ { {(\beta_{m.h.})}} ^l\\ {{ {(b_{m.h.})}} ^l} _k\\ { {(B_{m.h.})}} ^l\\ { {(\beta_{γ.h.})}} ^l\\ {{ {(b_{γ.h.})}} ^l} _k\\ { {(B_{γ.h.})}} ^l\end{array}\right]} _{,t}} + {{ \left[\begin{array}{c} {{-1}} {{\alpha}} \cdot {{{ \beta} ^r}}\\ {{-1}} {{{ \beta} ^r}} {{{{ \gamma} _i} _j}}\\ {{{-1}} {{{ \beta} ^r}} {{{ a} _k}}} + {{{(f \alpha)}} \cdot {{tr(K)}} \cdot {{{{ δ} ^r} _k}}} + {{{-2}} {{(f \alpha)}} \cdot {{\Theta}} \cdot {{{{ δ} ^r} _k}}}\\ {{{-1}} {{{ \beta} ^r}} {{{{{ d} _k} _i} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \gamma} _i} _l}} {{{{ b} ^l} _j}} {{{{ δ} ^r} _k}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \gamma} _j} _l}} {{{{ b} ^l} _i}} {{{{ δ} ^r} _k}}} + {{{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ δ} ^r} _k}}}\\ {{{-1}} {{\alpha}} \cdot {{{{{ \Gamma} ^r} _i} _j}}} + {{{-1}} {{{ \beta} ^r}} {{{{ K} _i} _j}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _j}} {{{{ δ} ^r} _i}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _i}} {{{{ δ} ^r} _j}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ d} _j}} {{{{ δ} ^r} _i}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ d} _i}} {{{{ δ} ^r} _j}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _i}} {{{{ δ} ^r} _j}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _j}} {{{{ δ} ^r} _i}}}\\ {{{-1}} {{\Theta}} \cdot {{{ \beta} ^r}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} ^r}}} + {{{\alpha}} \cdot {{{ d} ^r}}} + {{{-1}} {{\alpha}} \cdot {{{ e} ^r}}}\\ {{{-1}} {{\alpha}} \cdot {{{{ K} ^r} _k}}} + {{{-1}} {{{ Z} _k}} {{{ \beta} ^r}}} + {{{-1}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ δ} ^r} _k}}} + {{{\alpha}} \cdot {{tr(K)}} \cdot {{{{ δ} ^r} _k}}}\\ {{-1}} {{{ \beta} ^l}} {{{ \beta} ^r}}\\ {{{-1}} {{{ \beta} ^r}} {{{{ b} ^l} _k}}} + {{{{ a} ^l}} {{{{ δ} ^r} _k}} {{{\alpha}^{2}}}} + {{{{ d} ^l}} {{{{ δ} ^r} _k}} {{{\alpha}^{2}}}} + {{{-2}} {{{ e} ^l}} {{{{ δ} ^r} _k}} {{{\alpha}^{2}}}}\\ {{-1}} {{{ \beta} ^l}} {{{ \beta} ^r}}\\ {{{-1}} {{{ B} ^l}} {{{{ δ} ^r} _k}}} + {{{-1}} {{{ \beta} ^r}} {{{{ b} ^l} _k}}}\\ {{-1}} {{{ B} ^l}} {{{ \beta} ^r}}\\ {{-1}} {{{ \beta} ^l}} {{{ \beta} ^r}}\\ {{{-1}} {{{ B} ^l}} {{{{ δ} ^r} _k}}} + {{{-1}} {{{ \beta} ^r}} {{{{ b} ^l} _k}}}\\ {{{-1}} {{{\epsilon_{mde}}}} \cdot {{{{ (\nabla\beta)} ^l} ^r}}} + {{{-1}} {{{ B} ^l}} {{{ \beta} ^r}}} + {{{-1}} \cdot {{\frac{1}{3}}} {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}} \cdot {{{{ \gamma} ^r} ^l}}} + {{{\frac{1}{2}}} {{{\epsilon_{mde}}}} \cdot {{{ \beta} ^r}} {{{ d} _i}} {{{{ \gamma} ^l} ^i}}} + {{{\frac{1}{2}}} {{{\epsilon_{mde}}}} \cdot {{{ \beta} ^j}} {{{ d} _j}} {{{{ \gamma} ^l} ^r}}} + {{{2}} {{\alpha}} \cdot {{{\epsilon_{mde}}}} \cdot {{{{ A} ^l} ^r}}} + {{{-1}} {{{\epsilon_{mde}}}} \cdot {{{ \beta} ^j}} {{{{ \gamma} ^l} ^i}} {{{{{ \Gamma} ^r} _i} _j}}}\\ {{-1}} {{{ \beta} ^l}} {{{ \beta} ^r}}\\ {{{-1}} {{{ B} ^l}} {{{{ δ} ^r} _k}}} + {{{-1}} {{{ \beta} ^r}} {{{{ b} ^l} _k}}}\\ {{{-1}} \cdot {{\frac{1}{4}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{ \gamma} ^l} ^r}} {{{(1/W)}^{2}}}} + {{{-1}} {{{ B} ^l}} {{{ \beta} ^r}}} + {{{-3}} \cdot {{\frac{1}{4}}} {{{{ \gamma} ^r} ^k}} {{{{ {(\hat{\nabla}\beta)}} ^l} _k}} {{{(1/W)}^{2}}}} + {{{\alpha}} \cdot {{tr(K)}} \cdot {{{{ \gamma} ^l} ^r}} {{{(1/W)}^{2}}}}\end{array}\right]} _{,r}}} = {\left[\begin{array}{c} {{{-1}} {{\alpha}} \cdot {{tr(b)}}} + {{{-1}} {{(f \alpha)}} \cdot {{\alpha}} \cdot {{tr(K)}}} + {{{2}} {{(f \alpha)}} \cdot {{\Theta}} \cdot {{\alpha}}}\\ {{{ b} _i} _j} + {{{ b} _j} _i} + {{{-1}} {{tr(b)}} \cdot {{{{ \gamma} _i} _j}}} + {{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}\\ {{{-1}} {{tr(b)}} \cdot {{{ a} _k}}} + {{{{ a} _a}} {{{{ b} ^a} _k}}}\\ {{{-1}} {{tr(b)}} \cdot {{{{{ d} _k} _i} _j}}} + {{{{{ b} ^a} _k}} {{{{{ d} _a} _i} _j}}}\\ {{{-1}} {{tr(b)}} \cdot {{{{ K} _i} _j}}} + {{{{{ K} _a} _j}} {{{{ b} ^a} _i}}} + {{{{{ K} _a} _i}} {{{{ b} ^a} _j}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _j}} {{{ d} _i}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _i}} {{{ d} _j}}} + {{{\alpha}} \cdot {{tr(K)}} \cdot {{{{ K} _i} _j}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _i}} {{{ a} _j}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _j}} {{{ a} _i}}} + {{{\alpha}} \cdot {{{ d} _a}} {{{{{ \Gamma} ^a} _i} _j}}} + {{{-1}} {{\alpha}} \cdot {{{{{ \Gamma} ^a} _b} _j}} {{{{{ \Gamma} ^b} _i} _a}}} + {{{-2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{-2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{{ \Gamma} ^a} _i} _j}}} + {{{-2}} {{\alpha}} \cdot {{{{ K} _a} _j}} {{{{ K} _i} ^a}}} + {{{-8}} {{\alpha}} \cdot {{π}} \cdot {{{{ S} _i} _j}}} + {{{-1}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{{ \gamma} _i} _j}}} + {{{4}} {{S}} {{\alpha}} \cdot {{π}} \cdot {{{{ \gamma} _i} _j}}} + {{{-4}} {{\alpha}} \cdot {{\rho}} \cdot {{π}} \cdot {{{{ \gamma} _i} _j}}} + {{{-1}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}} \cdot {{{{ \gamma} _i} _j}}}\\ {{{\frac{1}{2}}} {{\alpha}} \cdot {{{tr(K)}^{2}}}} + {{{-1}} {{\Theta}} \cdot {{tr(b)}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{ d} ^a}} {{{ d} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ K} ^a} _b}} {{{{ K} ^b} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{{ d} ^a} ^b} ^c}} {{{{{ d} _a} _b} _c}}} + {{{-1}} {{\Theta}} \cdot {{\alpha}} \cdot {{tr(K)}}} + {{{\alpha}} \cdot {{{ Z} _a}} {{{ d} ^a}}} + {{{\alpha}} \cdot {{{ a} _a}} {{{ d} ^a}}} + {{{-1}} {{\alpha}} \cdot {{{ a} _a}} {{{ e} ^a}}} + {{{\alpha}} \cdot {{{{{ d} _a} _b} _c}} {{{{{ d} ^b} ^a} ^c}}} + {{{-2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}} + {{{-2}} {{\alpha}} \cdot {{{ Z} _a}} {{{ a} ^a}}} + {{{-8}} {{\alpha}} \cdot {{\rho}} \cdot {{π}}} + {{{-1}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}\\ {{{-1}} {{tr(b)}} \cdot {{{ Z} _k}}} + {{{{ Z} _a}} {{{{ b} ^a} _k}}} + {{{-1}} {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{ Z} _k}}} + {{{\alpha}} \cdot {{tr(K)}} \cdot {{{ a} _k}}} + {{{-1}} {{\alpha}} \cdot {{{ a} ^a}} {{{{ K} _k} _a}}} + {{{\alpha}} \cdot {{{ d} ^a}} {{{{ K} _k} _a}}} + {{{-1}} {{\alpha}} \cdot {{{{ K} ^a} ^b}} {{{{{ d} _k} _a} _b}}} + {{{-2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ a} _k}}} + {{{-2}} {{\alpha}} \cdot {{{ Z} ^a}} {{{{ K} _k} _a}}} + {{{-8}} {{\alpha}} \cdot {{π}} \cdot {{{ S} _k}}}\\ {{{-1}} {{tr(b)}} \cdot {{{ \beta} ^l}}} + {{{-1}} {{{ a} ^l}} {{{\alpha}^{2}}}} + {{{-1}} {{{ d} ^l}} {{{\alpha}^{2}}}} + {{{2}} {{{ e} ^l}} {{{\alpha}^{2}}}}\\ 0\\ {{ B} ^l} + {{{-1}} {{tr(b)}} \cdot {{{ \beta} ^l}}}\\ 0\\ {{{-1}} {{tr(b)}} \cdot {{{ B} ^l}}} + {{{-1}} {{{ a} ^l}} {{{\alpha}^{2}}}} + {{{-1}} {{{ d} ^l}} {{{\alpha}^{2}}}} + {{{2}} {{{ e} ^l}} {{{\alpha}^{2}}}}\\ {{ B} ^l} + {{{-1}} {{tr(b)}} \cdot {{{ \beta} ^l}}}\\ 0\\ {{{-1}} {{tr(b)}} \cdot {{{ B} ^l}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{\epsilon_{mde}}}} \cdot {{{ d} ^l}} {{{{ b} ^a} _a}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{\epsilon_{mde}}}} \cdot {{{ d} _a}} {{{{ b} ^a} ^l}}} + {{{2}} \cdot {{\frac{1}{3}}} {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}} \cdot {{{ e} ^l}}} + {{{{\epsilon_{mde}}}} \cdot {{{ d} _a}} {{{{ (\nabla\beta)} ^l} ^a}}} + {{{{\epsilon_{mde}}}} \cdot {{{{ (\nabla\beta)} ^a} ^b}} {{{{{ \Gamma} ^l} _a} _b}}} + {{{{\epsilon_{mde}}}} \cdot {{{{ b} ^a} _b}} {{{{{ \Gamma} ^b} ^l} _a}}} + {{{{\epsilon_{mde}}}} \cdot {{{ \beta} ^a}} {{{ d} _b}} {{{{{ \Gamma} ^b} ^l} _a}}} + {{{{\epsilon_{mde}}}} \cdot {{{ \beta} ^a}} {{{ d} _b}} {{{{{ d} _a} ^b} ^l}}} + {{{{\epsilon_{mde}}}} \cdot {{{ \beta} ^a}} {{{ d} _a}} {{{ e} ^l}}} + {{{-1}} {{{\epsilon_{mde}}}} \cdot {{{ \beta} ^a}} {{{{{ \Gamma} ^b} _c} _a}} {{{{{ \Gamma} ^c} ^l} _b}}} + {{{-2}} {{\alpha}} \cdot {{{\epsilon_{mde}}}} \cdot {{{{ A} ^l} ^a}} {{{{{ \Gamma} ^b} _b} _a}}} + {{{-2}} {{\alpha}} \cdot {{{\epsilon_{mde}}}} \cdot {{{{ A} ^a} ^b}} {{{{{ \Gamma} ^l} _b} _a}}} + {{{-2}} {{{\epsilon_{mde}}}} \cdot {{{ \beta} ^a}} {{{{{ \Gamma} ^b} _c} _a}} {{{{{ d} _b} ^c} ^l}}}\\ {{ B} ^l} + {{{-1}} {{tr(b)}} \cdot {{{ \beta} ^l}}}\\ 0\\ {{{-3}} \cdot {{\frac{1}{4}}} {{{ \bar{\Lambda}} ^a}} {{{{ b} ^l} _a}}} + {{{-1}} \cdot {{\frac{1}{6}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ \overset{\Delta}{G}} ^l}} {{{(1/W)}^{2}}}} + {{{-1}} {{\eta}} \cdot {{{ B} ^l}}} + {{{-1}} {{tr(b)}} \cdot {{{ B} ^l}}} + {{{-3}} \cdot {{\frac{1}{4}}} {{{{ b} ^l} _a}} {{{{{ \hat{\Gamma}} ^a} ^b} _b}} {{{(1/W)}^{2}}}} + {{{3}} \cdot {{\frac{1}{4}}} {{{{ b} ^a} _b}} {{{{{ \hat{\Gamma}} ^l} ^b} _a}} {{{(1/W)}^{2}}}} + {{{\frac{1}{2}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{ e} ^l}} {{{(1/W)}^{2}}}} + {{{\frac{1}{2}}} {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{{{ \Delta\Gamma} ^l} ^a} _a}} {{{(1/W)}^{2}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \overset{\Delta}{G}} ^a}} {{{{ {(\hat{\nabla}\beta)}} ^l} _a}} {{{(1/W)}^{2}}}} + {{{3}} \cdot {{\frac{1}{2}}} {{{ \overset{\Delta}{G}} _a}} {{{{ A} ^l} ^a}} {{{(1/W)}^{2}}}} + {{{3}} \cdot {{\frac{1}{2}}} {{{ e} ^a}} {{{{ {(\hat{\nabla}\beta)}} ^l} _a}} {{{(1/W)}^{2}}}} + {{{3}} \cdot {{\frac{1}{2}}} {{{{ A} ^a} ^b}} {{{{{ \Delta\Gamma} ^l} _a} _b}} {{{(1/W)}^{2}}}} + {{{-3}} \cdot {{\frac{1}{4}}} {{{ \beta} ^a}} {{{{{ \hat{\Gamma}} ^b} ^c} _c}} {{{{{ \hat{\Gamma}} ^l} _a} _b}} {{{(1/W)}^{2}}}} + {{{3}} \cdot {{\frac{1}{4}}} {{{ \beta} ^a}} {{{{{ \hat{\Gamma}} ^c} _a} _b}} {{{{{ \hat{\Gamma}} ^l} ^b} _c}} {{{(1/W)}^{2}}}} + {{{2}} \cdot {{\frac{1}{3}}} {{\alpha}} \cdot {{tr(K)}} \cdot {{{ \overset{\Delta}{G}} ^l}} {{{(1/W)}^{2}}}} + {{{-3}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{ a} _a}} {{{{ A} ^l} ^a}} {{{(1/W)}^{2}}}} + {{{\alpha}} \cdot {{tr(K)}} \cdot {{{ a} ^l}} {{{(1/W)}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{tr(K)}} \cdot {{{ e} ^l}} {{{(1/W)}^{2}}}}\end{array}\right]}$
unraveling flux vector...
${{\frac{\partial \alpha}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{\alpha}}}\right)} _{,r}}} = {{{\alpha}} \cdot {{\left({{-{tr(b)}}{-{{{(f \alpha)}} \cdot {{tr(K)}}}} + {{{2}} {{(f \alpha)}} \cdot {{\Theta}}}}\right)}}}$
${{\frac{\partial { {{ \gamma} _x} _x}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _x} _x}}}}\right)} _{,r}}} = {{{{2}} {{{ {{ b} _x} _x}}}}{-{{{{ {{ \gamma} _x} _x}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _x} _x}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { {{ \gamma} _x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _x} _y}}}}\right)} _{,r}}} = {{{ {{ b} _x} _y}} + {{ {{ b} _y} _x}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { {{ \gamma} _x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _x} _z}}}}\right)} _{,r}}} = {{{ {{ b} _x} _z}} + {{ {{ b} _z} _x}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { {{ \gamma} _y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _y} _y}}}}\right)} _{,r}}} = {{{{2}} {{{ {{ b} _y} _y}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _y} _y}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { {{ \gamma} _y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _y} _z}}}}\right)} _{,r}}} = {{{ {{ b} _y} _z}} + {{ {{ b} _z} _y}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { {{ \gamma} _z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} _z} _z}}}}\right)} _{,r}}} = {{{{2}} {{{ {{ b} _z} _z}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{tr(b)}}}}{-{{{2}} {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}}}$
${{\frac{\partial { { a} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ { a} _x}}}}} + {{{(f \alpha)}} \cdot {{tr(K)}}}{-{{{2}} {{(f \alpha)}} \cdot {{\Theta}}}}\right)} _{,r}}} = {{{{{ { a} _x}}} \cdot {{{ {{ b} ^x} _x}}}}{-{{{{ { a} _x}}} \cdot {{tr(b)}}}} + {{{{ { a} _y}}} \cdot {{{ {{ b} ^y} _x}}}} + {{{{ { a} _z}}} \cdot {{{ {{ b} ^z} _x}}}}}$
${{\frac{\partial { { a} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { a} _y}}}}\right)} _{,r}}} = {{{{{ { a} _x}}} \cdot {{{ {{ b} ^x} _y}}}} + {{{{ { a} _y}}} \cdot {{{ {{ b} ^y} _y}}}}{-{{{{ { a} _y}}} \cdot {{tr(b)}}}} + {{{{ { a} _z}}} \cdot {{{ {{ b} ^z} _y}}}}}$
${{\frac{\partial { { a} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { a} _z}}}}\right)} _{,r}}} = {{{{{ { a} _x}}} \cdot {{{ {{ b} ^x} _z}}}} + {{{{ { a} _y}}} \cdot {{{ {{ b} ^y} _z}}}} + {{{{ { a} _z}}} \cdot {{{ {{ b} ^z} _z}}}}{-{{{{ { a} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _x} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _x} _x}}}}} + {{{{ {{ K} _x} _x}}} \cdot {{\alpha}}}{-{{{{ {{ \gamma} _x} _x}}} \cdot {{{ {{ b} ^x} _x}}}}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^y} _x}}}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^z} _x}}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _x} _x}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _x} _x}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _x} _x}}}}{-{{{{ {{{ d} _x} _x} _x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _x} _y}}{\partial t}} + {{\left( {\frac{1}{2}}{\left({{-{{{{ {{ \gamma} _x} _x}}} \cdot {{{ {{ b} ^x} _y}}}}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^x} _x}}}}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^y} _y}}}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^z} _y}}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{{ {{ b} ^y} _x}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^z} _x}}}}}{-{{{2}} {{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _x} _y}}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _x} _y}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _x} _y}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _x} _y}}}}{-{{{{ {{{ d} _x} _x} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _x} _z}}{\partial t}} + {{\left( {\frac{1}{2}}{\left({{-{{{{ {{ \gamma} _x} _x}}} \cdot {{{ {{ b} ^x} _z}}}}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^y} _z}}}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^x} _x}}}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^z} _z}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^y} _x}}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{{ {{ b} ^z} _x}}}}}{-{{{2}} {{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _x} _z}}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _x} _z}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _x} _z}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _x} _z}}}}{-{{{{ {{{ d} _x} _x} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _y} _y}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _y} _y}}}}} + {{{{ {{ K} _y} _y}}} \cdot {{\alpha}}}{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^x} _y}}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{{ {{ b} ^y} _y}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^z} _y}}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _y} _y}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _y} _y}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _y} _y}}}}{-{{{{ {{{ d} _x} _y} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _y} _z}}{\partial t}} + {{\left( {\frac{1}{2}}{\left({{-{{{{ {{ \gamma} _x} _y}}} \cdot {{{ {{ b} ^x} _z}}}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^x} _y}}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{{ {{ b} ^y} _z}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^y} _y}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^z} _z}}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{{ {{ b} ^z} _y}}}}}{-{{{2}} {{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _y} _z}}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _y} _z}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _y} _z}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _y} _z}}}}{-{{{{ {{{ d} _x} _y} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _x} _z} _z}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _x} _z} _z}}}}} + {{{{ {{ K} _z} _z}}} \cdot {{\alpha}}}{-{{{{ {{ \gamma} _x} _z}}} \cdot {{{ {{ b} ^x} _z}}}}}{-{{{{ {{ \gamma} _y} _z}}} \cdot {{{ {{ b} ^y} _z}}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{{ {{ b} ^z} _z}}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _x}}} \cdot {{{ {{{ d} _x} _z} _z}}}} + {{{{ {{ b} ^y} _x}}} \cdot {{{ {{{ d} _y} _z} _z}}}} + {{{{ {{ b} ^z} _x}}} \cdot {{{ {{{ d} _z} _z} _z}}}}{-{{{{ {{{ d} _x} _z} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _x} _x}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _x} _x}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _x} _x}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _x} _x}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _x} _x}}}}{-{{{{ {{{ d} _y} _x} _x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _x} _y}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _x} _y}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _x} _y}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _x} _y}}}}{-{{{{ {{{ d} _y} _x} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _x} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _x} _z}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _x} _z}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _x} _z}}}}{-{{{{ {{{ d} _y} _x} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _y} _y}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _y} _y}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _y} _y}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _y} _y}}}}{-{{{{ {{{ d} _y} _y} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _y} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _y} _z}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _y} _z}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _y} _z}}}}{-{{{{ {{{ d} _y} _y} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _y} _z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _y} _z} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _y}}} \cdot {{{ {{{ d} _x} _z} _z}}}} + {{{{ {{ b} ^y} _y}}} \cdot {{{ {{{ d} _y} _z} _z}}}} + {{{{ {{ b} ^z} _y}}} \cdot {{{ {{{ d} _z} _z} _z}}}}{-{{{{ {{{ d} _y} _z} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _x} _x}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _x} _x}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _x} _x}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _x} _x}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _x} _x}}}}{-{{{{ {{{ d} _z} _x} _x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _x} _y}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _x} _y}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _x} _y}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _x} _y}}}}{-{{{{ {{{ d} _z} _x} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _x} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _x} _z}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _x} _z}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _x} _z}}}}{-{{{{ {{{ d} _z} _x} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _y} _y}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _y} _y}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _y} _y}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _y} _y}}}}{-{{{{ {{{ d} _z} _y} _y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _y} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _y} _z}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _y} _z}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _y} _z}}}}{-{{{{ {{{ d} _z} _y} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{{ d} _z} _z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{{ d} _z} _z} _z}}}}\right)} _{,r}}} = {{{{{ {{ b} ^x} _z}}} \cdot {{{ {{{ d} _x} _z} _z}}}} + {{{{ {{ b} ^y} _z}}} \cdot {{{ {{{ d} _y} _z} _z}}}} + {{{{ {{ b} ^z} _z}}} \cdot {{{ {{{ d} _z} _z} _z}}}}{-{{{{ {{{ d} _z} _z} _z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{ K} _x} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{ K} _x} _x}}}}} + {{{{ { a} _x}}} \cdot {{\alpha}}} + {{{{ { d} _x}}} \cdot {{\alpha}}}{-{{{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{\alpha}}}}\right)} _{,r}}} = {{-{{{{ {{ K} _x} _x}}} \cdot {{tr(b)}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^x} _x} _x}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^y} _x} _y}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^z} _x} _z}}^{2}}}}} + {{{2}} {{{ {{ K} _x} _x}}} \cdot {{{ {{ b} ^x} _x}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^y} _x}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^z} _x}}}} + {{{{ { a} _x}}} \cdot {{{ { d} _x}}} \cdot {{\alpha}}} + {{{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}}} + {{{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}}} + {{{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}}} + {{{{ {{ K} _x} _x}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ { a} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} _x}}} \cdot {{{ {{ K} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _x} ^y}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _x} ^z}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _x} _x}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{{ {{ \gamma} _x} _x}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{8}} {{{ {{ S} _x} _x}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{{ {{ \gamma} _x} _x}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}} + {{{4}} {{{ {{ \gamma} _x} _x}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{4}} {{{ {{ \gamma} _x} _x}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}}$
${{\frac{\partial { {{ K} _x} _y}}{\partial t}} + {{\left( {\frac{1}{2}}{\left({{{{{ { a} _y}}} \cdot {{\alpha}}} + {{{{ { d} _y}}} \cdot {{\alpha}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { \beta} ^x}}} \cdot {{{ {{ K} _x} _y}}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{2}}{\left({{{{2}} {{{ {{ K} _x} _x}}} \cdot {{{ {{ b} ^x} _y}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^x} _x}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^y} _y}}}}{-{{{2}} {{{ {{ K} _x} _y}}} \cdot {{tr(b)}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^z} _y}}}} + {{{2}} {{{ {{ K} _y} _y}}} \cdot {{{ {{ b} ^y} _x}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^z} _x}}}} + {{{{ { a} _x}}} \cdot {{{ { d} _y}}} \cdot {{\alpha}}} + {{{{ { a} _y}}} \cdot {{{ { d} _x}}} \cdot {{\alpha}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ { a} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ { a} _x}}} \cdot {{\alpha}}}} + {{{2}} {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} ^x} _x}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} ^y}}} \cdot {{{ {{ K} _y} _y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} ^z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} _y}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{16}} {{{ {{ S} _x} _y}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _x} _y}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}} + {{{8}} {{{ {{ \gamma} _x} _y}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{8}} {{{ {{ \gamma} _x} _y}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _x} _y}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}}}\right)}}$
${{\frac{\partial { {{ K} _x} _z}}{\partial t}} + {{\left( {\frac{1}{2}}{\left({{{{{ { a} _z}}} \cdot {{\alpha}}} + {{{{ { d} _z}}} \cdot {{\alpha}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { \beta} ^x}}} \cdot {{{ {{ K} _x} _z}}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{2}}{\left({{{{2}} {{{ {{ K} _x} _x}}} \cdot {{{ {{ b} ^x} _z}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^y} _z}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^x} _x}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^z} _z}}}}{-{{{2}} {{{ {{ K} _x} _z}}} \cdot {{tr(b)}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^y} _x}}}} + {{{2}} {{{ {{ K} _z} _z}}} \cdot {{{ {{ b} ^z} _x}}}} + {{{{ { a} _x}}} \cdot {{{ { d} _z}}} \cdot {{\alpha}}} + {{{{ { a} _z}}} \cdot {{{ { d} _x}}} \cdot {{\alpha}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ { a} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ { a} _x}}} \cdot {{\alpha}}}} + {{{2}} {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} ^x} _x}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} ^y}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} ^z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _x} _z}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{16}} {{{ {{ S} _x} _z}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _x} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}} + {{{8}} {{{ {{ \gamma} _x} _z}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{8}} {{{ {{ \gamma} _x} _z}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _x} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}}}\right)}}$
${{\frac{\partial { {{ K} _y} _y}}{\partial t}} + {{\left( -{\left({{{{{ { \beta} ^x}}} \cdot {{{ {{ K} _y} _y}}}} + {{{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{-{{{{ {{ K} _y} _y}}} \cdot {{tr(b)}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^x} _x} _y}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^y} _y} _y}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^z} _y} _z}}^{2}}}}} + {{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^x} _y}}}} + {{{2}} {{{ {{ K} _y} _y}}} \cdot {{{ {{ b} ^y} _y}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^z} _y}}}} + {{{{ { a} _y}}} \cdot {{{ { d} _y}}} \cdot {{\alpha}}} + {{{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{\alpha}}} + {{{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}}} + {{{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}}} + {{{{ {{ K} _y} _y}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ { a} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} _y}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} _y}}} \cdot {{{ {{ K} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _y} ^z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _y} _y}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{8}} {{{ {{ S} _y} _y}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{{ {{ \gamma} _y} _y}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}} + {{{4}} {{{ {{ \gamma} _y} _y}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{4}} {{{ {{ \gamma} _y} _y}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}}$
${{\frac{\partial { {{ K} _y} _z}}{\partial t}} + {{\left( -{\left({{{{{ { \beta} ^x}}} \cdot {{{ {{ K} _y} _z}}}} + {{{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{\frac{1}{2}}{\left({{{{2}} {{{ {{ K} _x} _y}}} \cdot {{{ {{ b} ^x} _z}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^x} _y}}}} + {{{2}} {{{ {{ K} _y} _y}}} \cdot {{{ {{ b} ^y} _z}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^y} _y}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^z} _z}}}}{-{{{2}} {{{ {{ K} _y} _z}}} \cdot {{tr(b)}}}} + {{{2}} {{{ {{ K} _z} _z}}} \cdot {{{ {{ b} ^z} _y}}}} + {{{{ { a} _y}}} \cdot {{{ { d} _z}}} \cdot {{\alpha}}} + {{{{ { a} _z}}} \cdot {{{ { d} _y}}} \cdot {{\alpha}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ { a} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ { a} _y}}} \cdot {{\alpha}}}} + {{{2}} {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} ^x} _y}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} ^y} _y}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _y} ^z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}}{-{{{4}} {{{ {{ K} _y} _z}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{16}} {{{ {{ S} _y} _z}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _y} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}} + {{{8}} {{{ {{ \gamma} _y} _z}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{8}} {{{ {{ \gamma} _y} _z}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}{-{{{2}} {{{ {{ \gamma} _y} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}}}\right)}}$
${{\frac{\partial { {{ K} _z} _z}}{\partial t}} + {{\left( -{\left({{{{{ { \beta} ^x}}} \cdot {{{ {{ K} _z} _z}}}} + {{{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{-{{{{ {{ K} _z} _z}}} \cdot {{tr(b)}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^x} _x} _z}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^y} _y} _z}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{{ \Gamma} ^z} _z} _z}}^{2}}}}} + {{{2}} {{{ {{ K} _x} _z}}} \cdot {{{ {{ b} ^x} _z}}}} + {{{2}} {{{ {{ K} _y} _z}}} \cdot {{{ {{ b} ^y} _z}}}} + {{{2}} {{{ {{ K} _z} _z}}} \cdot {{{ {{ b} ^z} _z}}}} + {{{{ { a} _z}}} \cdot {{{ { d} _z}}} \cdot {{\alpha}}} + {{{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{\alpha}}} + {{{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{\alpha}}} + {{{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}}} + {{{{ {{ K} _z} _z}}} \cdot {{\alpha}} \cdot {{tr(K)}}}{-{{{2}} {{{ { Z} _x}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _y}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ { a} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} _z}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} _z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^z} _z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} _z} _z}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{8}} {{{ {{ S} _z} _z}}} \cdot {{\alpha}} \cdot {{π}}}}{-{{{{ {{ \gamma} _z} _z}}} \cdot {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}} + {{{4}} {{{ {{ \gamma} _z} _z}}} \cdot {{S}} {{\alpha}} \cdot {{π}}}{-{{{4}} {{{ {{ \gamma} _z} _z}}} \cdot {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}}$
${{\frac{\partial \Theta}{\partial t}} + {{\left( {-{{{{ { Z} ^x}}} \cdot {{\alpha}}}}{-{{{{ { \beta} ^x}}} \cdot {{\Theta}}}} + {{{{ { d} ^x}}} \cdot {{\alpha}}}{-{{{{ { e} ^x}}} \cdot {{\alpha}}}}\right)} _{,r}}} = {{\frac{1}{2}}{\left({{-{{{\alpha}} \cdot {{{{ {{ K} ^x} _x}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{ K} ^y} _y}}^{2}}}}}{-{{{\alpha}} \cdot {{{{ {{ K} ^z} _z}}^{2}}}}} + {{{\alpha}} \cdot {{{tr(K)}^{2}}}}{-{{{2}} {{\Theta}} \cdot {{tr(b)}}}}{-{{{{ { d} ^x}}} \cdot {{{ { d} _x}}} \cdot {{\alpha}}}}{-{{{{ { d} ^y}}} \cdot {{{ { d} _y}}} \cdot {{\alpha}}}}{-{{{{ { d} ^z}}} \cdot {{{ { d} _z}}} \cdot {{\alpha}}}} + {{{{ {{{ d} ^x} ^x} ^x}}} \cdot {{{ {{{ d} _x} _x} _x}}} \cdot {{\alpha}}}{-{{{{ {{{ d} ^x} ^y} ^y}}} \cdot {{{ {{{ d} _x} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ {{{ d} ^x} ^z} ^z}}} \cdot {{{ {{{ d} _x} _z} _z}}} \cdot {{\alpha}}}}{-{{{{ {{{ d} ^y} ^x} ^x}}} \cdot {{{ {{{ d} _y} _x} _x}}} \cdot {{\alpha}}}} + {{{{ {{{ d} ^y} ^y} ^y}}} \cdot {{{ {{{ d} _y} _y} _y}}} \cdot {{\alpha}}}{-{{{{ {{{ d} ^y} ^z} ^z}}} \cdot {{{ {{{ d} _y} _z} _z}}} \cdot {{\alpha}}}}{-{{{{ {{{ d} ^z} ^x} ^x}}} \cdot {{{ {{{ d} _z} _x} _x}}} \cdot {{\alpha}}}}{-{{{{ {{{ d} ^z} ^y} ^y}}} \cdot {{{ {{{ d} _z} _y} _y}}} \cdot {{\alpha}}}} + {{{{ {{{ d} ^z} ^z} ^z}}} \cdot {{{ {{{ d} _z} _z} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ { Z} _x}}} \cdot {{{ { d} ^x}}} \cdot {{\alpha}}} + {{{2}} {{{ { Z} _y}}} \cdot {{{ { d} ^y}}} \cdot {{\alpha}}} + {{{2}} {{{ { Z} _z}}} \cdot {{{ { d} ^z}}} \cdot {{\alpha}}} + {{{2}} {{{ { a} _x}}} \cdot {{{ { d} ^x}}} \cdot {{\alpha}}}{-{{{2}} {{{ { a} _x}}} \cdot {{{ { e} ^x}}} \cdot {{\alpha}}}} + {{{2}} {{{ { a} _y}}} \cdot {{{ { d} ^y}}} \cdot {{\alpha}}}{-{{{2}} {{{ { a} _y}}} \cdot {{{ { e} ^y}}} \cdot {{\alpha}}}} + {{{2}} {{{ { a} _z}}} \cdot {{{ { d} ^z}}} \cdot {{\alpha}}}{-{{{2}} {{{ { a} _z}}} \cdot {{{ { e} ^z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} _y}}} \cdot {{{ {{ K} _x} ^y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} _z}}} \cdot {{{ {{ K} _x} ^z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} _z}}} \cdot {{{ {{ K} _y} ^z}}} \cdot {{\alpha}}}} + {{{2}} {{{ {{{ d} ^x} ^x} ^y}}} \cdot {{{ {{{ d} _y} _x} _x}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^x} ^x} ^z}}} \cdot {{{ {{{ d} _z} _x} _x}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^x} ^y} ^y}}} \cdot {{{ {{{ d} _y} _x} _y}}} \cdot {{\alpha}}}{-{{{2}} {{{ {{{ d} ^x} ^y} ^z}}} \cdot {{{ {{{ d} _x} _y} _z}}} \cdot {{\alpha}}}} + {{{2}} {{{ {{{ d} ^x} ^y} ^z}}} \cdot {{{ {{{ d} _y} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^x} ^y} ^z}}} \cdot {{{ {{{ d} _z} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^x} ^z} ^z}}} \cdot {{{ {{{ d} _z} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^y} ^x} ^x}}} \cdot {{{ {{{ d} _x} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^y} ^x} ^y}}} \cdot {{{ {{{ d} _x} _y} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^y} ^x} ^z}}} \cdot {{{ {{{ d} _x} _y} _z}}} \cdot {{\alpha}}}{-{{{2}} {{{ {{{ d} ^y} ^x} ^z}}} \cdot {{{ {{{ d} _y} _x} _z}}} \cdot {{\alpha}}}} + {{{2}} {{{ {{{ d} ^y} ^x} ^z}}} \cdot {{{ {{{ d} _z} _x} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^y} ^y} ^z}}} \cdot {{{ {{{ d} _z} _y} _y}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^y} ^z} ^z}}} \cdot {{{ {{{ d} _z} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^z} ^x} ^x}}} \cdot {{{ {{{ d} _x} _x} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^z} ^x} ^y}}} \cdot {{{ {{{ d} _x} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^z} ^x} ^y}}} \cdot {{{ {{{ d} _y} _x} _z}}} \cdot {{\alpha}}}{-{{{2}} {{{ {{{ d} ^z} ^x} ^y}}} \cdot {{{ {{{ d} _z} _x} _y}}} \cdot {{\alpha}}}} + {{{2}} {{{ {{{ d} ^z} ^x} ^z}}} \cdot {{{ {{{ d} _x} _z} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^z} ^y} ^y}}} \cdot {{{ {{{ d} _y} _y} _z}}} \cdot {{\alpha}}} + {{{2}} {{{ {{{ d} ^z} ^y} ^z}}} \cdot {{{ {{{ d} _y} _z} _z}}} \cdot {{\alpha}}}{-{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{tr(K)}}}}{-{{{4}} {{{ { Z} _x}}} \cdot {{{ { a} ^x}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _y}}} \cdot {{{ { a} ^y}}} \cdot {{\alpha}}}}{-{{{4}} {{{ { Z} _z}}} \cdot {{{ { a} ^z}}} \cdot {{\alpha}}}}{-{{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{16}} {{\alpha}} \cdot {{\rho}} \cdot {{π}}}}{-{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{\kappa_1}}} \cdot {{{\kappa_2}}}}}}\right)}}$
${{\frac{\partial { { Z} _x}}{\partial t}} + {{\left( {-{{{{ { Z} _x}}} \cdot {{{ { \beta} ^x}}}}}{-{{{{ {{ K} ^x} _x}}} \cdot {{\alpha}}}}{-{{{\Theta}} \cdot {{\alpha}}}} + {{{\alpha}} \cdot {{tr(K)}}}\right)} _{,r}}} = {{{{{ { Z} _x}}} \cdot {{{ {{ b} ^x} _x}}}}{-{{{{ { Z} _x}}} \cdot {{tr(b)}}}} + {{{{ { Z} _y}}} \cdot {{{ {{ b} ^y} _x}}}} + {{{{ { Z} _z}}} \cdot {{{ {{ b} ^z} _x}}}}{-{{{{ { Z} _x}}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{{ { a} ^x}}} \cdot {{{ {{ K} _x} _x}}} \cdot {{\alpha}}}}{-{{{{ { a} ^y}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{{ { a} ^z}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}} + {{{{ { a} _x}}} \cdot {{\alpha}} \cdot {{tr(K)}}} + {{{{ { d} ^x}}} \cdot {{{ {{ K} _x} _x}}} \cdot {{\alpha}}} + {{{{ { d} ^y}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}} + {{{{ { d} ^z}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}{-{{{{ {{ K} ^x} ^x}}} \cdot {{{ {{{ d} _x} _x} _x}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^y} ^y}}} \cdot {{{ {{{ d} _x} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^z} ^z}}} \cdot {{{ {{{ d} _x} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^x}}} \cdot {{{ {{ K} _x} _x}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^y}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^z}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { a} _x}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^y}}} \cdot {{{ {{{ d} _x} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^z}}} \cdot {{{ {{{ d} _x} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} ^z}}} \cdot {{{ {{{ d} _x} _y} _z}}} \cdot {{\alpha}}}}{-{{{8}} {{{ { S} _x}}} \cdot {{\alpha}} \cdot {{π}}}}}$
${{\frac{\partial { { Z} _y}}{\partial t}} + {{\left( -{\left({{{{{ { Z} _y}}} \cdot {{{ { \beta} ^x}}}} + {{{{ {{ K} ^x} _y}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{{{{ { Z} _x}}} \cdot {{{ {{ b} ^x} _y}}}} + {{{{ { Z} _y}}} \cdot {{{ {{ b} ^y} _y}}}}{-{{{{ { Z} _y}}} \cdot {{tr(b)}}}} + {{{{ { Z} _z}}} \cdot {{{ {{ b} ^z} _y}}}}{-{{{{ { Z} _y}}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{{ { a} ^x}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{{ { a} ^y}}} \cdot {{{ {{ K} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ { a} ^z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}} + {{{{ { a} _y}}} \cdot {{\alpha}} \cdot {{tr(K)}}} + {{{{ { d} ^x}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}} + {{{{ { d} ^y}}} \cdot {{{ {{ K} _y} _y}}} \cdot {{\alpha}}} + {{{{ { d} ^z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}{-{{{{ {{ K} ^x} ^x}}} \cdot {{{ {{{ d} _y} _x} _x}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^y} ^y}}} \cdot {{{ {{{ d} _y} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^z} ^z}}} \cdot {{{ {{{ d} _y} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^x}}} \cdot {{{ {{ K} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^y}}} \cdot {{{ {{ K} _y} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^z}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { a} _y}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^y}}} \cdot {{{ {{{ d} _y} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^z}}} \cdot {{{ {{{ d} _y} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} ^z}}} \cdot {{{ {{{ d} _y} _y} _z}}} \cdot {{\alpha}}}}{-{{{8}} {{{ { S} _y}}} \cdot {{\alpha}} \cdot {{π}}}}}$
${{\frac{\partial { { Z} _z}}{\partial t}} + {{\left( -{\left({{{{{ { Z} _z}}} \cdot {{{ { \beta} ^x}}}} + {{{{ {{ K} ^x} _z}}} \cdot {{\alpha}}}}\right)}\right)} _{,r}}} = {{{{{ { Z} _x}}} \cdot {{{ {{ b} ^x} _z}}}} + {{{{ { Z} _y}}} \cdot {{{ {{ b} ^y} _z}}}} + {{{{ { Z} _z}}} \cdot {{{ {{ b} ^z} _z}}}}{-{{{{ { Z} _z}}} \cdot {{tr(b)}}}}{-{{{{ { Z} _z}}} \cdot {{\alpha}} \cdot {{{\kappa_1}}}}}{-{{{{ { a} ^x}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{{ { a} ^y}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{{ { a} ^z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}} + {{{{ { a} _z}}} \cdot {{\alpha}} \cdot {{tr(K)}}} + {{{{ { d} ^x}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}} + {{{{ { d} ^y}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}} + {{{{ { d} ^z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}{-{{{{ {{ K} ^x} ^x}}} \cdot {{{ {{{ d} _z} _x} _x}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^y} ^y}}} \cdot {{{ {{{ d} _z} _y} _y}}} \cdot {{\alpha}}}}{-{{{{ {{ K} ^z} ^z}}} \cdot {{{ {{{ d} _z} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^x}}} \cdot {{{ {{ K} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^y}}} \cdot {{{ {{ K} _y} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { Z} ^z}}} \cdot {{{ {{ K} _z} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ { a} _z}}} \cdot {{\Theta}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^y}}} \cdot {{{ {{{ d} _z} _x} _y}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^x} ^z}}} \cdot {{{ {{{ d} _z} _x} _z}}} \cdot {{\alpha}}}}{-{{{2}} {{{ {{ K} ^y} ^z}}} \cdot {{{ {{{ d} _z} _y} _z}}} \cdot {{\alpha}}}}{-{{{8}} {{{ { S} _z}}} \cdot {{\alpha}} \cdot {{π}}}}}$
${{\frac{\partial { { {(\beta_{h.p.})}} ^x}}{\partial t}} + {{\left( -{{{ { \beta} ^x}}^{2}}\right)} _{,r}}} = {{-{{{{ { \beta} ^x}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^x}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^x}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^x}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { { {(\beta_{h.p.})}} ^y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^y}}}}\right)} _{,r}}} = {{-{{{{ { \beta} ^y}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^y}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^y}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^y}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { { {(\beta_{h.p.})}} ^z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^z}}}}\right)} _{,r}}} = {{-{{{{ { \beta} ^z}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^z}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^z}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^z}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^x} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _x}}}}} + {{{{ { a} ^x}}} \cdot {{{\alpha}^{2}}}} + {{{{ { d} ^x}}} \cdot {{{\alpha}^{2}}}}{-{{{2}} {{{ { e} ^x}}} \cdot {{{\alpha}^{2}}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^y} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _x}}}}} + {{{{ { a} ^y}}} \cdot {{{\alpha}^{2}}}} + {{{{ { d} ^y}}} \cdot {{{\alpha}^{2}}}}{-{{{2}} {{{ { e} ^y}}} \cdot {{{\alpha}^{2}}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^z} _x}}{\partial t}} + {{\left( {-{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _x}}}}} + {{{{ { a} ^z}}} \cdot {{{\alpha}^{2}}}} + {{{{ { d} ^z}}} \cdot {{{\alpha}^{2}}}}{-{{{2}} {{{ { e} ^z}}} \cdot {{{\alpha}^{2}}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^z} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.p.})}} ^z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { { {(\beta_{h.h.})}} ^x}}{\partial t}} + {{\left( -{{{ { \beta} ^x}}^{2}}\right)} _{,r}}} = {{{ { B} ^x}}{-{{{{ { \beta} ^x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{h.h.})}} ^y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^y}}}}\right)} _{,r}}} = {{{ { B} ^y}}{-{{{{ { \beta} ^y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{h.h.})}} ^z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^z}}}}\right)} _{,r}}} = {{{ { B} ^z}}{-{{{{ { \beta} ^z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^x} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^x}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^y} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^y}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^z} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^z}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^z} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{h.h.})}} ^z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { { {(B_{h.h.})}} ^x}}{\partial t}} + {{\left( -{{{{ { B} ^x}}} \cdot {{{ { \beta} ^x}}}}\right)} _{,r}}} = {{-{{{{ { B} ^x}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^x}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^x}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^x}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { { {(B_{h.h.})}} ^y}}{\partial t}} + {{\left( -{{{{ { B} ^y}}} \cdot {{{ { \beta} ^x}}}}\right)} _{,r}}} = {{-{{{{ { B} ^y}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^y}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^y}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^y}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { { {(B_{h.h.})}} ^z}}{\partial t}} + {{\left( -{{{{ { B} ^z}}} \cdot {{{ { \beta} ^x}}}}\right)} _{,r}}} = {{-{{{{ { B} ^z}}} \cdot {{tr(b)}}}}{-{{{{ { a} ^z}}} \cdot {{{\alpha}^{2}}}}}{-{{{{ { d} ^z}}} \cdot {{{\alpha}^{2}}}}} + {{{2}} {{{ { e} ^z}}} \cdot {{{\alpha}^{2}}}}}$
${{\frac{\partial { { {(\beta_{m.h.})}} ^x}}{\partial t}} + {{\left( -{{{ { \beta} ^x}}^{2}}\right)} _{,r}}} = {{{ { B} ^x}}{-{{{{ { \beta} ^x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{m.h.})}} ^y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^y}}}}\right)} _{,r}}} = {{{ { B} ^y}}{-{{{{ { \beta} ^y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{m.h.})}} ^z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^z}}}}\right)} _{,r}}} = {{{ { B} ^z}}{-{{{{ { \beta} ^z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^x} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^x}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^y} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^y}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^z} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^z}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^z} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{m.h.})}} ^z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { { {(B_{m.h.})}} ^x}}{\partial t}} + {{\left( {\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^x}}} \cdot {{{ { \beta} ^x}}}}}{-{{{6}} {{{ {{ (\nabla\beta)} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{2}} {{{ {{ \gamma} ^x} ^x}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ A} ^x} ^x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^x}}} \cdot {{tr(b)}}}}{-{{{3}} {{{ { d} ^x}}} \cdot {{{ {{ b} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^x}}} \cdot {{{ {{ b} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^x}}} \cdot {{{ {{ b} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _x}}} \cdot {{{ {{ b} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _y}}} \cdot {{{ {{ b} ^y} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _z}}} \cdot {{{ {{ b} ^z} ^x}}} \cdot {{{\epsilon_{mde}}}}}} + {{{4}} {{{ { e} ^x}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _x}}} \cdot {{{ {{ (\nabla\beta)} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _y}}} \cdot {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _z}}} \cdot {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ { e} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _x} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _y} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ { e} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _z} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ { e} ^x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{ {{{ d} _x} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{ {{{ d} _y} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{ {{{ d} _z} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^x} ^x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}}\right)}}$
${{\frac{\partial { { {(B_{m.h.})}} ^y}}{\partial t}} + {{\left( {\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^y}}} \cdot {{{ { \beta} ^x}}}}}{-{{{6}} {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{2}} {{{ {{ \gamma} ^x} ^y}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ A} ^x} ^y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^y}}} \cdot {{tr(b)}}}}{-{{{3}} {{{ { d} ^y}}} \cdot {{{ {{ b} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^y}}} \cdot {{{ {{ b} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^y}}} \cdot {{{ {{ b} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _x}}} \cdot {{{ {{ b} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _y}}} \cdot {{{ {{ b} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _z}}} \cdot {{{ {{ b} ^z} ^y}}} \cdot {{{\epsilon_{mde}}}}}} + {{{4}} {{{ { e} ^y}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _x}}} \cdot {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _y}}} \cdot {{{ {{ (\nabla\beta)} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _z}}} \cdot {{{ {{ (\nabla\beta)} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ { e} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _x} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ { e} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _y} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _z} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ { e} ^y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ d} _x} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{ {{{ d} _y} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{ {{{ d} _z} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^x} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^y} ^y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}}\right)}}$
${{\frac{\partial { { {(B_{m.h.})}} ^z}}{\partial t}} + {{\left( {\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^z}}} \cdot {{{ { \beta} ^x}}}}}{-{{{6}} {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{2}} {{{ {{ \gamma} ^x} ^z}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{3}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ A} ^x} ^z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{ \gamma} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{ \gamma} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{ \gamma} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{6}}{\left({{-{{{6}} {{{ { B} ^z}}} \cdot {{tr(b)}}}}{-{{{3}} {{{ { d} ^z}}} \cdot {{{ {{ b} ^x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^z}}} \cdot {{{ {{ b} ^y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} ^z}}} \cdot {{{ {{ b} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _x}}} \cdot {{{ {{ b} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _y}}} \cdot {{{ {{ b} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{3}} {{{ { d} _z}}} \cdot {{{ {{ b} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{4}} {{{ { e} ^z}}} \cdot {{(\nabla \cdot \beta)}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _x}}} \cdot {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _y}}} \cdot {{{ {{ (\nabla\beta)} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { d} _z}}} \cdot {{{ {{ (\nabla\beta)} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ (\nabla\beta)} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{12}} {{{ {{ (\nabla\beta)} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ { e} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^x}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _x} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ { e} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^y}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _y} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ \Gamma} ^x} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _x}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ \Gamma} ^y} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _y}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ { e} ^z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ \Gamma} ^z} ^z} _z}}} \cdot {{{\epsilon_{mde}}}}} + {{{6}} {{{ { \beta} ^z}}} \cdot {{{ { d} _z}}} \cdot {{{ {{{ d} _z} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ \Gamma} ^y} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{6}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} ^z} _z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _x}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _y}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{{ {{{ d} _x} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _y} _z}}} \cdot {{{ {{{ d} _x} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _z} _z}}} \cdot {{{ {{{ d} _x} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _z}}} \cdot {{{ {{{ d} _y} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{{ {{{ d} _y} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _z} _z}}} \cdot {{{ {{{ d} _y} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{{ {{{ d} _z} ^x} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{{ {{{ d} _z} ^y} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{{ {{{ d} _z} ^z} ^z}}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Gamma} ^z} _x} _x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _x}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _y} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^x} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{12}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^y} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _x} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{36}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _y} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Gamma} ^z} _x} _y}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}{-{{{24}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Gamma} ^z} _z} _z}}} \cdot {{\alpha}} \cdot {{{\epsilon_{mde}}}}}}}\right)}}$
${{\frac{\partial { { {(\beta_{γ.h.})}} ^x}}{\partial t}} + {{\left( -{{{ { \beta} ^x}}^{2}}\right)} _{,r}}} = {{{ { B} ^x}}{-{{{{ { \beta} ^x}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{γ.h.})}} ^y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^y}}}}\right)} _{,r}}} = {{{ { B} ^y}}{-{{{{ { \beta} ^y}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { { {(\beta_{γ.h.})}} ^z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ { \beta} ^z}}}}\right)} _{,r}}} = {{{ { B} ^z}}{-{{{{ { \beta} ^z}}} \cdot {{tr(b)}}}}}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^x} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^x}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^x} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^x} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^x} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^y} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^y}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^y} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^y} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^y} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^z} _x}}{\partial t}} + {{\left( -{\left({{{ { B} ^z}} + {{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _x}}}}}\right)}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^z} _y}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _y}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { {{ {(b_{γ.h.})}} ^z} _z}}{\partial t}} + {{\left( -{{{{ { \beta} ^x}}} \cdot {{{ {{ b} ^z} _z}}}}\right)} _{,r}}} = {0}$
${{\frac{\partial { { {(B_{γ.h.})}} ^x}}{\partial t}} + {{\left( {\frac{1}{4}}{\left({{-{{{{ {{ \gamma} ^x} ^x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{4}} {{{ { B} ^x}}} \cdot {{{ { \beta} ^x}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{4}} {{{ {{ \gamma} ^x} ^x}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{12}}{\left({{-{{{9}} {{{ { \bar{\Lambda}} ^x}}} \cdot {{{ {{ b} ^x} _x}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^y}}} \cdot {{{ {{ b} ^x} _y}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^z}}} \cdot {{{ {{ b} ^x} _z}}}}}{-{{{2}} {{{ { \overset{\Delta}{G}} ^x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{12}} {{{ { B} ^x}}} \cdot {{\eta}}}}{-{{{12}} {{{ { B} ^x}}} \cdot {{tr(b)}}}}{-{{{9}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{6}} {{{ { e} ^x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^x} ^x} _x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^x} ^y} _y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^x} ^z} _z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _x}}} \cdot {{{ {{ A} ^x} ^x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _y}}} \cdot {{{ {{ A} ^x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _z}}} \cdot {{{ {{ A} ^x} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^x} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _x}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _x}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{8}} {{{ { \overset{\Delta}{G}} ^x}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{18}} {{{ { a} _x}}} \cdot {{{ {{ A} ^x} ^x}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _y}}} \cdot {{{ {{ A} ^x} ^y}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _z}}} \cdot {{{ {{ A} ^x} ^z}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}} + {{{12}} {{{ { a} ^x}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{24}} {{{ { e} ^x}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}}\right)}}$
${{\frac{\partial { { {(B_{γ.h.})}} ^y}}{\partial t}} + {{\left( {\frac{1}{4}}{\left({{-{{{{ {{ \gamma} ^x} ^y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{4}} {{{ { B} ^y}}} \cdot {{{ { \beta} ^x}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{4}} {{{ {{ \gamma} ^x} ^y}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{12}}{\left({{-{{{9}} {{{ { \bar{\Lambda}} ^x}}} \cdot {{{ {{ b} ^y} _x}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^y}}} \cdot {{{ {{ b} ^y} _y}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^z}}} \cdot {{{ {{ b} ^y} _z}}}}}{-{{{2}} {{{ { \overset{\Delta}{G}} ^y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{12}} {{{ { B} ^y}}} \cdot {{\eta}}}}{-{{{12}} {{{ { B} ^y}}} \cdot {{tr(b)}}}} + {{{9}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{6}} {{{ { e} ^y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^y} ^x} _x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^y} ^y} _y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^y} ^z} _z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _x}}} \cdot {{{ {{ A} ^x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _y}}} \cdot {{{ {{ A} ^y} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _z}}} \cdot {{{ {{ A} ^y} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{8}} {{{ { \overset{\Delta}{G}} ^y}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{18}} {{{ { a} _x}}} \cdot {{{ {{ A} ^x} ^y}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _y}}} \cdot {{{ {{ A} ^y} ^y}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _z}}} \cdot {{{ {{ A} ^y} ^z}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}} + {{{12}} {{{ { a} ^y}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{24}} {{{ { e} ^y}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}}\right)}}$
${{\frac{\partial { { {(B_{γ.h.})}} ^z}}{\partial t}} + {{\left( {\frac{1}{4}}{\left({{-{{{{ {{ \gamma} ^x} ^z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{4}} {{{ { B} ^z}}} \cdot {{{ { \beta} ^x}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{3}} {{{ {{ \gamma} ^x} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{4}} {{{ {{ \gamma} ^x} ^z}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}\right)}\right)} _{,r}}} = {{\frac{1}{12}}{\left({{-{{{9}} {{{ { \bar{\Lambda}} ^x}}} \cdot {{{ {{ b} ^z} _x}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^y}}} \cdot {{{ {{ b} ^z} _y}}}}}{-{{{9}} {{{ { \bar{\Lambda}} ^z}}} \cdot {{{ {{ b} ^z} _z}}}}}{-{{{2}} {{{ { \overset{\Delta}{G}} ^z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}}}{-{{{12}} {{{ { B} ^z}}} \cdot {{\eta}}}}{-{{{12}} {{{ { B} ^z}}} \cdot {{tr(b)}}}} + {{{9}} {{{ {{ b} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^y} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ {{ b} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^z} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ {{ b} ^z} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ {{ b} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{6}} {{{ { \overset{\Delta}{G}} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{6}} {{{ { e} ^z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^z} ^x} _x}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^z} ^y} _y}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{6}} {{{ {{{ \Delta\Gamma} ^z} ^z} _z}}} \cdot {{{(\hat{\nabla}\cdot\beta)}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _x}}} \cdot {{{ {{ A} ^x} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _y}}} \cdot {{{ {{ A} ^y} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { \overset{\Delta}{G}} _z}}} \cdot {{{ {{ A} ^z} ^z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^x}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^y}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ { e} ^z}}} \cdot {{{ {{ {(\hat{\nabla}\beta)}} ^z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^x} ^x}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^y} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{18}} {{{ {{ A} ^z} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _z} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^y}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^x} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{36}} {{{ {{ A} ^y} ^z}}} \cdot {{{ {{{ \Delta\Gamma} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _x}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _y}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^x} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} ^z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{(1/W)}^{2}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^y} _z} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} ^z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _x}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^x} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _x} _z}}} \cdot {{{(1/W)}^{2}}}}{-{{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _y}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _z} _z}}} \cdot {{{(1/W)}^{2}}}}} + {{{9}} {{{ { \beta} ^z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} ^y} _z}}} \cdot {{{ {{{ \hat{\Gamma}} ^z} _y} _z}}} \cdot {{{(1/W)}^{2}}}} + {{{8}} {{{ { \overset{\Delta}{G}} ^z}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{18}} {{{ { a} _x}}} \cdot {{{ {{ A} ^x} ^z}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _y}}} \cdot {{{ {{ A} ^y} ^z}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}}{-{{{18}} {{{ { a} _z}}} \cdot {{{ {{ A} ^z} ^z}}} \cdot {{\alpha}} \cdot {{{(1/W)}^{2}}}}} + {{{12}} {{{ { a} ^z}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}{-{{{24}} {{{ { e} ^z}}} \cdot {{\alpha}} \cdot {{tr(K)}} \cdot {{{(1/W)}^{2}}}}}}\right)}}$
generating code
flux:
{\
(resultFlux)->alpha = 0.;\
(resultFlux)->gamma_ll.xx = 0.;\
(resultFlux)->gamma_ll.xy = 0.;\
(resultFlux)->gamma_ll.xz = 0.;\
(resultFlux)->gamma_ll.yy = 0.;\
(resultFlux)->gamma_ll.yz = 0.;\
(resultFlux)->gamma_ll.zz = 0.;\
(resultFlux)->a_l.x = f_alpha * (tr_K + -2. * Theta);\
(resultFlux)->a_l.y = 0.;\
(resultFlux)->a_l.z = 0.;\
(resultFlux)->d_lll.x.xx = K_ll.xx * alpha;\
(resultFlux)->d_lll.x.xy = K_ll.xy * alpha;\
(resultFlux)->d_lll.x.xz = K_ll.xz * alpha;\
(resultFlux)->d_lll.x.yy = K_ll.yy * alpha;\
(resultFlux)->d_lll.x.yz = K_ll.yz * alpha;\
(resultFlux)->d_lll.x.zz = K_ll.zz * alpha;\
(resultFlux)->d_lll.y.xx = 0.;\
(resultFlux)->d_lll.y.xy = 0.;\
(resultFlux)->d_lll.y.xz = 0.;\
(resultFlux)->d_lll.y.yy = 0.;\
(resultFlux)->d_lll.y.yz = 0.;\
(resultFlux)->d_lll.y.zz = 0.;\
(resultFlux)->d_lll.z.xx = 0.;\
(resultFlux)->d_lll.z.xy = 0.;\
(resultFlux)->d_lll.z.xz = 0.;\
(resultFlux)->d_lll.z.yy = 0.;\
(resultFlux)->d_lll.z.yz = 0.;\
(resultFlux)->d_lll.z.zz = 0.;\
(resultFlux)->K_ll.xx = alpha * (a_l.x + d_l.x + -2. * Z_l.x + -conn_ull.x.xx);\
(resultFlux)->K_ll.xy = (alpha * (a_l.y + d_l.y + -2. * conn_ull.x.xy + -2. * Z_l.y)) / 2.;\
(resultFlux)->K_ll.xz = (alpha * (a_l.z + d_l.z + -2. * conn_ull.x.xz + -2. * Z_l.z)) / 2.;\
(resultFlux)->K_ll.yy = -conn_ull.x.yy * alpha;\
(resultFlux)->K_ll.yz = -conn_ull.x.yz * alpha;\
(resultFlux)->K_ll.zz = -conn_ull.x.zz * alpha;\
(resultFlux)->Theta = alpha * (d_u.x + -Z_u.x + -e_u.x);\
(resultFlux)->Z_l.x = alpha * (tr_K + -K_ul.x.x + -Theta);\
(resultFlux)->Z_l.y = -K_ul.x.y * alpha;\
(resultFlux)->Z_l.z = -K_ul.x.z * alpha;\
}\
<? if eqn.useShift ~= "none" then ?>\
{\
{\
(resultFlux)->alpha += -beta_u.x * alpha;\
(resultFlux)->gamma_ll.xx += -beta_u.x * gamma_ll.xx;\
(resultFlux)->gamma_ll.xy += -beta_u.x * gamma_ll.xy;\
(resultFlux)->gamma_ll.xz += -beta_u.x * gamma_ll.xz;\
(resultFlux)->gamma_ll.yy += -beta_u.x * gamma_ll.yy;\
(resultFlux)->gamma_ll.yz += -beta_u.x * gamma_ll.yz;\
(resultFlux)->gamma_ll.zz += -beta_u.x * gamma_ll.zz;\
(resultFlux)->a_l.x += -beta_u.x * a_l.x;\
(resultFlux)->a_l.y += -beta_u.x * a_l.y;\
(resultFlux)->a_l.z += -beta_u.x * a_l.z;\
(resultFlux)->d_lll.x.xx += -(beta_u.x * d_lll.x.xx + gamma_ll.xx * b_ul.x.x + gamma_ll.xz * b_ul.z.x + gamma_ll.xy * b_ul.y.x);\
(resultFlux)->d_lll.x.xy += -(gamma_ll.xx * b_ul.x.y + gamma_ll.xy * b_ul.x.x + gamma_ll.xy * b_ul.y.y + gamma_ll.xz * b_ul.z.y + gamma_ll.yy * b_ul.y.x + 2. * beta_u.x * d_lll.x.xy + gamma_ll.yz * b_ul.z.x) / 2.;\
(resultFlux)->d_lll.x.xz += -(gamma_ll.xx * b_ul.x.z + gamma_ll.xy * b_ul.y.z + gamma_ll.xz * b_ul.x.x + gamma_ll.xz * b_ul.z.z + gamma_ll.yz * b_ul.y.x + 2. * beta_u.x * d_lll.x.xz + gamma_ll.zz * b_ul.z.x) / 2.;\
(resultFlux)->d_lll.x.yy += -(beta_u.x * d_lll.x.yy + gamma_ll.xy * b_ul.x.y + gamma_ll.yz * b_ul.z.y + gamma_ll.yy * b_ul.y.y);\
(resultFlux)->d_lll.x.yz += -(gamma_ll.xy * b_ul.x.z + gamma_ll.xz * b_ul.x.y + gamma_ll.yy * b_ul.y.z + gamma_ll.yz * b_ul.y.y + gamma_ll.yz * b_ul.z.z + 2. * beta_u.x * d_lll.x.yz + gamma_ll.zz * b_ul.z.y) / 2.;\
(resultFlux)->d_lll.x.zz += -(beta_u.x * d_lll.x.zz + gamma_ll.xz * b_ul.x.z + gamma_ll.zz * b_ul.z.z + gamma_ll.yz * b_ul.y.z);\
(resultFlux)->d_lll.y.xx += -beta_u.x * d_lll.y.xx;\
(resultFlux)->d_lll.y.xy += -beta_u.x * d_lll.y.xy;\
(resultFlux)->d_lll.y.xz += -beta_u.x * d_lll.y.xz;\
(resultFlux)->d_lll.y.yy += -beta_u.x * d_lll.y.yy;\
(resultFlux)->d_lll.y.yz += -beta_u.x * d_lll.y.yz;\
(resultFlux)->d_lll.y.zz += -beta_u.x * d_lll.y.zz;\
(resultFlux)->d_lll.z.xx += -beta_u.x * d_lll.z.xx;\
(resultFlux)->d_lll.z.xy += -beta_u.x * d_lll.z.xy;\
(resultFlux)->d_lll.z.xz += -beta_u.x * d_lll.z.xz;\
(resultFlux)->d_lll.z.yy += -beta_u.x * d_lll.z.yy;\
(resultFlux)->d_lll.z.yz += -beta_u.x * d_lll.z.yz;\
(resultFlux)->d_lll.z.zz += -beta_u.x * d_lll.z.zz;\
(resultFlux)->K_ll.xx += -beta_u.x * K_ll.xx;\
(resultFlux)->K_ll.xy += -beta_u.x * K_ll.xy;\
(resultFlux)->K_ll.xz += -beta_u.x * K_ll.xz;\
(resultFlux)->K_ll.yy += -beta_u.x * K_ll.yy;\
(resultFlux)->K_ll.yz += -beta_u.x * K_ll.yz;\
(resultFlux)->K_ll.zz += -beta_u.x * K_ll.zz;\
(resultFlux)->Theta += -beta_u.x * Theta;\
(resultFlux)->Z_l.x += -Z_l.x * beta_u.x;\
(resultFlux)->Z_l.y += -Z_l.y * beta_u.x;\
(resultFlux)->Z_l.z += -Z_l.z * beta_u.x;\
}\
<? if eqn.useShift == "HarmonicParabolic" then ?>\
{\
real const tmp1 = alpha * alpha;\
(resultFlux)->beta_u.x += -beta_u.x * beta_u.x;\
(resultFlux)->beta_u.y += -beta_u.x * beta_u.y;\
(resultFlux)->beta_u.z += -beta_u.x * beta_u.z;\
(resultFlux)->b_ul.x.x += -beta_u.x * b_ul.x.x + a_u.x * tmp1 + -2. * e_u.x * tmp1 + d_u.x * tmp1;\
(resultFlux)->b_ul.x.y += -beta_u.x * b_ul.x.y;\
(resultFlux)->b_ul.x.z += -beta_u.x * b_ul.x.z;\
(resultFlux)->b_ul.y.x += -beta_u.x * b_ul.y.x + a_u.y * tmp1 + -2. * e_u.y * tmp1 + d_u.y * tmp1;\
(resultFlux)->b_ul.y.y += -beta_u.x * b_ul.y.y;\
(resultFlux)->b_ul.y.z += -beta_u.x * b_ul.y.z;\
(resultFlux)->b_ul.z.x += -beta_u.x * b_ul.z.x + a_u.z * tmp1 + -2. * e_u.z * tmp1 + d_u.z * tmp1;\
(resultFlux)->b_ul.z.y += -beta_u.x * b_ul.z.y;\
(resultFlux)->b_ul.z.z += -beta_u.x * b_ul.z.z;\
}\
<? end ?>/* eqn.useShift == "HarmonicParabolic" */\
<? if eqn.useShift == "HarmonicHyperbolic" then ?>\
{\
(resultFlux)->beta_u.x += -beta_u.x * beta_u.x;\
(resultFlux)->beta_u.y += -beta_u.x * beta_u.y;\
(resultFlux)->beta_u.z += -beta_u.x * beta_u.z;\
(resultFlux)->b_ul.x.x += -(B_u.x + beta_u.x * b_ul.x.x);\
(resultFlux)->b_ul.x.y += -beta_u.x * b_ul.x.y;\
(resultFlux)->b_ul.x.z += -beta_u.x * b_ul.x.z;\
(resultFlux)->b_ul.y.x += -(B_u.y + beta_u.x * b_ul.y.x);\
(resultFlux)->b_ul.y.y += -beta_u.x * b_ul.y.y;\
(resultFlux)->b_ul.y.z += -beta_u.x * b_ul.y.z;\
(resultFlux)->b_ul.z.x += -(B_u.z + beta_u.x * b_ul.z.x);\
(resultFlux)->b_ul.z.y += -beta_u.x * b_ul.z.y;\
(resultFlux)->b_ul.z.z += -beta_u.x * b_ul.z.z;\
(resultFlux)->B_u.x += -B_u.x * beta_u.x;\
(resultFlux)->B_u.y += -B_u.y * beta_u.x;\
(resultFlux)->B_u.z += -B_u.z * beta_u.x;\
}\
<? end ?>/* eqn.useShift == "HarmonicHyperbolic" */\
<? if eqn.useShift == "MinimalDistortionHyperbolic" then ?>\
{\
real const tmp1 = tr_DBeta * mdeShiftEpsilon;\
real const tmp2 = gamma_uu.xy * mdeShiftEpsilon;\
real const tmp3 = d_l.y * tmp2;\
real const tmp4 = gamma_uu.xz * mdeShiftEpsilon;\
real const tmp5 = d_l.z * tmp4;\
real const tmp6 = gamma_uu.xx * mdeShiftEpsilon;\
real const tmp7 = alpha * mdeShiftEpsilon;\
real const tmp8 = conn_ull.x.xx * mdeShiftEpsilon;\
real const tmp9 = conn_ull.x.xy * mdeShiftEpsilon;\
real const tmp10 = gamma_uu.xy * tmp9;\
real const tmp11 = conn_ull.x.xz * mdeShiftEpsilon;\
real const tmp12 = gamma_uu.xz * tmp11;\
real const tmp13 = conn_ull.x.yy * mdeShiftEpsilon;\
real const tmp14 = conn_ull.x.yz * mdeShiftEpsilon;\
real const tmp15 = conn_ull.x.zz * mdeShiftEpsilon;\
real const tmp16 = gamma_uu.yz * mdeShiftEpsilon;\
real const tmp17 = gamma_uu.yz * tmp14;\
(resultFlux)->beta_u.x += -beta_u.x * beta_u.x;\
(resultFlux)->beta_u.y += -beta_u.x * beta_u.y;\
(resultFlux)->beta_u.z += -beta_u.x * beta_u.z;\
(resultFlux)->b_ul.x.x += -(B_u.x + beta_u.x * b_ul.x.x);\
(resultFlux)->b_ul.x.y += -beta_u.x * b_ul.x.y;\
(resultFlux)->b_ul.x.z += -beta_u.x * b_ul.x.z;\
(resultFlux)->b_ul.y.x += -(B_u.y + beta_u.x * b_ul.y.x);\
(resultFlux)->b_ul.y.y += -beta_u.x * b_ul.y.y;\
(resultFlux)->b_ul.y.z += -beta_u.x * b_ul.y.z;\
(resultFlux)->b_ul.z.x += -(B_u.z + beta_u.x * b_ul.z.x);\
(resultFlux)->b_ul.z.y += -beta_u.x * b_ul.z.y;\
(resultFlux)->b_ul.z.z += -beta_u.x * b_ul.z.z;\
(resultFlux)->B_u.x += (-6. * B_u.x * beta_u.x + -6. * DBeta_uu.xx * mdeShiftEpsilon + -2. * gamma_uu.xx * tmp1 + 3. * beta_u.x * tmp3 + 3. * beta_u.x * tmp5 + 3. * beta_u.y * d_l.y * tmp6 + 3. * beta_u.z * d_l.z * tmp6 + 12. * A_uu.xx * tmp7 + 6. * beta_u.x * d_l.x * tmp6 + -6. * beta_u.x * gamma_uu.xx * tmp8 + -6. * beta_u.x * tmp10 + -6. * beta_u.x * tmp12 + -6. * beta_u.y * gamma_uu.xx * tmp9 + -6. * beta_u.y * gamma_uu.xy * tmp13 + -6. * beta_u.y * gamma_uu.xz * tmp14 + -6. * beta_u.z * gamma_uu.xx * tmp11 + -6. * beta_u.z * gamma_uu.xz * tmp15 + -6. * beta_u.z * gamma_uu.xy * tmp14) / 6.;\
(resultFlux)->B_u.y += (-6. * B_u.y * beta_u.x + -6. * DBeta_uu.xy * mdeShiftEpsilon + -2. * gamma_uu.xy * tmp1 + 3. * beta_u.x * d_l.y * gamma_uu.yy * mdeShiftEpsilon + 3. * beta_u.x * d_l.z * tmp16 + 3. * beta_u.y * tmp3 + 3. * beta_u.z * d_l.z * tmp2 + 12. * A_uu.xy * tmp7 + 6. * beta_u.x * d_l.x * tmp2 + -6. * beta_u.x * gamma_uu.xy * tmp8 + -6. * beta_u.x * gamma_uu.yy * tmp9 + -6. * beta_u.x * gamma_uu.yz * tmp11 + -6. * beta_u.y * tmp10 + -6. * beta_u.y * gamma_uu.yy * tmp13 + -6. * beta_u.y * tmp17 + -6. * beta_u.z * gamma_uu.xy * tmp11 + -6. * beta_u.z * gamma_uu.yz * tmp15 + -6. * beta_u.z * gamma_uu.yy * tmp14) / 6.;\
(resultFlux)->B_u.z += (-6. * B_u.z * beta_u.x + -6. * DBeta_uu.xz * mdeShiftEpsilon + -2. * gamma_uu.xz * tmp1 + 3. * beta_u.x * d_l.y * tmp16 + 3. * beta_u.x * d_l.z * gamma_uu.zz * mdeShiftEpsilon + 3. * beta_u.y * d_l.y * tmp4 + 3. * beta_u.z * tmp5 + 12. * A_uu.xz * tmp7 + 6. * beta_u.x * d_l.x * tmp4 + -6. * beta_u.x * gamma_uu.xz * tmp8 + -6. * beta_u.x * gamma_uu.yz * tmp9 + -6. * beta_u.x * gamma_uu.zz * tmp11 + -6. * beta_u.y * gamma_uu.xz * tmp9 + -6. * beta_u.y * gamma_uu.yz * tmp13 + -6. * beta_u.y * gamma_uu.zz * tmp14 + -6. * beta_u.z * tmp12 + -6. * beta_u.z * gamma_uu.zz * tmp15 + -6. * beta_u.z * tmp17) / 6.;\
}\
<? end ?>/* eqn.useShift == "MinimalDistortionHyperbolic" */\
<? if eqn.useShift == "GammaDriverHyperbolic" then ?>\
{\
real const tmp1 = invW * invW;\
real const tmp2 = tr_DHatBeta * tmp1;\
real const tmp3 = tr_K * tmp1;\
real const tmp4 = alpha * tmp3;\
(resultFlux)->beta_u.x += -beta_u.x * beta_u.x;\
(resultFlux)->beta_u.y += -beta_u.x * beta_u.y;\
(resultFlux)->beta_u.z += -beta_u.x * beta_u.z;\
(resultFlux)->b_ul.x.x += -(B_u.x + beta_u.x * b_ul.x.x);\
(resultFlux)->b_ul.x.y += -beta_u.x * b_ul.x.y;\
(resultFlux)->b_ul.x.z += -beta_u.x * b_ul.x.z;\
(resultFlux)->b_ul.y.x += -(B_u.y + beta_u.x * b_ul.y.x);\
(resultFlux)->b_ul.y.y += -beta_u.x * b_ul.y.y;\
(resultFlux)->b_ul.y.z += -beta_u.x * b_ul.y.z;\
(resultFlux)->b_ul.z.x += -(B_u.z + beta_u.x * b_ul.z.x);\
(resultFlux)->b_ul.z.y += -beta_u.x * b_ul.z.y;\
(resultFlux)->b_ul.z.z += -beta_u.x * b_ul.z.z;\
(resultFlux)->B_u.x += (-gamma_uu.xx * tmp2 + -4. * B_u.x * beta_u.x + -3. * gamma_uu.xx * DHatBeta_ul.x.x * tmp1 + -3. * gamma_uu.xy * DHatBeta_ul.x.y * tmp1 + 4. * gamma_uu.xx * tmp4 + -3. * gamma_uu.xz * DHatBeta_ul.x.z * tmp1) / 4.;\
(resultFlux)->B_u.y += (-gamma_uu.xy * tmp2 + -4. * B_u.y * beta_u.x + -3. * gamma_uu.xx * DHatBeta_ul.y.x * tmp1 + -3. * gamma_uu.xy * DHatBeta_ul.y.y * tmp1 + 4. * gamma_uu.xy * tmp4 + -3. * gamma_uu.xz * DHatBeta_ul.y.z * tmp1) / 4.;\
(resultFlux)->B_u.z += (-gamma_uu.xz * tmp2 + -4. * B_u.z * beta_u.x + -3. * gamma_uu.xx * DHatBeta_ul.z.x * tmp1 + -3. * gamma_uu.xy * DHatBeta_ul.z.y * tmp1 + 4. * gamma_uu.xz * tmp4 + -3. * gamma_uu.xz * DHatBeta_ul.z.z * tmp1) / 4.;\
}\
<? end ?>/* eqn.useShift == "GammaDriverHyperbolic" */\
}\
<? end ?>/* eqn.useShift ~= "none" */\
source:
{
real const tmp1 = Theta * solver->kappa1;
real const tmp2 = solver->kappa1 * solver->kappa2;
real const tmp3 = Theta * tmp2;
real const tmp4 = S * M_PI;
real const tmp5 = rho * M_PI;
(deriv)->alpha += f_alpha * alpha * (2. * Theta + -tr_K);
(deriv)->gamma_ll.xx += -2. * K_ll.xx * alpha;
(deriv)->gamma_ll.xy += -2. * K_ll.xy * alpha;
(deriv)->gamma_ll.xz += -2. * K_ll.xz * alpha;
(deriv)->gamma_ll.yy += -2. * K_ll.yy * alpha;
(deriv)->gamma_ll.yz += -2. * K_ll.yz * alpha;
(deriv)->gamma_ll.zz += -2. * K_ll.zz * alpha;
(deriv)->K_ll.xx += alpha * (-conn_ull.x.xx * conn_ull.x.xx + -conn_ull.y.xy * conn_ull.y.xy + -conn_ull.z.xz * conn_ull.z.xz + a_l.x * d_l.x + d_l.x * conn_ull.x.xx + d_l.y * conn_ull.y.xx + d_l.z * conn_ull.z.xx + K_ll.xx * tr_K + -2. * Z_l.x * a_l.x + -2. * Z_l.x * conn_ull.x.xx + -2. * Z_l.y * conn_ull.y.xx + -2. * Z_l.z * conn_ull.z.xx + -2. * K_ul.x.x * K_ll.xx + -2. * K_ul.x.y * K_ll.xy + -2. * K_ul.x.z * K_ll.xz + -2. * K_ll.xx * Theta + -2. * conn_ull.x.xy * conn_ull.y.xx + -2. * conn_ull.x.xz * conn_ull.z.xx + -2. * conn_ull.y.xz * conn_ull.z.xy + -gamma_ll.xx * tmp1 + -8. * S_ll.xx * M_PI + -gamma_ll.xx * tmp3 + -4. * gamma_ll.xx * tmp5 + 4. * gamma_ll.xx * tmp4);
(deriv)->K_ll.xy += (alpha * (a_l.x * d_l.y + a_l.y * d_l.x + -2. * Z_l.x * a_l.y + -2. * Z_l.y * a_l.x + 2. * d_l.x * conn_ull.x.xy + 2. * d_l.y * conn_ull.y.xy + 2. * d_l.z * conn_ull.z.xy + 2. * K_ll.xy * tr_K + -2. * conn_ull.x.xx * conn_ull.x.xy + -2. * conn_ull.x.xy * conn_ull.y.xy + -2. * conn_ull.x.xz * conn_ull.z.xy + -2. * conn_ull.x.yy * conn_ull.y.xx + -2. * conn_ull.x.yz * conn_ull.z.xx + -2. * conn_ull.y.xy * conn_ull.y.yy + -2. * conn_ull.y.xz * conn_ull.z.yy + -2. * conn_ull.y.yz * conn_ull.z.xy + -2. * conn_ull.z.xz * conn_ull.z.yz + -4. * Z_l.x * conn_ull.x.xy + -4. * Z_l.y * conn_ull.y.xy + -4. * Z_l.z * conn_ull.z.xy + -4. * K_ul.x.x * K_ll.xy + -4. * K_ul.x.y * K_ll.yy + -4. * K_ul.x.z * K_ll.yz + -4. * K_ll.xy * Theta + -16. * S_ll.xy * M_PI + -2. * gamma_ll.xy * tmp1 + 8. * gamma_ll.xy * tmp4 + -2. * gamma_ll.xy * tmp3 + -8. * gamma_ll.xy * tmp5)) / 2.;
(deriv)->K_ll.xz += (alpha * (a_l.x * d_l.z + a_l.z * d_l.x + -2. * Z_l.x * a_l.z + -2. * Z_l.z * a_l.x + 2. * d_l.x * conn_ull.x.xz + 2. * d_l.y * conn_ull.y.xz + 2. * d_l.z * conn_ull.z.xz + 2. * K_ll.xz * tr_K + -2. * conn_ull.x.xx * conn_ull.x.xz + -2. * conn_ull.x.xy * conn_ull.y.xz + -2. * conn_ull.x.xz * conn_ull.z.xz + -2. * conn_ull.x.yz * conn_ull.y.xx + -2. * conn_ull.x.zz * conn_ull.z.xx + -2. * conn_ull.y.xy * conn_ull.y.yz + -2. * conn_ull.y.xz * conn_ull.z.yz + -2. * conn_ull.y.zz * conn_ull.z.xy + -2. * conn_ull.z.xz * conn_ull.z.zz + -4. * Z_l.x * conn_ull.x.xz + -4. * Z_l.y * conn_ull.y.xz + -4. * Z_l.z * conn_ull.z.xz + -4. * K_ul.x.x * K_ll.xz + -4. * K_ul.x.y * K_ll.yz + -4. * K_ul.x.z * K_ll.zz + -4. * K_ll.xz * Theta + -16. * S_ll.xz * M_PI + -2. * gamma_ll.xz * tmp1 + 8. * gamma_ll.xz * tmp4 + -2. * gamma_ll.xz * tmp3 + -8. * gamma_ll.xz * tmp5)) / 2.;
(deriv)->K_ll.yy += alpha * (-conn_ull.x.xy * conn_ull.x.xy + -conn_ull.y.yy * conn_ull.y.yy + -conn_ull.z.yz * conn_ull.z.yz + a_l.y * d_l.y + d_l.x * conn_ull.x.yy + d_l.y * conn_ull.y.yy + d_l.z * conn_ull.z.yy + K_ll.yy * tr_K + -2. * Z_l.x * conn_ull.x.yy + -2. * Z_l.y * a_l.y + -2. * Z_l.y * conn_ull.y.yy + -2. * Z_l.z * conn_ull.z.yy + -2. * K_ul.x.y * K_ll.xy + -2. * K_ul.y.y * K_ll.yy + -2. * K_ul.y.z * K_ll.yz + -2. * K_ll.yy * Theta + -2. * conn_ull.x.yy * conn_ull.y.xy + -2. * conn_ull.x.yz * conn_ull.z.xy + -2. * conn_ull.y.yz * conn_ull.z.yy + -gamma_ll.yy * tmp1 + -8. * S_ll.yy * M_PI + -gamma_ll.yy * tmp3 + -4. * gamma_ll.yy * tmp5 + 4. * gamma_ll.yy * tmp4);
(deriv)->K_ll.yz += (alpha * (a_l.y * d_l.z + a_l.z * d_l.y + -2. * Z_l.y * a_l.z + -2. * Z_l.z * a_l.y + 2. * d_l.x * conn_ull.x.yz + 2. * d_l.y * conn_ull.y.yz + 2. * d_l.z * conn_ull.z.yz + 2. * K_ll.yz * tr_K + -2. * conn_ull.x.xy * conn_ull.x.xz + -2. * conn_ull.x.yy * conn_ull.y.xz + -2. * conn_ull.x.yz * conn_ull.y.xy + -2. * conn_ull.x.yz * conn_ull.z.xz + -2. * conn_ull.x.zz * conn_ull.z.xy + -2. * conn_ull.y.yy * conn_ull.y.yz + -2. * conn_ull.y.yz * conn_ull.z.yz + -2. * conn_ull.y.zz * conn_ull.z.yy + -2. * conn_ull.z.yz * conn_ull.z.zz + -4. * Z_l.x * conn_ull.x.yz + -4. * Z_l.y * conn_ull.y.yz + -4. * Z_l.z * conn_ull.z.yz + -4. * K_ul.x.y * K_ll.xz + -4. * K_ul.y.y * K_ll.yz + -4. * K_ul.y.z * K_ll.zz + -4. * K_ll.yz * Theta + -16. * S_ll.yz * M_PI + -2. * gamma_ll.yz * tmp1 + 8. * gamma_ll.yz * tmp4 + -2. * gamma_ll.yz * tmp3 + -8. * gamma_ll.yz * tmp5)) / 2.;
(deriv)->K_ll.zz += alpha * (-conn_ull.x.xz * conn_ull.x.xz + -conn_ull.y.yz * conn_ull.y.yz + -conn_ull.z.zz * conn_ull.z.zz + a_l.z * d_l.z + d_l.x * conn_ull.x.zz + d_l.y * conn_ull.y.zz + d_l.z * conn_ull.z.zz + K_ll.zz * tr_K + -2. * Z_l.x * conn_ull.x.zz + -2. * Z_l.y * conn_ull.y.zz + -2. * Z_l.z * a_l.z + -2. * Z_l.z * conn_ull.z.zz + -2. * K_ul.x.z * K_ll.xz + -2. * K_ul.y.z * K_ll.yz + -2. * K_ul.z.z * K_ll.zz + -2. * K_ll.zz * Theta + -2. * conn_ull.x.yz * conn_ull.y.xz + -2. * conn_ull.x.zz * conn_ull.z.xz + -2. * conn_ull.y.zz * conn_ull.z.yz + -gamma_ll.zz * tmp1 + -8. * S_ll.zz * M_PI + -gamma_ll.zz * tmp3 + -4. * gamma_ll.zz * tmp5 + 4. * gamma_ll.zz * tmp4);
(deriv)->Theta += (alpha * (-K_ul.x.x * K_ul.x.x + -K_ul.y.y * K_ul.y.y + -K_ul.z.z * K_ul.z.z + tr_K * tr_K + -d_u.x * d_l.x + -d_u.y * d_l.y + -d_u.z * d_l.z + d_uuu.x.xx * d_lll.x.xx + -d_uuu.x.yy * d_lll.x.yy + -d_uuu.x.zz * d_lll.x.zz + -d_uuu.y.xx * d_lll.y.xx + d_uuu.y.yy * d_lll.y.yy + -d_uuu.y.zz * d_lll.y.zz + -d_uuu.z.xx * d_lll.z.xx + -d_uuu.z.yy * d_lll.z.yy + d_uuu.z.zz * d_lll.z.zz + 2. * Z_l.x * d_u.x + 2. * Z_l.y * d_u.y + 2. * Z_l.z * d_u.z + 2. * a_l.x * d_u.x + -2. * a_l.x * e_u.x + 2. * a_l.y * d_u.y + -2. * a_l.y * e_u.y + 2. * a_l.z * d_u.z + -2. * a_l.z * e_u.z + -2. * K_ul.x.y * K_ul.x.y + -2. * K_ul.x.z * K_ul.x.z + -2. * K_ul.y.z * K_ul.y.z + 2. * d_uuu.x.xy * d_lll.y.xx + 2. * d_uuu.x.xz * d_lll.z.xx + 2. * d_uuu.x.yy * d_lll.y.xy + -2. * d_uuu.x.yz * d_lll.x.yz + 2. * d_uuu.x.yz * d_lll.y.xz + 2. * d_uuu.x.yz * d_lll.z.xy + 2. * d_uuu.x.zz * d_lll.z.xz + 2. * d_uuu.y.xx * d_lll.x.xy + 2. * d_uuu.y.xy * d_lll.x.yy + 2. * d_uuu.y.xz * d_lll.x.yz + -2. * d_uuu.y.xz * d_lll.y.xz + 2. * d_uuu.y.xz * d_lll.z.xy + 2. * d_uuu.y.yz * d_lll.z.yy + 2. * d_uuu.y.zz * d_lll.z.yz + 2. * d_uuu.z.xx * d_lll.x.xz + 2. * d_uuu.z.xy * d_lll.x.yz + 2. * d_uuu.z.xy * d_lll.y.xz + -2. * d_uuu.z.xy * d_lll.z.xy + 2. * d_uuu.z.xz * d_lll.x.zz + 2. * d_uuu.z.yy * d_lll.y.yz + 2. * d_uuu.z.yz * d_lll.y.zz + -2. * Theta * tr_K + -4. * Z_l.x * a_u.x + -4. * Z_l.y * a_u.y + -4. * Z_l.z * a_u.z + -4. * tmp1 + -2. * tmp3 + -16. * tmp5)) / 2.;
(deriv)->Z_l.x += alpha * (-Z_l.x * solver->kappa1 + -a_u.x * K_ll.xx + -a_u.y * K_ll.xy + -a_u.z * K_ll.xz + a_l.x * tr_K + d_u.x * K_ll.xx + d_u.y * K_ll.xy + d_u.z * K_ll.xz + -K_uu.xx * d_lll.x.xx + -K_uu.yy * d_lll.x.yy + -K_uu.zz * d_lll.x.zz + -2. * Z_u.x * K_ll.xx + -2. * Z_u.y * K_ll.xy + -2. * Z_u.z * K_ll.xz + -2. * a_l.x * Theta + -2. * K_uu.xy * d_lll.x.xy + -2. * K_uu.xz * d_lll.x.xz + -8. * S_l.x * M_PI + -2. * K_uu.yz * d_lll.x.yz);
(deriv)->Z_l.y += alpha * (-Z_l.y * solver->kappa1 + -a_u.x * K_ll.xy + -a_u.y * K_ll.yy + -a_u.z * K_ll.yz + a_l.y * tr_K + d_u.x * K_ll.xy + d_u.y * K_ll.yy + d_u.z * K_ll.yz + -K_uu.xx * d_lll.y.xx + -K_uu.yy * d_lll.y.yy + -K_uu.zz * d_lll.y.zz + -2. * Z_u.x * K_ll.xy + -2. * Z_u.y * K_ll.yy + -2. * Z_u.z * K_ll.yz + -2. * a_l.y * Theta + -2. * K_uu.xy * d_lll.y.xy + -2. * K_uu.xz * d_lll.y.xz + -8. * S_l.y * M_PI + -2. * K_uu.yz * d_lll.y.yz);
(deriv)->Z_l.z += alpha * (-Z_l.z * solver->kappa1 + -a_u.x * K_ll.xz + -a_u.y * K_ll.yz + -a_u.z * K_ll.zz + a_l.z * tr_K + d_u.x * K_ll.xz + d_u.y * K_ll.yz + d_u.z * K_ll.zz + -K_uu.xx * d_lll.z.xx + -K_uu.yy * d_lll.z.yy + -K_uu.zz * d_lll.z.zz + -2. * Z_u.x * K_ll.xz + -2. * Z_u.y * K_ll.yz + -2. * Z_u.z * K_ll.zz + -2. * a_l.z * Theta + -2. * K_uu.xy * d_lll.z.xy + -2. * K_uu.xz * d_lll.z.xz + -8. * S_l.z * M_PI + -2. * K_uu.yz * d_lll.z.yz);
}
<? if eqn.useShift ~= "none" then ?>
{
{
(deriv)->alpha += -alpha * tr_b;
(deriv)->gamma_ll.xx += -gamma_ll.xx * tr_b + 2. * b_ll.x.x;
(deriv)->gamma_ll.xy += b_ll.x.y + b_ll.y.x + -gamma_ll.xy * tr_b;
(deriv)->gamma_ll.xz += b_ll.x.z + b_ll.z.x + -gamma_ll.xz * tr_b;
(deriv)->gamma_ll.yy += -gamma_ll.yy * tr_b + 2. * b_ll.y.y;
(deriv)->gamma_ll.yz += b_ll.y.z + b_ll.z.y + -gamma_ll.yz * tr_b;
(deriv)->gamma_ll.zz += -gamma_ll.zz * tr_b + 2. * b_ll.z.z;
(deriv)->a_l.x += a_l.x * b_ul.x.x + -a_l.x * tr_b + a_l.z * b_ul.z.x + a_l.y * b_ul.y.x;
(deriv)->a_l.y += a_l.x * b_ul.x.y + a_l.y * b_ul.y.y + a_l.z * b_ul.z.y + -a_l.y * tr_b;
(deriv)->a_l.z += a_l.x * b_ul.x.z + a_l.y * b_ul.y.z + -a_l.z * tr_b + a_l.z * b_ul.z.z;
(deriv)->d_lll.x.xx += b_ul.x.x * d_lll.x.xx + b_ul.y.x * d_lll.y.xx + -d_lll.x.xx * tr_b + b_ul.z.x * d_lll.z.xx;
(deriv)->d_lll.x.xy += b_ul.x.x * d_lll.x.xy + b_ul.y.x * d_lll.y.xy + -d_lll.x.xy * tr_b + b_ul.z.x * d_lll.z.xy;
(deriv)->d_lll.x.xz += b_ul.x.x * d_lll.x.xz + b_ul.y.x * d_lll.y.xz + -d_lll.x.xz * tr_b + b_ul.z.x * d_lll.z.xz;
(deriv)->d_lll.x.yy += b_ul.x.x * d_lll.x.yy + b_ul.y.x * d_lll.y.yy + -d_lll.x.yy * tr_b + b_ul.z.x * d_lll.z.yy;
(deriv)->d_lll.x.yz += b_ul.x.x * d_lll.x.yz + b_ul.y.x * d_lll.y.yz + -d_lll.x.yz * tr_b + b_ul.z.x * d_lll.z.yz;
(deriv)->d_lll.x.zz += b_ul.x.x * d_lll.x.zz + b_ul.y.x * d_lll.y.zz + -d_lll.x.zz * tr_b + b_ul.z.x * d_lll.z.zz;
(deriv)->d_lll.y.xx += b_ul.x.y * d_lll.x.xx + b_ul.y.y * d_lll.y.xx + -d_lll.y.xx * tr_b + b_ul.z.y * d_lll.z.xx;
(deriv)->d_lll.y.xy += b_ul.x.y * d_lll.x.xy + b_ul.y.y * d_lll.y.xy + -d_lll.y.xy * tr_b + b_ul.z.y * d_lll.z.xy;
(deriv)->d_lll.y.xz += b_ul.x.y * d_lll.x.xz + b_ul.y.y * d_lll.y.xz + -d_lll.y.xz * tr_b + b_ul.z.y * d_lll.z.xz;
(deriv)->d_lll.y.yy += b_ul.x.y * d_lll.x.yy + b_ul.y.y * d_lll.y.yy + -d_lll.y.yy * tr_b + b_ul.z.y * d_lll.z.yy;
(deriv)->d_lll.y.yz += b_ul.x.y * d_lll.x.yz + b_ul.y.y * d_lll.y.yz + -d_lll.y.yz * tr_b + b_ul.z.y * d_lll.z.yz;
(deriv)->d_lll.y.zz += b_ul.x.y * d_lll.x.zz + b_ul.y.y * d_lll.y.zz + -d_lll.y.zz * tr_b + b_ul.z.y * d_lll.z.zz;
(deriv)->d_lll.z.xx += b_ul.x.z * d_lll.x.xx + b_ul.y.z * d_lll.y.xx + -d_lll.z.xx * tr_b + b_ul.z.z * d_lll.z.xx;
(deriv)->d_lll.z.xy += b_ul.x.z * d_lll.x.xy + b_ul.y.z * d_lll.y.xy + -d_lll.z.xy * tr_b + b_ul.z.z * d_lll.z.xy;
(deriv)->d_lll.z.xz += b_ul.x.z * d_lll.x.xz + b_ul.y.z * d_lll.y.xz + -d_lll.z.xz * tr_b + b_ul.z.z * d_lll.z.xz;
(deriv)->d_lll.z.yy += b_ul.x.z * d_lll.x.yy + b_ul.y.z * d_lll.y.yy + -d_lll.z.yy * tr_b + b_ul.z.z * d_lll.z.yy;
(deriv)->d_lll.z.yz += b_ul.x.z * d_lll.x.yz + b_ul.y.z * d_lll.y.yz + -d_lll.z.yz * tr_b + b_ul.z.z * d_lll.z.yz;
(deriv)->d_lll.z.zz += b_ul.x.z * d_lll.x.zz + b_ul.y.z * d_lll.y.zz + -d_lll.z.zz * tr_b + b_ul.z.z * d_lll.z.zz;
(deriv)->K_ll.xx += -K_ll.xx * tr_b + 2. * K_ll.xx * b_ul.x.x + 2. * K_ll.xz * b_ul.z.x + 2. * K_ll.xy * b_ul.y.x;
(deriv)->K_ll.xy += K_ll.xx * b_ul.x.y + K_ll.xy * b_ul.x.x + K_ll.xy * b_ul.y.y + -K_ll.xy * tr_b + K_ll.xz * b_ul.z.y + K_ll.yz * b_ul.z.x + K_ll.yy * b_ul.y.x;
(deriv)->K_ll.xz += K_ll.xx * b_ul.x.z + K_ll.xy * b_ul.y.z + K_ll.xz * b_ul.x.x + K_ll.xz * b_ul.z.z + -K_ll.xz * tr_b + K_ll.zz * b_ul.z.x + K_ll.yz * b_ul.y.x;
(deriv)->K_ll.yy += -K_ll.yy * tr_b + 2. * K_ll.xy * b_ul.x.y + 2. * K_ll.yz * b_ul.z.y + 2. * K_ll.yy * b_ul.y.y;
(deriv)->K_ll.yz += K_ll.xy * b_ul.x.z + K_ll.xz * b_ul.x.y + K_ll.yy * b_ul.y.z + K_ll.yz * b_ul.y.y + K_ll.yz * b_ul.z.z + K_ll.zz * b_ul.z.y + -K_ll.yz * tr_b;
(deriv)->K_ll.zz += -K_ll.zz * tr_b + 2. * K_ll.xz * b_ul.x.z + 2. * K_ll.zz * b_ul.z.z + 2. * K_ll.yz * b_ul.y.z;
(deriv)->Theta += -Theta * tr_b;
(deriv)->Z_l.x += Z_l.x * b_ul.x.x + -Z_l.x * tr_b + Z_l.z * b_ul.z.x + Z_l.y * b_ul.y.x;
(deriv)->Z_l.y += Z_l.x * b_ul.x.y + Z_l.y * b_ul.y.y + Z_l.z * b_ul.z.y + -Z_l.y * tr_b;
(deriv)->Z_l.z += Z_l.x * b_ul.x.z + Z_l.y * b_ul.y.z + -Z_l.z * tr_b + Z_l.z * b_ul.z.z;
}
<? if eqn.useShift == "HarmonicParabolic" then ?>
{
real const tmp1 = alpha * alpha;
(deriv)->beta_u.x += -beta_u.x * tr_b + -a_u.x * tmp1 + 2. * e_u.x * tmp1 + -d_u.x * tmp1;
(deriv)->beta_u.y += -beta_u.y * tr_b + -a_u.y * tmp1 + 2. * e_u.y * tmp1 + -d_u.y * tmp1;
(deriv)->beta_u.z += -beta_u.z * tr_b + -a_u.z * tmp1 + 2. * e_u.z * tmp1 + -d_u.z * tmp1;
}
<? end ?>/* eqn.useShift == "HarmonicParabolic" */
<? if eqn.useShift == "HarmonicHyperbolic" then ?>
{
real const tmp1 = alpha * alpha;
(deriv)->beta_u.x += B_u.x + -beta_u.x * tr_b;
(deriv)->beta_u.y += B_u.y + -beta_u.y * tr_b;
(deriv)->beta_u.z += B_u.z + -beta_u.z * tr_b;
(deriv)->B_u.x += -B_u.x * tr_b + -a_u.x * tmp1 + 2. * e_u.x * tmp1 + -d_u.x * tmp1;
(deriv)->B_u.y += -B_u.y * tr_b + -a_u.y * tmp1 + 2. * e_u.y * tmp1 + -d_u.y * tmp1;
(deriv)->B_u.z += -B_u.z * tr_b + -a_u.z * tmp1 + 2. * e_u.z * tmp1 + -d_u.z * tmp1;
}
<? end ?>/* eqn.useShift == "HarmonicHyperbolic" */
<? if eqn.useShift == "MinimalDistortionHyperbolic" then ?>
{
real const tmp1 = b_ul.x.x * mdeShiftEpsilon;
real const tmp2 = b_ul.y.y * mdeShiftEpsilon;
real const tmp3 = b_ul.z.z * mdeShiftEpsilon;
real const tmp4 = tr_DBeta * mdeShiftEpsilon;
real const tmp5 = DBeta_uu.xy * mdeShiftEpsilon;
real const tmp6 = DBeta_uu.xz * mdeShiftEpsilon;
real const tmp7 = conn_ull.x.xx * mdeShiftEpsilon;
real const tmp8 = conn_uul.x.x.x * mdeShiftEpsilon;
real const tmp9 = conn_uul.y.x.x * mdeShiftEpsilon;
real const tmp10 = conn_uul.z.x.x * mdeShiftEpsilon;
real const tmp11 = conn_uul.x.x.y * mdeShiftEpsilon;
real const tmp12 = conn_uul.y.x.y * mdeShiftEpsilon;
real const tmp13 = conn_uul.z.x.y * mdeShiftEpsilon;
real const tmp14 = conn_uul.x.x.z * mdeShiftEpsilon;
real const tmp15 = conn_uul.y.x.z * mdeShiftEpsilon;
real const tmp16 = conn_uul.z.x.z * mdeShiftEpsilon;
real const tmp17 = conn_ull.x.xy * mdeShiftEpsilon;
real const tmp18 = conn_ull.x.xz * mdeShiftEpsilon;
real const tmp19 = e_u.x * mdeShiftEpsilon;
real const tmp20 = d_luu.x.xx * mdeShiftEpsilon;
real const tmp21 = d_luu.x.xy * mdeShiftEpsilon;
real const tmp22 = d_luu.x.xz * mdeShiftEpsilon;
real const tmp23 = conn_ull.y.xx * mdeShiftEpsilon;
real const tmp24 = conn_ull.z.xx * mdeShiftEpsilon;
real const tmp25 = conn_ull.y.xy * mdeShiftEpsilon;
real const tmp26 = conn_ull.z.xy * mdeShiftEpsilon;
real const tmp27 = conn_ull.z.xz * mdeShiftEpsilon;
real const tmp28 = d_luu.y.xx * mdeShiftEpsilon;
real const tmp29 = d_luu.y.xy * mdeShiftEpsilon;
real const tmp30 = d_luu.y.xz * mdeShiftEpsilon;
real const tmp31 = conn_ull.y.yy * mdeShiftEpsilon;
real const tmp32 = conn_ull.z.yy * mdeShiftEpsilon;
real const tmp33 = conn_ull.z.yz * mdeShiftEpsilon;
real const tmp34 = d_luu.z.xx * mdeShiftEpsilon;
real const tmp35 = d_luu.z.xy * mdeShiftEpsilon;
real const tmp36 = d_luu.z.xz * mdeShiftEpsilon;
real const tmp37 = conn_ull.y.xz * mdeShiftEpsilon;
real const tmp38 = conn_ull.y.yz * mdeShiftEpsilon;
real const tmp39 = conn_ull.z.zz * mdeShiftEpsilon;
real const tmp40 = conn_ull.x.xy * tmp21;
real const tmp41 = conn_ull.x.xz * tmp22;
real const tmp42 = conn_ull.y.xy * tmp29;
real const tmp43 = conn_ull.y.xz * tmp30;
real const tmp44 = conn_ull.z.xy * tmp35;
real const tmp45 = conn_ull.z.xz * tmp36;
real const tmp46 = alpha * mdeShiftEpsilon;
real const tmp47 = conn_ull.y.xy * tmp46;
real const tmp48 = conn_ull.z.xz * tmp46;
real const tmp49 = conn_ull.y.yy * tmp46;
real const tmp50 = conn_ull.z.yz * tmp46;
real const tmp51 = conn_ull.y.yz * tmp46;
real const tmp52 = conn_ull.z.zz * tmp46;
real const tmp53 = conn_ull.x.xy * tmp46;
real const tmp54 = conn_ull.x.xz * tmp46;
real const tmp55 = conn_ull.x.xx * tmp46;
real const tmp56 = DBeta_uu.yz * mdeShiftEpsilon;
real const tmp57 = conn_uul.x.x.y * mdeShiftEpsilon;
real const tmp58 = conn_uul.y.x.y * mdeShiftEpsilon;
real const tmp59 = conn_uul.z.x.y * mdeShiftEpsilon;
real const tmp60 = conn_uul.x.y.y * mdeShiftEpsilon;
real const tmp61 = conn_uul.y.y.y * mdeShiftEpsilon;
real const tmp62 = conn_uul.z.y.y * mdeShiftEpsilon;
real const tmp63 = conn_uul.x.y.z * mdeShiftEpsilon;
real const tmp64 = conn_uul.y.y.z * mdeShiftEpsilon;
real const tmp65 = conn_uul.z.y.z * mdeShiftEpsilon;
real const tmp66 = e_u.y * mdeShiftEpsilon;
real const tmp67 = d_luu.x.yy * mdeShiftEpsilon;
real const tmp68 = d_luu.x.yz * mdeShiftEpsilon;
real const tmp69 = d_luu.y.yy * mdeShiftEpsilon;
real const tmp70 = d_luu.y.yz * mdeShiftEpsilon;
real const tmp71 = d_luu.z.yy * mdeShiftEpsilon;
real const tmp72 = d_luu.z.yz * mdeShiftEpsilon;
real const tmp73 = conn_ull.x.yz * tmp68;
real const tmp74 = conn_ull.y.yz * tmp70;
real const tmp75 = conn_ull.z.yz * tmp72;
real const tmp76 = conn_uul.x.x.z * mdeShiftEpsilon;
real const tmp77 = conn_uul.y.x.z * mdeShiftEpsilon;
real const tmp78 = conn_uul.z.x.z * mdeShiftEpsilon;
real const tmp79 = conn_uul.x.y.z * mdeShiftEpsilon;
real const tmp80 = conn_uul.y.y.z * mdeShiftEpsilon;
real const tmp81 = conn_uul.z.y.z * mdeShiftEpsilon;
real const tmp82 = conn_uul.x.z.z * mdeShiftEpsilon;
real const tmp83 = conn_uul.y.z.z * mdeShiftEpsilon;
real const tmp84 = conn_uul.z.z.z * mdeShiftEpsilon;
real const tmp85 = e_u.z * mdeShiftEpsilon;
real const tmp86 = d_luu.x.zz * mdeShiftEpsilon;
real const tmp87 = d_luu.y.zz * mdeShiftEpsilon;
real const tmp88 = d_luu.z.zz * mdeShiftEpsilon;
(deriv)->beta_u.x += B_u.x + -beta_u.x * tr_b;
(deriv)->beta_u.y += B_u.y + -beta_u.y * tr_b;
(deriv)->beta_u.z += B_u.z + -beta_u.z * tr_b;
(deriv)->B_u.x += (-6. * B_u.x * tr_b + -3. * d_u.x * tmp1 + -3. * d_u.x * tmp2 + -3. * d_u.x * tmp3 + -3. * d_l.x * b_uu.x.x * mdeShiftEpsilon + -3. * d_l.y * b_uu.y.x * mdeShiftEpsilon + -3. * d_l.z * b_uu.z.x * mdeShiftEpsilon + 4. * e_u.x * tmp4 + 6. * d_l.x * DBeta_uu.xx * mdeShiftEpsilon + 6. * d_l.y * tmp5 + 6. * d_l.z * tmp6 + 6. * DBeta_uu.xx * tmp7 + 6. * DBeta_uu.yy * conn_ull.x.yy * mdeShiftEpsilon + 6. * DBeta_uu.zz * conn_ull.x.zz * mdeShiftEpsilon + 6. * b_ul.x.x * tmp8 + 6. * b_ul.x.y * tmp9 + 6. * b_ul.x.z * tmp10 + 6. * b_ul.y.x * tmp11 + 6. * b_ul.y.y * tmp12 + 6. * b_ul.y.z * tmp13 + 6. * b_ul.z.x * tmp14 + 6. * b_ul.z.y * tmp15 + 6. * b_ul.z.z * tmp16 + 12. * DBeta_uu.xy * tmp17 + 12. * DBeta_uu.xz * tmp18 + 12. * DBeta_uu.yz * conn_ull.x.yz * mdeShiftEpsilon + 6. * beta_u.x * d_l.x * tmp19 + 6. * beta_u.x * d_l.x * tmp8 + 6. * beta_u.x * d_l.x * tmp20 + 6. * beta_u.x * d_l.y * tmp9 + 6. * beta_u.x * d_l.y * tmp21 + 6. * beta_u.x * d_l.z * tmp10 + 6. * beta_u.x * d_l.z * tmp22 + -6. * beta_u.x * conn_uul.x.x.x * tmp7 + -6. * beta_u.x * conn_uul.x.x.y * tmp23 + -6. * beta_u.x * conn_uul.x.x.z * tmp24 + -6. * beta_u.x * conn_ull.x.xy * tmp9 + -6. * beta_u.x * conn_ull.x.xz * tmp10 + -6. * beta_u.x * conn_uul.y.x.y * tmp25 + -6. * beta_u.x * conn_uul.y.x.z * tmp26 + -6. * beta_u.x * conn_ull.y.xz * tmp13 + -6. * beta_u.x * conn_uul.z.x.z * tmp27 + 6. * beta_u.y * d_l.x * tmp11 + 6. * beta_u.y * d_l.x * tmp28 + 6. * beta_u.y * d_l.y * tmp19 + 6. * beta_u.y * d_l.y * tmp12 + 6. * beta_u.y * d_l.y * tmp29 + 6. * beta_u.y * d_l.z * tmp13 + 6. * beta_u.y * d_l.z * tmp30 + -6. * beta_u.y * conn_uul.x.x.x * tmp17 + -6. * beta_u.y * conn_uul.x.x.y * tmp25 + -6. * beta_u.y * conn_uul.x.x.z * tmp26 + -6. * beta_u.y * conn_ull.x.yy * tmp9 + -6. * beta_u.y * conn_ull.x.yz * tmp10 + -6. * beta_u.y * conn_uul.y.x.y * tmp31 + -6. * beta_u.y * conn_uul.y.x.z * tmp32 + -6. * beta_u.y * conn_ull.y.yz * tmp13 + -6. * beta_u.y * conn_uul.z.x.z * tmp33 + 6. * beta_u.z * d_l.x * tmp14 + 6. * beta_u.z * d_l.x * tmp34 + 6. * beta_u.z * d_l.y * tmp15 + 6. * beta_u.z * d_l.y * tmp35 + 6. * beta_u.z * d_l.z * tmp19 + 6. * beta_u.z * d_l.z * tmp16 + 6. * beta_u.z * d_l.z * tmp36 + -6. * beta_u.z * conn_uul.x.x.x * tmp18 + -6. * beta_u.z * conn_uul.x.x.y * tmp37 + -6. * beta_u.z * conn_uul.x.x.z * tmp27 + -6. * beta_u.z * conn_ull.x.yz * tmp9 + -6. * beta_u.z * conn_ull.x.zz * tmp10 + -6. * beta_u.z * conn_uul.y.x.y * tmp38 + -6. * beta_u.z * conn_uul.y.x.z * tmp33 + -6. * beta_u.z * conn_ull.y.zz * tmp13 + -6. * beta_u.z * conn_uul.z.x.z * tmp39 + -12. * beta_u.x * conn_ull.x.xx * tmp20 + -12. * beta_u.x * tmp40 + -12. * beta_u.x * tmp41 + -12. * beta_u.x * conn_ull.y.xx * tmp28 + -12. * beta_u.x * tmp42 + -12. * beta_u.x * tmp43 + -12. * beta_u.x * conn_ull.z.xx * tmp34 + -12. * beta_u.x * tmp44 + -12. * beta_u.x * tmp45 + -12. * beta_u.y * conn_ull.x.xy * tmp20 + -12. * beta_u.y * conn_ull.x.yy * tmp21 + -12. * beta_u.y * conn_ull.x.yz * tmp22 + -12. * beta_u.y * conn_ull.y.xy * tmp28 + -12. * beta_u.y * conn_ull.y.yy * tmp29 + -12. * beta_u.y * conn_ull.y.yz * tmp30 + -12. * beta_u.y * conn_ull.z.xy * tmp34 + -12. * beta_u.y * conn_ull.z.yy * tmp35 + -12. * beta_u.y * conn_ull.z.yz * tmp36 + -12. * beta_u.z * conn_ull.x.xz * tmp20 + -12. * beta_u.z * conn_ull.x.yz * tmp21 + -12. * beta_u.z * conn_ull.x.zz * tmp22 + -12. * beta_u.z * conn_ull.y.xz * tmp28 + -12. * beta_u.z * conn_ull.y.yz * tmp29 + -12. * beta_u.z * conn_ull.y.zz * tmp30 + -12. * beta_u.z * conn_ull.z.xz * tmp34 + -12. * beta_u.z * conn_ull.z.yz * tmp35 + -12. * beta_u.z * conn_ull.z.zz * tmp36 + -12. * A_uu.xx * tmp47 + -12. * A_uu.xx * tmp48 + -12. * A_uu.xy * tmp49 + -12. * A_uu.xy * tmp50 + -12. * A_uu.xz * tmp51 + -12. * A_uu.xz * tmp52 + -12. * A_uu.yy * conn_ull.x.yy * tmp46 + -12. * A_uu.zz * conn_ull.x.zz * tmp46 + -36. * A_uu.xy * tmp53 + -36. * A_uu.xz * tmp54 + -24. * A_uu.yz * conn_ull.x.yz * tmp46 + -24. * A_uu.xx * tmp55) / 6.;
(deriv)->B_u.y += (-6. * B_u.y * tr_b + -3. * d_u.y * tmp1 + -3. * d_u.y * tmp2 + -3. * d_u.y * tmp3 + -3. * d_l.x * b_uu.x.y * mdeShiftEpsilon + -3. * d_l.y * b_uu.y.y * mdeShiftEpsilon + -3. * d_l.z * b_uu.z.y * mdeShiftEpsilon + 4. * e_u.y * tmp4 + 6. * d_l.x * tmp5 + 6. * d_l.y * DBeta_uu.yy * mdeShiftEpsilon + 6. * d_l.z * tmp56 + 6. * DBeta_uu.xx * tmp23 + 6. * DBeta_uu.yy * tmp31 + 6. * DBeta_uu.zz * conn_ull.y.zz * mdeShiftEpsilon + 6. * b_ul.x.x * tmp57 + 6. * b_ul.x.y * tmp58 + 6. * b_ul.x.z * tmp59 + 6. * b_ul.y.x * tmp60 + 6. * b_ul.y.y * tmp61 + 6. * b_ul.y.z * tmp62 + 6. * b_ul.z.x * tmp63 + 6. * b_ul.z.y * tmp64 + 6. * b_ul.z.z * tmp65 + 12. * DBeta_uu.xy * tmp25 + 12. * DBeta_uu.xz * tmp37 + 12. * DBeta_uu.yz * tmp38 + 6. * beta_u.x * d_l.x * tmp66 + 6. * beta_u.x * d_l.x * tmp57 + 6. * beta_u.x * d_l.x * tmp21 + 6. * beta_u.x * d_l.y * tmp58 + 6. * beta_u.x * d_l.y * tmp67 + 6. * beta_u.x * d_l.z * tmp59 + 6. * beta_u.x * d_l.z * tmp68 + -6. * beta_u.x * conn_uul.x.y.y * tmp23 + -6. * beta_u.x * conn_uul.x.y.z * tmp24 + -6. * beta_u.x * conn_uul.x.x.y * tmp7 + -6. * beta_u.x * conn_ull.x.xy * tmp58 + -6. * beta_u.x * conn_ull.x.xz * tmp59 + -6. * beta_u.x * conn_uul.y.y.y * tmp25 + -6. * beta_u.x * conn_uul.y.y.z * tmp26 + -6. * beta_u.x * conn_ull.y.xz * tmp62 + -6. * beta_u.x * conn_uul.z.y.z * tmp27 + 6. * beta_u.y * d_l.x * tmp60 + 6. * beta_u.y * d_l.x * tmp29 + 6. * beta_u.y * d_l.y * tmp66 + 6. * beta_u.y * d_l.y * tmp61 + 6. * beta_u.y * d_l.y * tmp69 + 6. * beta_u.y * d_l.z * tmp62 + 6. * beta_u.y * d_l.z * tmp70 + -6. * beta_u.y * conn_uul.x.y.y * tmp25 + -6. * beta_u.y * conn_uul.x.y.z * tmp26 + -6. * beta_u.y * conn_uul.x.x.y * tmp17 + -6. * beta_u.y * conn_ull.x.yy * tmp58 + -6. * beta_u.y * conn_ull.x.yz * tmp59 + -6. * beta_u.y * conn_uul.y.y.y * tmp31 + -6. * beta_u.y * conn_uul.y.y.z * tmp32 + -6. * beta_u.y * conn_ull.y.yz * tmp62 + -6. * beta_u.y * conn_uul.z.y.z * tmp33 + 6. * beta_u.z * d_l.x * tmp63 + 6. * beta_u.z * d_l.x * tmp35 + 6. * beta_u.z * d_l.y * tmp64 + 6. * beta_u.z * d_l.y * tmp71 + 6. * beta_u.z * d_l.z * tmp66 + 6. * beta_u.z * d_l.z * tmp65 + 6. * beta_u.z * d_l.z * tmp72 + -6. * beta_u.z * conn_uul.x.y.y * tmp37 + -6. * beta_u.z * conn_uul.x.y.z * tmp27 + -6. * beta_u.z * conn_uul.x.x.y * tmp18 + -6. * beta_u.z * conn_ull.x.yz * tmp58 + -6. * beta_u.z * conn_ull.x.zz * tmp59 + -6. * beta_u.z * conn_uul.y.y.y * tmp38 + -6. * beta_u.z * conn_uul.y.y.z * tmp33 + -6. * beta_u.z * conn_ull.y.zz * tmp62 + -6. * beta_u.z * conn_uul.z.y.z * tmp39 + -12. * beta_u.x * conn_ull.x.xx * tmp21 + -12. * beta_u.x * conn_ull.x.xy * tmp67 + -12. * beta_u.x * conn_ull.x.xz * tmp68 + -12. * beta_u.x * conn_ull.y.xx * tmp29 + -12. * beta_u.x * conn_ull.y.xy * tmp69 + -12. * beta_u.x * conn_ull.y.xz * tmp70 + -12. * beta_u.x * conn_ull.z.xx * tmp35 + -12. * beta_u.x * conn_ull.z.xy * tmp71 + -12. * beta_u.x * conn_ull.z.xz * tmp72 + -12. * beta_u.y * tmp40 + -12. * beta_u.y * conn_ull.x.yy * tmp67 + -12. * beta_u.y * tmp73 + -12. * beta_u.y * tmp42 + -12. * beta_u.y * conn_ull.y.yy * tmp69 + -12. * beta_u.y * tmp74 + -12. * beta_u.y * tmp44 + -12. * beta_u.y * conn_ull.z.yy * tmp71 + -12. * beta_u.y * tmp75 + -12. * beta_u.z * conn_ull.x.xz * tmp21 + -12. * beta_u.z * conn_ull.x.yz * tmp67 + -12. * beta_u.z * conn_ull.x.zz * tmp68 + -12. * beta_u.z * conn_ull.y.xz * tmp29 + -12. * beta_u.z * conn_ull.y.yz * tmp69 + -12. * beta_u.z * conn_ull.y.zz * tmp70 + -12. * beta_u.z * conn_ull.z.xz * tmp35 + -12. * beta_u.z * conn_ull.z.yz * tmp71 + -12. * beta_u.z * conn_ull.z.zz * tmp72 + -12. * A_uu.xx * conn_ull.y.xx * tmp46 + -12. * A_uu.xy * tmp55 + -12. * A_uu.xy * tmp48 + -12. * A_uu.yy * tmp53 + -12. * A_uu.yy * tmp50 + -12. * A_uu.yz * tmp54 + -12. * A_uu.yz * tmp52 + -12. * A_uu.zz * conn_ull.y.zz * tmp46 + -36. * A_uu.xy * tmp47 + -36. * A_uu.yz * tmp51 + -24. * A_uu.yy * tmp49 + -24. * A_uu.xz * conn_ull.y.xz * tmp46) / 6.;
(deriv)->B_u.z += (-6. * B_u.z * tr_b + -3. * d_u.z * tmp1 + -3. * d_u.z * tmp2 + -3. * d_u.z * tmp3 + -3. * d_l.x * b_uu.x.z * mdeShiftEpsilon + -3. * d_l.y * b_uu.y.z * mdeShiftEpsilon + -3. * d_l.z * b_uu.z.z * mdeShiftEpsilon + 4. * e_u.z * tmp4 + 6. * d_l.x * tmp6 + 6. * d_l.y * tmp56 + 6. * d_l.z * DBeta_uu.zz * mdeShiftEpsilon + 6. * DBeta_uu.xx * tmp24 + 6. * DBeta_uu.yy * tmp32 + 6. * DBeta_uu.zz * tmp39 + 6. * b_ul.x.x * tmp76 + 6. * b_ul.x.y * tmp77 + 6. * b_ul.x.z * tmp78 + 6. * b_ul.y.x * tmp79 + 6. * b_ul.y.y * tmp80 + 6. * b_ul.y.z * tmp81 + 6. * b_ul.z.x * tmp82 + 6. * b_ul.z.y * tmp83 + 6. * b_ul.z.z * tmp84 + 12. * DBeta_uu.xy * tmp26 + 12. * DBeta_uu.xz * tmp27 + 12. * DBeta_uu.yz * tmp33 + 6. * beta_u.x * d_l.x * tmp85 + 6. * beta_u.x * d_l.x * tmp76 + 6. * beta_u.x * d_l.x * tmp22 + 6. * beta_u.x * d_l.y * tmp77 + 6. * beta_u.x * d_l.y * tmp68 + 6. * beta_u.x * d_l.z * tmp78 + 6. * beta_u.x * d_l.z * tmp86 + -6. * beta_u.x * conn_uul.x.z.z * tmp24 + -6. * beta_u.x * conn_uul.x.x.z * tmp7 + -6. * beta_u.x * conn_ull.x.xy * tmp77 + -6. * beta_u.x * conn_ull.x.xz * tmp78 + -6. * beta_u.x * conn_uul.x.y.z * tmp23 + -6. * beta_u.x * conn_uul.y.z.z * tmp26 + -6. * beta_u.x * conn_ull.y.xy * tmp80 + -6. * beta_u.x * conn_ull.y.xz * tmp81 + -6. * beta_u.x * conn_uul.z.z.z * tmp27 + 6. * beta_u.y * d_l.x * tmp79 + 6. * beta_u.y * d_l.x * tmp30 + 6. * beta_u.y * d_l.y * tmp85 + 6. * beta_u.y * d_l.y * tmp80 + 6. * beta_u.y * d_l.y * tmp70 + 6. * beta_u.y * d_l.z * tmp81 + 6. * beta_u.y * d_l.z * tmp87 + -6. * beta_u.y * conn_uul.x.z.z * tmp26 + -6. * beta_u.y * conn_uul.x.x.z * tmp17 + -6. * beta_u.y * conn_uul.x.y.z * tmp25 + -6. * beta_u.y * conn_ull.x.yy * tmp77 + -6. * beta_u.y * conn_ull.x.yz * tmp78 + -6. * beta_u.y * conn_uul.y.z.z * tmp32 + -6. * beta_u.y * conn_uul.y.y.z * tmp31 + -6. * beta_u.y * conn_ull.y.yz * tmp81 + -6. * beta_u.y * conn_uul.z.z.z * tmp33 + 6. * beta_u.z * d_l.x * tmp82 + 6. * beta_u.z * d_l.x * tmp36 + 6. * beta_u.z * d_l.y * tmp83 + 6. * beta_u.z * d_l.y * tmp72 + 6. * beta_u.z * d_l.z * tmp85 + 6. * beta_u.z * d_l.z * tmp84 + 6. * beta_u.z * d_l.z * tmp88 + -6. * beta_u.z * conn_uul.x.z.z * tmp27 + -6. * beta_u.z * conn_uul.x.x.z * tmp18 + -6. * beta_u.z * conn_uul.x.y.z * tmp37 + -6. * beta_u.z * conn_ull.x.yz * tmp77 + -6. * beta_u.z * conn_ull.x.zz * tmp78 + -6. * beta_u.z * conn_uul.y.z.z * tmp33 + -6. * beta_u.z * conn_uul.y.y.z * tmp38 + -6. * beta_u.z * conn_ull.y.zz * tmp81 + -6. * beta_u.z * conn_uul.z.z.z * tmp39 + -12. * beta_u.x * conn_ull.x.xx * tmp22 + -12. * beta_u.x * conn_ull.x.xy * tmp68 + -12. * beta_u.x * conn_ull.x.xz * tmp86 + -12. * beta_u.x * conn_ull.y.xx * tmp30 + -12. * beta_u.x * conn_ull.y.xy * tmp70 + -12. * beta_u.x * conn_ull.y.xz * tmp87 + -12. * beta_u.x * conn_ull.z.xx * tmp36 + -12. * beta_u.x * conn_ull.z.xy * tmp72 + -12. * beta_u.x * conn_ull.z.xz * tmp88 + -12. * beta_u.y * conn_ull.x.xy * tmp22 + -12. * beta_u.y * conn_ull.x.yy * tmp68 + -12. * beta_u.y * conn_ull.x.yz * tmp86 + -12. * beta_u.y * conn_ull.y.xy * tmp30 + -12. * beta_u.y * conn_ull.y.yy * tmp70 + -12. * beta_u.y * conn_ull.y.yz * tmp87 + -12. * beta_u.y * conn_ull.z.xy * tmp36 + -12. * beta_u.y * conn_ull.z.yy * tmp72 + -12. * beta_u.y * conn_ull.z.yz * tmp88 + -12. * beta_u.z * tmp41 + -12. * beta_u.z * tmp73 + -12. * beta_u.z * conn_ull.x.zz * tmp86 + -12. * beta_u.z * tmp43 + -12. * beta_u.z * tmp74 + -12. * beta_u.z * conn_ull.y.zz * tmp87 + -12. * beta_u.z * tmp45 + -12. * beta_u.z * tmp75 + -12. * beta_u.z * conn_ull.z.zz * tmp88 + -12. * A_uu.xx * conn_ull.z.xx * tmp46 + -12. * A_uu.xz * tmp55 + -12. * A_uu.xz * tmp47 + -12. * A_uu.yy * conn_ull.z.yy * tmp46 + -12. * A_uu.yz * tmp53 + -12. * A_uu.yz * tmp49 + -12. * A_uu.zz * tmp54 + -12. * A_uu.zz * tmp51 + -36. * A_uu.xz * tmp48 + -36. * A_uu.yz * tmp50 + -24. * A_uu.zz * tmp52 + -24. * A_uu.xy * conn_ull.z.xy * tmp46) / 6.;
}
<? end ?>/* eqn.useShift == "MinimalDistortionHyperbolic" */
<? if eqn.useShift == "GammaDriverHyperbolic" then ?>
{
real const tmp1 = invW * invW;
real const tmp2 = tr_DHatBeta * tmp1;
real const tmp3 = connHat_uul.x.y.y * tmp1;
real const tmp4 = connHat_uul.x.z.z * tmp1;
real const tmp5 = connHat_uul.y.x.x * tmp1;
real const tmp6 = connHat_uul.y.y.y * tmp1;
real const tmp7 = connHat_uul.y.z.z * tmp1;
real const tmp8 = connHat_uul.z.x.x * tmp1;
real const tmp9 = connHat_uul.z.y.y * tmp1;
real const tmp10 = connHat_uul.z.z.z * tmp1;
real const tmp11 = DHatBeta_ul.x.x * tmp1;
real const tmp12 = DHatBeta_ul.x.y * tmp1;
real const tmp13 = DHatBeta_ul.x.z * tmp1;
real const tmp14 = A_uu.xy * tmp1;
real const tmp15 = A_uu.xz * tmp1;
real const tmp16 = connHat_ull.y.xx * tmp1;
real const tmp17 = connHat_ull.z.xx * tmp1;
real const tmp18 = connHat_ull.x.xx * tmp1;
real const tmp19 = connHat_ull.y.xy * tmp1;
real const tmp20 = connHat_uul.x.y.y * tmp19;
real const tmp21 = connHat_ull.z.xy * tmp1;
real const tmp22 = connHat_ull.z.xz * tmp1;
real const tmp23 = connHat_uul.x.z.z * tmp22;
real const tmp24 = connHat_ull.x.xy * tmp1;
real const tmp25 = connHat_ull.x.xz * tmp1;
real const tmp26 = connHat_ull.x.xy * tmp5;
real const tmp27 = connHat_ull.x.xz * tmp8;
real const tmp28 = connHat_ull.y.xz * tmp1;
real const tmp29 = connHat_ull.y.yy * tmp1;
real const tmp30 = connHat_ull.z.yy * tmp1;
real const tmp31 = connHat_ull.z.yz * tmp1;
real const tmp32 = connHat_ull.x.yz * tmp1;
real const tmp33 = connHat_ull.y.yz * tmp1;
real const tmp34 = connHat_ull.z.zz * tmp1;
real const tmp35 = connHat_ull.y.zz * tmp1;
real const tmp36 = tr_K * tmp1;
real const tmp37 = alpha * tmp36;
real const tmp38 = alpha * tmp1;
real const tmp39 = A_uu.xy * tmp38;
real const tmp40 = A_uu.xz * tmp38;
real const tmp41 = connHat_uul.y.x.y * tmp1;
real const tmp42 = connHat_uul.y.x.z * tmp1;
real const tmp43 = connHat_uul.x.x.x * tmp1;
real const tmp44 = connHat_uul.y.y.z * tmp1;
real const tmp45 = DHatBeta_ul.y.x * tmp1;
real const tmp46 = DHatBeta_ul.y.y * tmp1;
real const tmp47 = DHatBeta_ul.y.z * tmp1;
real const tmp48 = A_uu.yz * tmp1;
real const tmp49 = connHat_uul.y.z.z * tmp31;
real const tmp50 = connHat_ull.y.yz * tmp9;
real const tmp51 = A_uu.yz * tmp38;
real const tmp52 = connHat_uul.z.x.y * tmp1;
real const tmp53 = connHat_uul.z.x.z * tmp1;
real const tmp54 = connHat_uul.z.x.y * tmp1;
real const tmp55 = connHat_uul.z.y.z * tmp1;
real const tmp56 = DHatBeta_ul.z.x * tmp1;
real const tmp57 = DHatBeta_ul.z.y * tmp1;
real const tmp58 = DHatBeta_ul.z.z * tmp1;
(deriv)->beta_u.x += B_u.x + -beta_u.x * tr_b;
(deriv)->beta_u.y += B_u.y + -beta_u.y * tr_b;
(deriv)->beta_u.z += B_u.z + -beta_u.z * tr_b;
(deriv)->B_u.x += (-9. * LambdaBar_u.x * b_ul.x.x + -9. * LambdaBar_u.y * b_ul.x.y + -9. * LambdaBar_u.z * b_ul.x.z + -2. * GDelta_u.x * tmp2 + -12. * B_u.x * gammaDriver_eta + -12. * B_u.x * tr_b + -9. * b_ul.x.x * tmp3 + -9. * b_ul.x.x * tmp4 + 9. * b_ul.x.y * connHat_uul.x.x.y * tmp1 + -9. * b_ul.x.y * tmp5 + -9. * b_ul.x.y * tmp6 + -9. * b_ul.x.y * tmp7 + 9. * b_ul.x.z * connHat_uul.x.x.z * tmp1 + -9. * b_ul.x.z * tmp8 + -9. * b_ul.x.z * tmp9 + -9. * b_ul.x.z * tmp10 + 9. * b_ul.y.x * connHat_uul.x.x.y * tmp1 + 9. * b_ul.y.y * tmp3 + 9. * b_ul.y.z * connHat_uul.x.y.z * tmp1 + 9. * b_ul.z.x * connHat_uul.x.x.z * tmp1 + 9. * b_ul.z.y * connHat_uul.x.y.z * tmp1 + 9. * b_ul.z.z * tmp4 + -6. * GDelta_u.x * tmp11 + -6. * GDelta_u.y * tmp12 + -6. * GDelta_u.z * tmp13 + 6. * e_u.x * tmp2 + 6. * DeltaGamma_uul.x.x.x * tmp2 + 6. * DeltaGamma_uul.x.y.y * tmp2 + 6. * DeltaGamma_uul.x.z.z * tmp2 + 18. * GDelta_l.x * A_uu.xx * tmp1 + 18. * GDelta_l.y * tmp14 + 18. * GDelta_l.z * tmp15 + 18. * e_u.x * tmp11 + 18. * e_u.y * tmp12 + 18. * e_u.z * tmp13 + 18. * A_uu.xx * DeltaGamma_ull.x.xx * tmp1 + 18. * A_uu.yy * DeltaGamma_ull.x.yy * tmp1 + 18. * A_uu.zz * DeltaGamma_ull.x.zz * tmp1 + 36. * A_uu.xy * DeltaGamma_ull.x.xy * tmp1 + 36. * A_uu.xz * DeltaGamma_ull.x.xz * tmp1 + 36. * A_uu.yz * DeltaGamma_ull.x.yz * tmp1 + 9. * beta_u.x * connHat_uul.x.x.y * tmp16 + 9. * beta_u.x * connHat_uul.x.x.z * tmp17 + -9. * beta_u.x * connHat_uul.x.y.y * tmp18 + 9. * beta_u.x * tmp20 + 9. * beta_u.x * connHat_uul.x.y.z * tmp21 + -9. * beta_u.x * connHat_uul.x.z.z * tmp18 + 9. * beta_u.x * tmp23 + 9. * beta_u.x * connHat_uul.x.x.y * tmp24 + 9. * beta_u.x * connHat_uul.x.x.z * tmp25 + -9. * beta_u.x * tmp26 + -9. * beta_u.x * connHat_ull.x.xy * tmp6 + -9. * beta_u.x * connHat_ull.x.xy * tmp7 + -9. * beta_u.x * tmp27 + -9. * beta_u.x * connHat_ull.x.xz * tmp9 + -9. * beta_u.x * connHat_ull.x.xz * tmp10 + 9. * beta_u.x * connHat_uul.x.y.z * tmp28 + 9. * beta_u.y * connHat_uul.x.x.y * tmp19 + 9. * beta_u.y * connHat_uul.x.x.z * tmp21 + -9. * beta_u.y * connHat_uul.x.y.y * tmp24 + 9. * beta_u.y * connHat_uul.x.y.y * tmp29 + 9. * beta_u.y * connHat_uul.x.y.z * tmp30 + -9. * beta_u.y * connHat_uul.x.z.z * tmp24 + 9. * beta_u.y * connHat_uul.x.z.z * tmp31 + 9. * beta_u.y * connHat_uul.x.x.y * connHat_ull.x.yy * tmp1 + 9. * beta_u.y * connHat_uul.x.x.z * tmp32 + 9. * beta_u.y * connHat_uul.x.y.z * tmp33 + -9. * beta_u.y * connHat_ull.x.yy * tmp5 + -9. * beta_u.y * connHat_ull.x.yy * tmp6 + -9. * beta_u.y * connHat_ull.x.yy * tmp7 + -9. * beta_u.y * connHat_ull.x.yz * tmp8 + -9. * beta_u.y * connHat_ull.x.yz * tmp9 + -9. * beta_u.y * connHat_ull.x.yz * tmp10 + 9. * beta_u.z * connHat_uul.x.x.y * tmp28 + 9. * beta_u.z * connHat_uul.x.x.z * tmp22 + -9. * beta_u.z * connHat_uul.x.y.y * tmp25 + 9. * beta_u.z * connHat_uul.x.y.y * tmp33 + 9. * beta_u.z * connHat_uul.x.y.z * tmp31 + -9. * beta_u.z * connHat_uul.x.z.z * tmp25 + 9. * beta_u.z * connHat_uul.x.z.z * tmp34 + 9. * beta_u.z * connHat_uul.x.x.y * tmp32 + 9. * beta_u.z * connHat_uul.x.x.z * connHat_ull.x.zz * tmp1 + 9. * beta_u.z * connHat_uul.x.y.z * tmp35 + -9. * beta_u.z * connHat_ull.x.yz * tmp5 + -9. * beta_u.z * connHat_ull.x.yz * tmp6 + -9. * beta_u.z * connHat_ull.x.yz * tmp7 + -9. * beta_u.z * connHat_ull.x.zz * tmp8 + -9. * beta_u.z * connHat_ull.x.zz * tmp9 + -9. * beta_u.z * connHat_ull.x.zz * tmp10 + 8. * GDelta_u.x * tmp37 + -18. * a_l.x * A_uu.xx * tmp38 + -18. * a_l.y * tmp39 + -18. * a_l.z * tmp40 + -24. * e_u.x * tmp37 + 12. * a_u.x * tmp37) / 12.;
(deriv)->B_u.y += (-9. * LambdaBar_u.x * b_ul.y.x + -9. * LambdaBar_u.y * b_ul.y.y + -9. * LambdaBar_u.z * b_ul.y.z + -2. * GDelta_u.y * tmp2 + -12. * B_u.y * gammaDriver_eta + -12. * B_u.y * tr_b + 9. * b_ul.x.x * tmp5 + 9. * b_ul.x.y * tmp41 + 9. * b_ul.x.z * tmp42 + -9. * b_ul.y.x * tmp43 + -9. * b_ul.y.x * tmp3 + -9. * b_ul.y.x * tmp4 + 9. * b_ul.y.x * connHat_uul.y.x.y * tmp1 + -9. * b_ul.y.y * tmp5 + -9. * b_ul.y.y * tmp7 + 9. * b_ul.y.z * tmp44 + -9. * b_ul.y.z * tmp8 + -9. * b_ul.y.z * tmp9 + -9. * b_ul.y.z * tmp10 + 9. * b_ul.z.x * connHat_uul.y.x.z * tmp1 + 9. * b_ul.z.y * connHat_uul.y.y.z * tmp1 + 9. * b_ul.z.z * tmp7 + -6. * GDelta_u.x * tmp45 + -6. * GDelta_u.y * tmp46 + -6. * GDelta_u.z * tmp47 + 6. * e_u.y * tmp2 + 6. * DeltaGamma_uul.y.x.x * tmp2 + 6. * DeltaGamma_uul.y.y.y * tmp2 + 6. * DeltaGamma_uul.y.z.z * tmp2 + 18. * GDelta_l.x * tmp14 + 18. * GDelta_l.y * A_uu.yy * tmp1 + 18. * GDelta_l.z * tmp48 + 18. * e_u.x * tmp45 + 18. * e_u.y * tmp46 + 18. * e_u.z * tmp47 + 18. * A_uu.xx * DeltaGamma_ull.y.xx * tmp1 + 18. * A_uu.yy * DeltaGamma_ull.y.yy * tmp1 + 18. * A_uu.zz * DeltaGamma_ull.y.zz * tmp1 + 36. * A_uu.xy * DeltaGamma_ull.y.xy * tmp1 + 36. * A_uu.xz * DeltaGamma_ull.y.xz * tmp1 + 36. * A_uu.yz * DeltaGamma_ull.y.yz * tmp1 + -9. * beta_u.x * connHat_uul.x.x.x * tmp16 + -9. * beta_u.x * connHat_uul.x.y.y * tmp16 + -9. * beta_u.x * connHat_uul.x.z.z * tmp16 + 9. * beta_u.x * connHat_ull.x.xx * tmp5 + 9. * beta_u.x * connHat_ull.x.xy * tmp41 + 9. * beta_u.x * connHat_ull.x.xz * tmp42 + -9. * beta_u.x * connHat_uul.y.x.x * tmp19 + 9. * beta_u.x * connHat_uul.y.x.y * tmp16 + 9. * beta_u.x * connHat_uul.y.x.z * tmp17 + 9. * beta_u.x * connHat_uul.y.y.z * tmp21 + -9. * beta_u.x * connHat_uul.y.z.z * tmp19 + 9. * beta_u.x * connHat_uul.y.z.z * tmp22 + 9. * beta_u.x * connHat_ull.y.xz * tmp44 + -9. * beta_u.x * connHat_ull.y.xz * tmp8 + -9. * beta_u.x * connHat_ull.y.xz * tmp9 + -9. * beta_u.x * connHat_ull.y.xz * tmp10 + -9. * beta_u.y * connHat_uul.x.x.x * tmp19 + -9. * beta_u.y * tmp20 + -9. * beta_u.y * connHat_uul.x.z.z * tmp19 + 9. * beta_u.y * tmp26 + 9. * beta_u.y * connHat_ull.x.yy * tmp41 + 9. * beta_u.y * connHat_ull.x.yz * tmp42 + -9. * beta_u.y * connHat_uul.y.x.x * tmp29 + 9. * beta_u.y * connHat_uul.y.x.y * tmp19 + 9. * beta_u.y * connHat_uul.y.x.z * tmp21 + 9. * beta_u.y * connHat_uul.y.y.z * tmp30 + -9. * beta_u.y * connHat_uul.y.z.z * tmp29 + 9. * beta_u.y * tmp49 + 9. * beta_u.y * connHat_uul.y.y.z * tmp33 + -9. * beta_u.y * connHat_ull.y.yz * tmp8 + -9. * beta_u.y * tmp50 + -9. * beta_u.y * connHat_ull.y.yz * tmp10 + -9. * beta_u.z * connHat_uul.x.x.x * tmp28 + -9. * beta_u.z * connHat_uul.x.y.y * tmp28 + -9. * beta_u.z * connHat_uul.x.z.z * tmp28 + 9. * beta_u.z * connHat_ull.x.xz * tmp5 + 9. * beta_u.z * connHat_ull.x.yz * tmp41 + 9. * beta_u.z * connHat_ull.x.zz * tmp42 + -9. * beta_u.z * connHat_uul.y.x.x * tmp33 + 9. * beta_u.z * connHat_uul.y.x.y * tmp28 + 9. * beta_u.z * connHat_uul.y.x.z * tmp22 + 9. * beta_u.z * connHat_uul.y.y.z * tmp31 + -9. * beta_u.z * connHat_uul.y.z.z * tmp33 + 9. * beta_u.z * connHat_uul.y.z.z * tmp34 + 9. * beta_u.z * connHat_uul.y.y.z * tmp35 + -9. * beta_u.z * connHat_ull.y.zz * tmp8 + -9. * beta_u.z * connHat_ull.y.zz * tmp9 + -9. * beta_u.z * connHat_ull.y.zz * tmp10 + 8. * GDelta_u.y * tmp37 + -18. * a_l.x * tmp39 + -18. * a_l.y * A_uu.yy * tmp38 + -18. * a_l.z * tmp51 + -24. * e_u.y * tmp37 + 12. * a_u.y * tmp37) / 12.;
(deriv)->B_u.z += (-9. * LambdaBar_u.x * b_ul.z.x + -9. * LambdaBar_u.y * b_ul.z.y + -9. * LambdaBar_u.z * b_ul.z.z + -2. * GDelta_u.z * tmp2 + -12. * B_u.z * gammaDriver_eta + -12. * B_u.z * tr_b + 9. * b_ul.x.x * tmp8 + 9. * b_ul.x.y * tmp52 + 9. * b_ul.x.z * tmp53 + 9. * b_ul.y.x * tmp54 + 9. * b_ul.y.y * tmp9 + 9. * b_ul.y.z * tmp55 + -9. * b_ul.z.x * tmp43 + -9. * b_ul.z.x * tmp3 + -9. * b_ul.z.x * tmp4 + 9. * b_ul.z.x * connHat_uul.z.x.z * tmp1 + -9. * b_ul.z.y * tmp5 + -9. * b_ul.z.y * tmp6 + -9. * b_ul.z.y * tmp7 + 9. * b_ul.z.y * connHat_uul.z.y.z * tmp1 + -9. * b_ul.z.z * tmp8 + -9. * b_ul.z.z * tmp9 + -6. * GDelta_u.x * tmp56 + -6. * GDelta_u.y * tmp57 + -6. * GDelta_u.z * tmp58 + 6. * e_u.z * tmp2 + 6. * DeltaGamma_uul.z.x.x * tmp2 + 6. * DeltaGamma_uul.z.y.y * tmp2 + 6. * DeltaGamma_uul.z.z.z * tmp2 + 18. * GDelta_l.x * tmp15 + 18. * GDelta_l.y * tmp48 + 18. * GDelta_l.z * A_uu.zz * tmp1 + 18. * e_u.x * tmp56 + 18. * e_u.y * tmp57 + 18. * e_u.z * tmp58 + 18. * A_uu.xx * DeltaGamma_ull.z.xx * tmp1 + 18. * A_uu.yy * DeltaGamma_ull.z.yy * tmp1 + 18. * A_uu.zz * DeltaGamma_ull.z.zz * tmp1 + 36. * A_uu.xy * DeltaGamma_ull.z.xy * tmp1 + 36. * A_uu.xz * DeltaGamma_ull.z.xz * tmp1 + 36. * A_uu.yz * DeltaGamma_ull.z.yz * tmp1 + -9. * beta_u.x * connHat_uul.x.x.x * tmp17 + -9. * beta_u.x * connHat_uul.x.y.y * tmp17 + -9. * beta_u.x * connHat_uul.x.z.z * tmp17 + 9. * beta_u.x * connHat_ull.x.xx * tmp8 + 9. * beta_u.x * connHat_ull.x.xy * tmp52 + 9. * beta_u.x * connHat_ull.x.xz * tmp53 + -9. * beta_u.x * connHat_uul.y.x.x * tmp21 + -9. * beta_u.x * connHat_uul.y.y.y * tmp21 + -9. * beta_u.x * connHat_uul.y.z.z * tmp21 + 9. * beta_u.x * connHat_ull.y.xx * tmp54 + 9. * beta_u.x * connHat_ull.y.xy * tmp9 + 9. * beta_u.x * connHat_ull.y.xz * tmp55 + -9. * beta_u.x * connHat_uul.z.x.x * tmp22 + 9. * beta_u.x * connHat_uul.z.x.z * tmp17 + -9. * beta_u.x * connHat_uul.z.y.y * tmp22 + 9. * beta_u.x * connHat_uul.z.y.z * tmp21 + -9. * beta_u.y * connHat_uul.x.x.x * tmp21 + -9. * beta_u.y * connHat_uul.x.y.y * tmp21 + -9. * beta_u.y * connHat_uul.x.z.z * tmp21 + 9. * beta_u.y * connHat_ull.x.xy * tmp8 + 9. * beta_u.y * connHat_ull.x.yy * tmp52 + 9. * beta_u.y * connHat_ull.x.yz * tmp53 + -9. * beta_u.y * connHat_uul.y.x.x * tmp30 + -9. * beta_u.y * connHat_uul.y.y.y * tmp30 + -9. * beta_u.y * connHat_uul.y.z.z * tmp30 + 9. * beta_u.y * connHat_ull.y.xy * tmp54 + 9. * beta_u.y * connHat_ull.y.yy * tmp9 + 9. * beta_u.y * connHat_ull.y.yz * tmp55 + -9. * beta_u.y * connHat_uul.z.x.x * tmp31 + 9. * beta_u.y * connHat_uul.z.x.z * tmp21 + -9. * beta_u.y * connHat_uul.z.y.y * tmp31 + 9. * beta_u.y * connHat_uul.z.y.z * tmp30 + -9. * beta_u.z * connHat_uul.x.x.x * tmp22 + -9. * beta_u.z * connHat_uul.x.y.y * tmp22 + -9. * beta_u.z * tmp23 + 9. * beta_u.z * tmp27 + 9. * beta_u.z * connHat_ull.x.yz * tmp52 + 9. * beta_u.z * connHat_ull.x.zz * tmp53 + -9. * beta_u.z * connHat_uul.y.x.x * tmp31 + -9. * beta_u.z * connHat_uul.y.y.y * tmp31 + -9. * beta_u.z * tmp49 + 9. * beta_u.z * connHat_ull.y.xz * tmp54 + 9. * beta_u.z * tmp50 + 9. * beta_u.z * connHat_ull.y.zz * tmp55 + -9. * beta_u.z * connHat_uul.z.x.x * tmp34 + 9. * beta_u.z * connHat_uul.z.x.z * tmp22 + -9. * beta_u.z * connHat_uul.z.y.y * tmp34 + 9. * beta_u.z * connHat_uul.z.y.z * tmp31 + 8. * GDelta_u.z * tmp37 + -18. * a_l.x * tmp40 + -18. * a_l.y * tmp51 + -18. * a_l.z * A_uu.zz * tmp38 + -24. * e_u.z * tmp37 + 12. * a_u.z * tmp37) / 12.;
}
<? end ?>/* eqn.useShift == "GammaDriverHyperbolic" */
}
<? end ?>/* eqn.useShift ~= "none" */
analyzing flux jacobian:
${{ \alpha} _{,t}} = {{{{\alpha}} \cdot {{{{ \beta} ^r} _{,r}}}} + {{{{ \alpha} _{,r}}} {{{ \beta} ^r}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{{ \beta} ^r}} {{{{{ \gamma} _i} _j} _{,r}}}} + {{{{{ \beta} ^r} _{,r}}} {{{{ \gamma} _i} _j}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^r}} {{{{ a} _k} _{,r}}}} + {{{{ a} _k}} {{{{ \beta} ^r} _{,r}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _k}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,r}}} {{{{ δ} ^r} _k}}} + {{{-1}} {{\alpha}} \cdot {{f}} {{{{ \gamma} ^m} ^n}} {{{{ δ} ^r} _k}} {{{{{ K} _m} _n} _{,r}}}} + {{{-1}} {{f}} {{{ \alpha} _{,r}}} {{{{ K} _m} _n}} {{{{ \gamma} ^m} ^n}} {{{{ δ} ^r} _k}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _k}} {{\frac{\partial f}{\partial \alpha}}}} + {{{-1}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ K} _m} _n}} {{{{ \gamma} ^m} ^n}} {{{{ δ} ^r} _k}} {{\frac{\partial f}{\partial \alpha}}}} + {{{\alpha}} \cdot {{f}} {{{{ K} _m} _n}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^b} ^n}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _a} _b} _{,r}}}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{{{{ \beta} ^r}} {{{{{{ d} _k} _i} _j} _{,r}}}} + {{{{{ \beta} ^r} _{,r}}} {{{{{ d} _k} _i} _j}}} + {{{\frac{1}{2}}} {{{{ \gamma} _i} _l}} {{{{ δ} ^r} _k}} {{{{{ b} ^l} _j} _{,r}}}} + {{{\frac{1}{2}}} {{{{ \gamma} _j} _l}} {{{{ δ} ^r} _k}} {{{{{ b} ^l} _i} _{,r}}}} + {{{\frac{1}{2}}} {{{{ b} ^l} _j}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _i} _l} _{,r}}}} + {{{\frac{1}{2}}} {{{{ b} ^l} _i}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _j} _l} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ δ} ^r} _k}} {{{{{ K} _i} _j} _{,r}}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ K} _i} _j}} {{{{ δ} ^r} _k}}}}$
${{{{ K} _i} _j} _{,t}} = {{{{{ \beta} ^r}} {{{{{ K} _i} _j} _{,r}}}} + {{{{{ K} _i} _j}} {{{{ \beta} ^r} _{,r}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _j} _{,r}}} {{{{ δ} ^r} _i}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _i} _{,r}}} {{{{ δ} ^r} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{ a} _i}} {{{{ δ} ^r} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{ a} _j}} {{{{ δ} ^r} _i}}} + {{{\alpha}} \cdot {{{{ Z} _i} _{,r}}} {{{{ δ} ^r} _j}}} + {{{\alpha}} \cdot {{{{ Z} _j} _{,r}}} {{{{ δ} ^r} _i}}} + {{{\alpha}} \cdot {{{{ \gamma} ^r} ^d}} {{{{{{ d} _i} _j} _d} _{,r}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^r} ^e}} {{{{{{ d} _j} _i} _e} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^r} ^c}} {{{{{{ d} _c} _i} _j} _{,r}}}} + {{{{ Z} _i}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _j}}} + {{{{ Z} _j}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _i}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^r} ^g}} {{{{{ d} _g} _i} _j}}} + {{{{ \alpha} _{,r}}} {{{{ \gamma} ^r} ^h}} {{{{{ d} _i} _j} _h}}} + {{{{ \alpha} _{,r}}} {{{{ \gamma} ^r} ^f}} {{{{{ d} _j} _i} _f}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _i}} {{{{{{ d} _j} _a} _b} _{,r}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _j}} {{{{{{ d} _i} _a} _b} _{,r}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _i}} {{{{{ d} _j} _a} _b}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _j}} {{{{{ d} _i} _a} _b}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^d}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _i} _j} _d}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^c}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _c} _i} _j}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^e}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _j} _i} _e}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^r} _j}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _i} _a} _b}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^r} _i}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _j} _a} _b}}}}$
${{ \Theta} _{,t}} = {{{{\Theta}} \cdot {{{{ \beta} ^r} _{,r}}}} + {{{{ \Theta} _{,r}}} {{{ \beta} ^r}}} + {{{\alpha}} \cdot {{{{ Z} _i} _{,r}}} {{{{ \gamma} ^r} ^i}}} + {{{{ Z} _j}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^r} ^j}}} + {{{\alpha}} \cdot {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^r} ^e}} {{{{{{ d} _g} _h} _e} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^r} ^a}} {{{{{{ d} _a} _c} _d} _{,r}}}} + {{{{ \alpha} _{,r}}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^r} ^f}} {{{{{ d} _g} _h} _f}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^r} ^b}} {{{{{ d} _b} _c} _d}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _i}} {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^i}} {{{{{ \gamma} _k} _l} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^g}} {{{{ \gamma} ^l} ^h}} {{{{ \gamma} ^r} ^e}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _g} _h} _e}}} + {{{\alpha}} \cdot {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^a}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _a} _c} _d}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^c}} {{{{ \gamma} ^l} ^d}} {{{{ \gamma} ^r} ^a}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _a} _c} _d}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^k} ^r}} {{{{ \gamma} ^l} ^e}} {{{{{ \gamma} _k} _l} _{,r}}} {{{{{ d} _g} _h} _e}}}}$
${{{ Z} _k} _{,t}} = {{{{{ Z} _k}} {{{{ \beta} ^r} _{,r}}}} + {{{{ \beta} ^r}} {{{{ Z} _k} _{,r}}}} + {{{\Theta}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _k}}} + {{{\alpha}} \cdot {{{ \Theta} _{,r}}} {{{{ δ} ^r} _k}}} + {{{\alpha}} \cdot {{{{ \gamma} ^r} ^a}} {{{{{ K} _a} _k} _{,r}}}} + {{{{ \alpha} _{,r}}} {{{{ K} _b} _k}} {{{{ \gamma} ^r} ^b}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^m} ^n}} {{{{ δ} ^r} _k}} {{{{{ K} _m} _n} _{,r}}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ K} _m} _n}} {{{{ \gamma} ^m} ^n}} {{{{ δ} ^r} _k}}} + {{{-1}} {{\alpha}} \cdot {{{{ K} _a} _k}} {{{{ \gamma} ^c} ^r}} {{{{ \gamma} ^d} ^a}} {{{{{ \gamma} _c} _d} _{,r}}}} + {{{\alpha}} \cdot {{{{ K} _m} _n}} {{{{ \gamma} ^c} ^m}} {{{{ \gamma} ^d} ^n}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _c} _d} _{,r}}}}}$
${{{ \beta} ^l} _{,t}} = {{{{{ \beta} ^r}} {{{{ \beta} ^l} _{,r}}}} + {{{{ \beta} ^l}} {{{{ \beta} ^r} _{,r}}}}}$
${{ {{ b} ^l} _k} _{,t}} = {{{{{ \beta} ^r}} {{{{{ b} ^l} _k} _{,r}}}} + {{{{{ \beta} ^r} _{,r}}} {{{{ b} ^l} _k}}} + {{{-1}} {{{{ \gamma} ^l} ^i}} {{{{ a} _i} _{,r}}} {{{{ δ} ^r} _k}} {{{\alpha}^{2}}}} + {{{-1}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^a}} {{{{ δ} ^r} _k}} {{{{{{ d} _a} _c} _d} _{,r}}} {{{\alpha}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{ a} _j}} {{{{ \gamma} ^l} ^j}} {{{{ δ} ^r} _k}}} + {{{2}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^e}} {{{{ δ} ^r} _k}} {{{{{{ d} _g} _h} _e} _{,r}}} {{{\alpha}^{2}}}} + {{{{ a} _i}} {{{{ \gamma} ^m} ^l}} {{{{ \gamma} ^n} ^i}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _m} _n} _{,r}}} {{{\alpha}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^r} _k}} {{{{{ d} _b} _c} _d}}} + {{{{{ \gamma} ^l} ^a}} {{{{ \gamma} ^m} ^c}} {{{{ \gamma} ^n} ^d}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _m} _n} _{,r}}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^m} ^l}} {{{{ \gamma} ^n} ^a}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _m} _n} _{,r}}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{4}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^f}} {{{{ δ} ^r} _k}} {{{{{ d} _g} _h} _f}}} + {{{-2}} {{{{ \gamma} ^l} ^e}} {{{{ \gamma} ^m} ^g}} {{{{ \gamma} ^n} ^h}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _m} _n} _{,r}}} {{{{{ d} _g} _h} _e}} {{{\alpha}^{2}}}} + {{{-2}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^m} ^l}} {{{{ \gamma} ^n} ^e}} {{{{ δ} ^r} _k}} {{{{{ \gamma} _m} _n} _{,r}}} {{{{{ d} _g} _h} _e}} {{{\alpha}^{2}}}}}$
inserting deltas to help factor linear system
${{ \left[\begin{array}{c} \alpha\\ {{ \gamma} _i} _j\\ { a} _k\\ {{{ d} _k} _i} _j\\ {{ K} _i} _j\\ \Theta\\ { Z} _k\\ { \beta} ^l\\ {{ b} ^l} _k\end{array}\right]} _{,t}} = {\left[\begin{array}{c} {{{\alpha}} \cdot {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}} + {{{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{ \beta} ^a}}}\\ {{{{ \beta} ^a}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _j}} {{{{ δ} ^p} _i}}} + {{{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}} {{{{ \gamma} _i} _j}}}\\ {{{{ \beta} ^a}} {{{{ a} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _k}}} + {{{{ a} _k}} {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _k}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _k}}} + {{{-1}} {{\alpha}} \cdot {{f}} {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _k}} {{{{{ K} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}}} + {{{-1}} {{f}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{{{ δ} ^a} _k}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _k}} {{\frac{\partial f}{\partial \alpha}}}} + {{{-1}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{{{ δ} ^a} _k}} {{\frac{\partial f}{\partial \alpha}}}} + {{{\alpha}} \cdot {{f}} {{{{ K} _c} _d}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^d}} {{{{ δ} ^e} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _e}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}}}\\ {{{{ \beta} ^a}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _j}} {{{{ δ} ^p} _i}} {{{{ δ} ^m} _k}}} + {{{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}} {{{{{ d} _k} _i} _j}}} + {{{\frac{1}{2}}} {{{{ \gamma} _j} _l}} {{{{ δ} ^a} _k}} {{{{{ b} ^n} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _i}} {{{{ δ} ^l} _n}}} + {{{\frac{1}{2}}} {{{{ \gamma} _i} _l}} {{{{ δ} ^a} _k}} {{{{{ b} ^n} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _j}} {{{{ δ} ^l} _n}}} + {{{\frac{1}{2}}} {{{{ b} ^l} _i}} {{{{ δ} ^a} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _j}}} + {{{\frac{1}{2}}} {{{{ b} ^l} _j}} {{{{ δ} ^a} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _i}}} + {{{-1}} {{\alpha}} \cdot {{{{ δ} ^a} _k}} {{{{{ K} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _j}} {{{{ δ} ^p} _i}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ K} _i} _j}} {{{{ δ} ^a} _k}}}\\ {{{{ \beta} ^a}} {{{{{ K} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _j}} {{{{ δ} ^p} _i}}} + {{{{{ K} _i} _j}} {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _i}} {{{{ δ} ^a} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _j}} {{{{ δ} ^a} _i}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{ a} _i}} {{{{ δ} ^a} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{ a} _j}} {{{{ δ} ^a} _i}}} + {{{\alpha}} \cdot {{{{ Z} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _j}} {{{{ δ} ^a} _i}}} + {{{\alpha}} \cdot {{{{ Z} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _i}} {{{{ δ} ^a} _j}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^d}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _d}} {{{{ δ} ^p} _j}} {{{{ δ} ^m} _i}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _j}} {{{{ δ} ^p} _i}} {{{{ δ} ^m} _c}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^e}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _e}} {{{{ δ} ^p} _i}} {{{{ δ} ^m} _j}}} + {{{{ Z} _i}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _j}}} + {{{{ Z} _j}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _i}}} + {{{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^a} ^f}} {{{{{ d} _j} _i} _f}}} + {{{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^a} ^h}} {{{{{ d} _i} _j} _h}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^a} ^g}} {{{{{ d} _g} _i} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _i}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}} {{{{ δ} ^m} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _j}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}} {{{{ δ} ^m} _i}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _c}} {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _i}} {{{{{ d} _j} _a} _b}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _c}} {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _j}} {{{{{ d} _i} _a} _b}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^e}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _j} _i} _e}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^d}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _i} _j} _d}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^c}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _c} _i} _j}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^c} _j}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _i} _a} _b}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^c} _i}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _j} _a} _b}}}\\ {{{\Theta}} \cdot {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}} + {{{{ \Theta} _{,r}}} {{{{ δ} ^r} _a}} {{{ \beta} ^a}}} + {{{\alpha}} \cdot {{{{ Z} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _i}} {{{{ \gamma} ^a} ^i}}} + {{{{ Z} _j}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^a} ^j}}} + {{{\alpha}} \cdot {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^a} ^e}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _e}} {{{{ δ} ^p} _h}} {{{{ δ} ^m} _g}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^b} ^a}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _d}} {{{{ δ} ^p} _c}} {{{{ δ} ^m} _a}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _c} _d}}} + {{{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^a} ^f}} {{{{{ d} _g} _h} _f}}} + {{{-1}} {{\alpha}} \cdot {{{ Z} _i}} {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^i}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^c}} {{{{ \gamma} ^l} ^d}} {{{{ \gamma} ^b} ^a}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _a} _c} _d}}} + {{{\alpha}} \cdot {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^k} ^b}} {{{{ \gamma} ^l} ^a}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _a} _c} _d}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^g}} {{{{ \gamma} ^l} ^h}} {{{{ \gamma} ^a} ^e}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _g} _h} _e}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^e}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _l}} {{{{ δ} ^p} _k}} {{{{{ d} _g} _h} _e}}}\\ {{{{ Z} _k}} {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}} + {{{{ \beta} ^a}} {{{{ Z} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _k}}} + {{{\Theta}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _k}}} + {{{\alpha}} \cdot {{{ \Theta} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _k}}} + {{{\alpha}} \cdot {{{{ \gamma} ^b} ^a}} {{{{{ K} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _k}} {{{{ δ} ^p} _a}}} + {{{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ K} _b} _k}} {{{{ \gamma} ^a} ^b}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ δ} ^c} _k}} {{{{{ K} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{{{ δ} ^a} _k}}} + {{{-1}} {{\alpha}} \cdot {{{{ K} _a} _k}} {{{{ \gamma} ^c} ^b}} {{{{ \gamma} ^d} ^a}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _d}} {{{{ δ} ^p} _c}}} + {{{\alpha}} \cdot {{{{ K} _a} _b}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^d} ^b}} {{{{ δ} ^e} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _e}} {{{{ δ} ^q} _d}} {{{{ δ} ^p} _c}}}\\ {{{{ \beta} ^a}} {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^l} _n}}} + {{{{ \beta} ^l}} {{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}}}\\ {{{{ \beta} ^a}} {{{{{ b} ^n} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _k}} {{{{ δ} ^l} _n}}} + {{{{{ \beta} ^n} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^a} _n}} {{{{ b} ^l} _k}}} + {{{-1}} {{{{ \gamma} ^l} ^i}} {{{{ a} _m} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^m} _i}} {{{{ δ} ^a} _k}} {{{\alpha}^{2}}}} + {{{-1}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^a}} {{{{ δ} ^b} _k}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _b}} {{{{ δ} ^q} _d}} {{{{ δ} ^p} _c}} {{{{ δ} ^m} _a}} {{{\alpha}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{ a} _j}} {{{{ \gamma} ^l} ^j}} {{{{ δ} ^a} _k}}} + {{{2}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^e}} {{{{ δ} ^a} _k}} {{{{{{ d} _m} _p} _q} _{,r}}} {{{{ δ} ^r} _a}} {{{{ δ} ^q} _e}} {{{{ δ} ^p} _h}} {{{{ δ} ^m} _g}} {{{\alpha}^{2}}}} + {{{{ a} _i}} {{{{ \gamma} ^a} ^l}} {{{{ \gamma} ^b} ^i}} {{{{ δ} ^c} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}} {{{\alpha}^{2}}}} + {{{-2}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^b}} {{{{ δ} ^a} _k}} {{{{{ d} _b} _c} _d}}} + {{{{{ \gamma} ^l} ^a}} {{{{ \gamma} ^b} ^c}} {{{{ \gamma} ^e} ^d}} {{{{ δ} ^f} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _f}} {{{{ δ} ^q} _e}} {{{{ δ} ^p} _b}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^e} ^a}} {{{{ δ} ^f} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _f}} {{{{ δ} ^q} _e}} {{{{ δ} ^p} _b}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{4}} {{\alpha}} \cdot {{{ \alpha} _{,r}}} {{{{ δ} ^r} _a}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^f}} {{{{ δ} ^a} _k}} {{{{{ d} _g} _h} _f}}} + {{{-2}} {{{{ \gamma} ^l} ^e}} {{{{ \gamma} ^a} ^g}} {{{{ \gamma} ^b} ^h}} {{{{ δ} ^c} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}} {{{{{ d} _g} _h} _e}} {{{\alpha}^{2}}}} + {{{-2}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^a} ^l}} {{{{ \gamma} ^b} ^e}} {{{{ δ} ^c} _k}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{ δ} ^r} _c}} {{{{ δ} ^q} _b}} {{{{ δ} ^p} _a}} {{{{{ d} _g} _h} _e}} {{{\alpha}^{2}}}}\end{array}\right]}$
as a balance law system:
${{{ \left[\begin{array}{c} \alpha\\ {{ \gamma} _i} _j\\ { a} _k\\ {{{ d} _k} _i} _j\\ {{ K} _i} _j\\ \Theta\\ { Z} _k\\ { \beta} ^l\\ {{ b} ^l} _k\end{array}\right]} _{,t}} + {{{\left[\begin{array}{ccccccccc} -{{ \beta} ^r}& 0& 0& 0& 0& 0& 0& -{{{\alpha}} \cdot {{{{ δ} ^r} _n}}}& 0\\ 0& -{{{{ \beta} ^r}} {{{{ δ} ^p} _i}} {{{{ δ} ^q} _j}}}& 0& 0& 0& 0& 0& -{{{{{ \gamma} _i} _j}} {{{{ δ} ^r} _n}}}& 0\\ {{{{ δ} ^r} _k}} {{\left({{-{{{2}} {{\Theta}} \cdot {{f}}}} + {{{f}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}}}{-{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{\frac{\partial f}{\partial \alpha}}}}} + {{{\alpha}} \cdot {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{\frac{\partial f}{\partial \alpha}}}}}\right)}}& -{{{\alpha}} \cdot {{f}} {{{{ K} _c} _d}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{ δ} ^r} _k}}}& -{{{{ \beta} ^r}} {{{{ δ} ^m} _k}}}& 0& {{\alpha}} \cdot {{f}} {{{{ \gamma} ^p} ^q}} {{{{ δ} ^r} _k}}& -{{{2}} {{\alpha}} \cdot {{f}} {{{{ δ} ^r} _k}}}& 0& -{{{{ a} _k}} {{{{ δ} ^r} _n}}}& 0\\ {{{{ K} _i} _j}} {{{{ δ} ^r} _k}}& -{{\frac{1}{2}} {{{{{ δ} ^r} _k}} {{\left({{{{{{ b} ^q} _j}} {{{{ δ} ^p} _i}}} + {{{{{ b} ^q} _i}} {{{{ δ} ^p} _j}}}}\right)}}}}& 0& -{{{{ \beta} ^r}} {{{{ δ} ^m} _k}} {{{{ δ} ^p} _i}} {{{{ δ} ^q} _j}}}& {{\alpha}} \cdot {{{{ δ} ^p} _i}} {{{{ δ} ^q} _j}} {{{{ δ} ^r} _k}}& 0& 0& -{{{{{ δ} ^r} _n}} {{{{{ d} _k} _i} _j}}}& -{{\frac{1}{2}} {{{{{ δ} ^r} _k}} {{\left({{{{{{ \gamma} _i} _n}} {{{{ δ} ^m} _j}}} + {{{{{ \gamma} _j} _n}} {{{{ δ} ^m} _i}}}}\right)}}}}\\ {\frac{1}{2}}{\left({{{{{ a} _j}} {{{{ δ} ^r} _i}}} + {{{{ a} _i}} {{{{ δ} ^r} _j}}}{-{{{2}} {{{ Z} _j}} {{{{ δ} ^r} _i}}}}{-{{{2}} {{{ Z} _i}} {{{{ δ} ^r} _j}}}} + {{{2}} {{{{ \gamma} ^g} ^r}} {{{{{ d} _g} _i} _j}}}{-{{{2}} {{{{ \gamma} ^h} ^r}} {{{{{ d} _i} _h} _j}}}}{-{{{2}} {{{{ \gamma} ^f} ^r}} {{{{{ d} _j} _f} _i}}}} + {{{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _i}} {{{{{ d} _j} _a} _b}}} + {{{{{ \gamma} ^a} ^b}} {{{{ δ} ^r} _j}} {{{{{ d} _i} _a} _b}}}}\right)}& {\frac{1}{2}} {{{\alpha}} \cdot {{\left({{{{2}} {{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ d} _j} _e} _i}}} + {{{2}} {{{{ \gamma} ^d} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ d} _i} _d} _j}}}{-{{{2}} {{{{ \gamma} ^c} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ d} _c} _i} _j}}}}{-{{{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{ δ} ^r} _j}} {{{{{ d} _i} _a} _b}}}}{-{{{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{ δ} ^r} _i}} {{{{{ d} _j} _a} _b}}}}}\right)}}}& {\frac{1}{2}} {{{\alpha}} \cdot {{\left({{{{{{ δ} ^m} _j}} {{{{ δ} ^r} _i}}} + {{{{{ δ} ^m} _i}} {{{{ δ} ^r} _j}}}}\right)}}}& {\frac{1}{2}} {{{\alpha}} \cdot {{\left({{{{{{ \gamma} ^p} ^q}} {{{{ δ} ^m} _j}} {{{{ δ} ^r} _i}}} + {{{{{ \gamma} ^p} ^q}} {{{{ δ} ^m} _i}} {{{{ δ} ^r} _j}}}{-{{{2}} {{{{ \gamma} ^q} ^r}} {{{{ δ} ^m} _i}} {{{{ δ} ^p} _j}}}}{-{{{2}} {{{{ \gamma} ^q} ^r}} {{{{ δ} ^m} _j}} {{{{ δ} ^p} _i}}}} + {{{2}} {{{{ \gamma} ^m} ^r}} {{{{ δ} ^p} _i}} {{{{ δ} ^q} _j}}}}\right)}}}& -{{{{ \beta} ^r}} {{{{ δ} ^p} _i}} {{{{ δ} ^q} _j}}}& 0& -{{{\alpha}} \cdot {{\left({{{{{{ δ} ^m} _i}} {{{{ δ} ^r} _j}}} + {{{{{ δ} ^m} _j}} {{{{ δ} ^r} _i}}}}\right)}}}& -{{{{{ K} _i} _j}} {{{{ δ} ^r} _n}}}& 0\\ {-{{{{ Z} _j}} {{{{ \gamma} ^j} ^r}}}}{-{{{{{ \gamma} ^f} ^r}} {{{{ \gamma} ^g} ^h}} {{{{{ d} _g} _f} _h}}}} + {{{{{ \gamma} ^b} ^r}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _b} _c} _d}}}& {{\alpha}} \cdot {{\left({{{{{ Z} _i}} {{{{ \gamma} ^i} ^q}} {{{{ \gamma} ^p} ^r}}} + {{{{{ \gamma} ^e} ^r}} {{{{ \gamma} ^g} ^p}} {{{{ \gamma} ^h} ^q}} {{{{{ d} _g} _e} _h}}}{-{{{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^p} ^r}} {{{{{ d} _a} _c} _d}}}}{-{{{{{ \gamma} ^a} ^r}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{{ d} _a} _c} _d}}}} + {{{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^p} ^r}} {{{{{ d} _g} _e} _h}}}}\right)}}& 0& {{\alpha}} \cdot {{\left({{-{{{{{ \gamma} ^m} ^p}} {{{{ \gamma} ^q} ^r}}}} + {{{{{ \gamma} ^m} ^r}} {{{{ \gamma} ^p} ^q}}}}\right)}}& 0& -{{ \beta} ^r}& -{{{\alpha}} \cdot {{{{ \gamma} ^m} ^r}}}& -{{{\Theta}} \cdot {{{{ δ} ^r} _n}}}& 0\\ {-{{{\Theta}} \cdot {{{{ δ} ^r} _k}}}}{-{{{{{ K} _b} _k}} {{{{ \gamma} ^b} ^r}}}} + {{{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{{{ δ} ^r} _k}}}& {{\alpha}} \cdot {{\left({{{{{{ K} _a} _k}} {{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^p} ^r}}}{-{{{{{ K} _a} _b}} {{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{ δ} ^r} _k}}}}}\right)}}& 0& 0& {{\alpha}} \cdot {{\left({{-{{{{{ \gamma} ^p} ^r}} {{{{ δ} ^q} _k}}}} + {{{{{ \gamma} ^p} ^q}} {{{{ δ} ^r} _k}}}}\right)}}& -{{{\alpha}} \cdot {{{{ δ} ^r} _k}}}& -{{{{ \beta} ^r}} {{{{ δ} ^m} _k}}}& -{{{{ Z} _k}} {{{{ δ} ^r} _n}}}& 0\\ 0& 0& 0& 0& 0& 0& 0& -{\left({{{{{ \beta} ^r}} {{{{ δ} ^l} _n}}} + {{{{ \beta} ^l}} {{{{ δ} ^r} _n}}}}\right)}& 0\\ {{2}} {{\alpha}} \cdot {{{{ δ} ^r} _k}} {{\left({{{{{ a} _j}} {{{{ \gamma} ^j} ^l}}} + {{{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _b} _c} _d}}}{-{{{2}} {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^g} ^h}} {{{{{ d} _g} _f} _h}}}}}\right)}}& {{{{ δ} ^r} _k}} {{{\alpha}^{2}}} {{\left({{-{{{{ a} _i}} {{{{ \gamma} ^i} ^q}} {{{{ \gamma} ^l} ^p}}}}{-{{{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^p}} {{{{{ d} _a} _c} _d}}}}{-{{{{{ \gamma} ^a} ^l}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{{ d} _a} _c} _d}}}} + {{{2}} {{{{ \gamma} ^e} ^l}} {{{{ \gamma} ^g} ^p}} {{{{ \gamma} ^h} ^q}} {{{{{ d} _g} _e} _h}}} + {{{2}} {{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^p}} {{{{{ d} _g} _e} _h}}}}\right)}}& {{{{ \gamma} ^l} ^m}} {{{{ δ} ^r} _k}} {{{\alpha}^{2}}}& {{{{ δ} ^r} _k}} {{{\alpha}^{2}}} {{\left({{{{{{ \gamma} ^l} ^m}} {{{{ \gamma} ^p} ^q}}}{-{{{2}} {{{{ \gamma} ^l} ^q}} {{{{ \gamma} ^m} ^p}}}}}\right)}}& 0& 0& 0& -{{{{{ b} ^l} _k}} {{{{ δ} ^r} _n}}}& -{{{{ \beta} ^r}} {{{{ δ} ^l} _n}} {{{{ δ} ^m} _k}}}\end{array}\right]}} {{{ \left[\begin{array}{c} \alpha\\ {{ \gamma} _p} _q\\ { a} _m\\ {{{ d} _m} _p} _q\\ {{ K} _p} _q\\ \Theta\\ { Z} _m\\ { \beta} ^n\\ {{ b} ^n} _m\end{array}\right]} _{,r}}}}} = {\left[\begin{array}{c} 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]}$
expanding:
${{\left[\begin{array}{c} \frac{\partial \alpha}{\partial t}\\ \frac{\partial {{ \gamma} _i} _j}{\partial t}\\ \frac{\partial { a} _k}{\partial t}\\ \frac{\partial {{{ d} _k} _i} _j}{\partial t}\\ \frac{\partial {{ K} _i} _j}{\partial t}\\ \frac{\partial \Theta}{\partial t}\\ \frac{\partial { Z} _k}{\partial t}\\ \frac{\partial { \beta} ^l}{\partial t}\\ \frac{\partial {{ b} ^l} _k}{\partial t}\end{array}\right]} + {\left[\begin{array}{c} {{{-1}} {{{ \alpha} _{,r}}} {{{ \beta} ^r}}} + {{{-1}} {{\alpha}} \cdot {{{{ \beta} ^n} _{,n}}}}\\ {{{-1}} {{{{ \beta} ^n} _{,n}}} {{{{ \gamma} _i} _j}}} + {{{-1}} {{{ \beta} ^r}} {{{{{ \gamma} _i} _j} _{,r}}}}\\ {{{-1}} {{{ \beta} ^r}} {{{{ a} _k} _{,r}}}} + {{{-1}} {{{ a} _k}} {{{{ \beta} ^n} _{,n}}}} + {{{-2}} {{\Theta}} \cdot {{f}} {{{ \alpha} _{,k}}}} + {{{-2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} + {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^p} ^q}} {{{{{ K} _p} _q} _{,k}}}} + {{{f}} {{{ \alpha} _{,k}}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}}} + {{{-2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ \alpha} _{,k}}} {{\frac{\partial f}{\partial \alpha}}}} + {{{\alpha}} \cdot {{{ \alpha} _{,k}}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}} {{\frac{\partial f}{\partial \alpha}}}} + {{{-1}} {{\alpha}} \cdot {{f}} {{{{ K} _c} _d}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{{ \gamma} _p} _q} _{,k}}}}\\ {{{{ \alpha} _{,k}}} {{{{ K} _i} _j}}} + {{{-1}} {{{{ \beta} ^n} _{,n}}} {{{{{ d} _k} _i} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \gamma} _i} _n}} {{{{{ b} ^n} _j} _{,k}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ \gamma} _j} _n}} {{{{{ b} ^n} _i} _{,k}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ b} ^q} _i}} {{{{{ \gamma} _j} _q} _{,k}}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{{{ b} ^q} _j}} {{{{{ \gamma} _i} _q} _{,k}}}} + {{{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}} + {{{-1}} {{{ \beta} ^r}} {{{{{{ d} _k} _i} _j} _{,r}}}}\\ {{{\frac{1}{2}}} {{{ \alpha} _{,i}}} {{{ a} _j}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,j}}} {{{ a} _i}}} + {{{-1}} {{{ Z} _j}} {{{ \alpha} _{,i}}}} + {{{-1}} {{{ Z} _i}} {{{ \alpha} _{,j}}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^h} ^r}} {{{{{ d} _i} _h} _j}}} + {{{{ \alpha} _{,r}}} {{{{ \gamma} ^g} ^r}} {{{{{ d} _g} _i} _j}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^f} ^r}} {{{{{ d} _j} _f} _i}}} + {{{-1}} {{{{ K} _i} _j}} {{{{ \beta} ^n} _{,n}}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _j} _{,i}}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ a} _i} _{,j}}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,i}}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _a} _b}}} + {{{\frac{1}{2}}} {{{ \alpha} _{,j}}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _a} _b}}} + {{{-1}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{-1}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} + {{{-1}} {{{ \beta} ^r}} {{{{{ K} _i} _j} _{,r}}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^p} ^q}} {{{{{{ d} _j} _p} _q} _{,i}}}} + {{{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^p} ^q}} {{{{{{ d} _i} _p} _q} _{,j}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^c} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _c} _i} _j}}} + {{{\alpha}} \cdot {{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _j} _e} _i}}} + {{{\alpha}} \cdot {{{{ \gamma} ^m} ^r}} {{{{{{ d} _m} _i} _j} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^q} ^r}} {{{{{{ d} _j} _i} _q} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^q} ^r}} {{{{{{ d} _i} _j} _q} _{,r}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^d} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _i} _d} _j}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{{ \gamma} _p} _q} _{,j}}} {{{{{ d} _i} _a} _b}}} + {{{-1}} \cdot {{\frac{1}{2}}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{{ \gamma} _p} _q} _{,i}}} {{{{{ d} _j} _a} _b}}}\\ {{{-1}} {{{ \Theta} _{,r}}} {{{ \beta} ^r}}} + {{{-1}} {{\Theta}} \cdot {{{{ \beta} ^n} _{,n}}}} + {{{-1}} {{\alpha}} \cdot {{{{ Z} _m} _{,r}}} {{{{ \gamma} ^m} ^r}}} + {{{-1}} {{{ Z} _j}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^j} ^r}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^m} ^p}} {{{{ \gamma} ^q} ^r}} {{{{{{ d} _m} _p} _q} _{,r}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^m} ^r}} {{{{ \gamma} ^p} ^q}} {{{{{{ d} _m} _p} _q} _{,r}}}} + {{{{ \alpha} _{,r}}} {{{{ \gamma} ^b} ^r}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _b} _c} _d}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ \gamma} ^f} ^r}} {{{{ \gamma} ^g} ^h}} {{{{{ d} _g} _f} _h}}} + {{{\alpha}} \cdot {{{ Z} _i}} {{{{ \gamma} ^i} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^e} ^r}} {{{{ \gamma} ^g} ^p}} {{{{ \gamma} ^h} ^q}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _g} _e} _h}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _a} _c} _d}}} + {{{\alpha}} \cdot {{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _g} _e} _h}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^r}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{{ \gamma} _p} _q} _{,r}}} {{{{{ d} _a} _c} _d}}}\\ {{{-1}} {{\Theta}} \cdot {{{ \alpha} _{,k}}}} + {{{-1}} {{\alpha}} \cdot {{{ \Theta} _{,k}}}} + {{{-1}} {{{ Z} _k}} {{{{ \beta} ^n} _{,n}}}} + {{{-1}} {{{ \alpha} _{,r}}} {{{{ K} _b} _k}} {{{{ \gamma} ^b} ^r}}} + {{{-1}} {{{ \beta} ^r}} {{{{ Z} _k} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ \gamma} ^p} ^r}} {{{{{ K} _p} _k} _{,r}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^p} ^q}} {{{{{ K} _p} _q} _{,k}}}} + {{{{ \alpha} _{,k}}} {{{{ K} _b} _c}} {{{{ \gamma} ^b} ^c}}} + {{{\alpha}} \cdot {{{{ K} _a} _k}} {{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^p} ^r}} {{{{{ \gamma} _p} _q} _{,r}}}} + {{{-1}} {{\alpha}} \cdot {{{{ K} _a} _b}} {{{{ \gamma} ^a} ^p}} {{{{ \gamma} ^b} ^q}} {{{{{ \gamma} _p} _q} _{,k}}}}\\ {{{-1}} {{{ \beta} ^r}} {{{{ \beta} ^l} _{,r}}}} + {{{-1}} {{{ \beta} ^l}} {{{{ \beta} ^n} _{,n}}}}\\ {{{-1}} {{{{ \beta} ^n} _{,n}}} {{{{ b} ^l} _k}}} + {{{-1}} {{{ \beta} ^r}} {{{{{ b} ^l} _k} _{,r}}}} + {{{{{ \gamma} ^l} ^m}} {{{{ a} _m} _{,k}}} {{{\alpha}^{2}}}} + {{{{{ \gamma} ^l} ^m}} {{{{ \gamma} ^p} ^q}} {{{{{{ d} _m} _p} _q} _{,k}}} {{{\alpha}^{2}}}} + {{{2}} {{\alpha}} \cdot {{{ \alpha} _{,k}}} {{{ a} _j}} {{{{ \gamma} ^j} ^l}}} + {{{-2}} {{{{ \gamma} ^l} ^q}} {{{{ \gamma} ^m} ^p}} {{{{{{ d} _m} _p} _q} _{,k}}} {{{\alpha}^{2}}}} + {{{-1}} {{{ a} _i}} {{{{ \gamma} ^i} ^q}} {{{{ \gamma} ^l} ^p}} {{{{{ \gamma} _p} _q} _{,k}}} {{{\alpha}^{2}}}} + {{{2}} {{\alpha}} \cdot {{{ \alpha} _{,k}}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _b} _c} _d}}} + {{{-1}} {{{{ \gamma} ^a} ^q}} {{{{ \gamma} ^c} ^d}} {{{{ \gamma} ^l} ^p}} {{{{{ \gamma} _p} _q} _{,k}}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{-1}} {{{{ \gamma} ^a} ^l}} {{{{ \gamma} ^c} ^p}} {{{{ \gamma} ^d} ^q}} {{{{{ \gamma} _p} _q} _{,k}}} {{{{{ d} _a} _c} _d}} {{{\alpha}^{2}}}} + {{{-4}} {{\alpha}} \cdot {{{ \alpha} _{,k}}} {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^g} ^h}} {{{{{ d} _g} _f} _h}}} + {{{2}} {{{{ \gamma} ^e} ^q}} {{{{ \gamma} ^g} ^h}} {{{{ \gamma} ^l} ^p}} {{{{{ \gamma} _p} _q} _{,k}}} {{{{{ d} _g} _e} _h}} {{{\alpha}^{2}}}} + {{{2}} {{{{ \gamma} ^e} ^l}} {{{{ \gamma} ^g} ^p}} {{{{ \gamma} ^h} ^q}} {{{{{ \gamma} _p} _q} _{,k}}} {{{{{ d} _g} _e} _h}} {{{\alpha}^{2}}}}\end{array}\right]}} = {\left[\begin{array}{c} 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]}$