gauge vars
${Q} = {{{\alpha}} \cdot {{f}} {{\left({{{{{{ \gamma} ^i} ^l}} {{{{ K} _i} _l}}} - {{{2}} {{\Theta}}}}\right)}}}$
primitive $\partial_t$ defs
${{ \alpha} _{,t}} = {{ {-{\alpha}} {{Q}}} + {{{{ \alpha} _{,i}}} {{{ \beta} ^i}}}}$
${{ \alpha} _{,t}} = {{-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {{{{ \alpha} _{,i}}} {{{ \beta} ^i}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{{{{ \gamma} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ \gamma} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{ \gamma} _i} _k}} {{{{ \beta} ^k} _{,j}}}}}$
${{{{ K} _i} _j} _{,t}} = {{-{{{ \alpha} _{,i}} _{,j}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{\left({{{{{{{{{ R} _i} _j} + {{{ Z} _j} _{,i}}} - {{{{{{ \Gamma} ^k} _j} _i}} {{{ Z} _k}}}} + {{{ Z} _i} _{,j}}} - {{{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}}} + {{{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {{{2}} {{\Theta}}}}\right)}} {{{{ K} _i} _j}}}} - {{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _j} _l}}}}\right)}}} + {{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{4}} {{\pi}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S} - {\rho}}\right)}}} - {{{2}} {{{{ S} _i} _j}}}}\right)}}}}$
${{ \Theta} _{,t}} = {{{{{{{ \beta} ^k}} {{{ \Theta} _{,k}}}} - {{\left( {{\alpha}} \cdot {{\left({{{{{{ d} ^k} ^j} _j} - {{{{ d} _j} ^j} ^k}} - {{ Z} ^k}}\right)}}\right)} _{,k}}} + {{{{\frac{1}{2}} {\alpha}}} {{\left({{{{{{{2}} {{{ a} _k}} {{\left({{{{{{ d} ^k} ^j} _j} - {{{{ d} _j} ^j} ^k}} - {{{2}} {{{ Z} ^k}}}}\right)}}} + {{{{{{ d} _k} ^r} ^s}} {{{{{ \Gamma} ^k} _r} _s}}}} - {{{{{{ d} ^k} ^j} _j}} {{\left({{{{{ d} _k} _l} ^l} - {{{2}} {{{ Z} _k}}}}\right)}}}} - {{{{{ K} _k} _l}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}} {{{{ K} _m} _n}}}} + {{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}} {{\left({{{{{{ \gamma} ^m} ^n}} {{{{ K} _m} _n}}} - {{{2}} {{\Theta}}}}\right)}}}}\right)}}}} - {{{8}} {{\pi}} \cdot {{\alpha}} \cdot {{\rho}}}}$
${{{ Z} _i} _{,t}} = {{{{{{{\left( {{{ \beta} ^k}} {{{ Z} _i}}\right)} _{,k}} + {{\left( {{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}}\right)} _{,k}}} - {{\left( {{\alpha}} \cdot {{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {\Theta}}\right)}}\right)} _{,i}}} - {{{{ Z} _i}} {{{{ b} ^k} _k}}}} + {{{{ Z} _k}} {{{{ b} ^k} _i}}} + {{{\alpha}} \cdot {{\left({{{{{{{ a} _i}} {{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {{{2}} {{\Theta}}}}\right)}}} - {{{{ a} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}}}} - {{{{{ \gamma} ^k} ^l}} {{{{ K} _l} _r}} {{{{{ \Gamma} ^r} _k} _i}}}} + {{{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}} {{\left({{{{{ d} _k} _m} ^m} - {{{2}} {{{ Z} _k}}}}\right)}}}}\right)}}}} - {{{8}} {{\pi}} \cdot {{\alpha}} \cdot {{{ S} _i}}}}$
lapse vars
${{ f} _{,k}} = {{{f'}} \cdot {{\alpha}} \cdot {{{ a} _k}}}$
hyperbolic state variables
${{ a} _k} = {{\left( \log\left( \alpha\right)\right)} _{,k}}$
${{ a} _k} = {{\frac{1}{\alpha}} {{ \alpha} _{,k}}}$
${{ \alpha} _{,k}} = {{{\alpha}} \cdot {{{ a} _k}}}$
${{{{ d} _k} _i} _j} = {{{\frac{1}{2}}} {{{{{ \gamma} _i} _j} _{,k}}}}$
${{{{ \gamma} _i} _j} _{,k}} = {{{2}} {{{{{ d} _k} _i} _j}}}$
connections wrt aux vars
${{{{ \Gamma} ^k} _i} _j} = {{{\frac{1}{2}}} {{{{ \gamma} ^k} ^l}} {{\left({{{{{{ \gamma} _l} _i} _{,j}} + {{{{ \gamma} _l} _j} _{,i}}} - {{{{ \gamma} _i} _j} _{,l}}}\right)}}}$
${{{{ \Gamma} _i} _j} _k} = {{{\frac{1}{2}}} {{\left({{{{{{ \gamma} _i} _j} _{,k}} + {{{{ \gamma} _i} _k} _{,j}}} - {{{{ \gamma} _j} _k} _{,i}}}\right)}}}$
${{{{ \gamma} _i} _j} _{,k}} = {{{{{ \Gamma} _i} _j} _k} + {{{{ \Gamma} _j} _i} _k}}$
${{{{ \gamma} _i} _j} _{,k}} = {{{{{{ \gamma} _i} _a}} {{{{{ \Gamma} ^a} _j} _k}}} + {{{{{ \gamma} _j} _a}} {{{{{ \Gamma} ^a} _i} _k}}}}$
${{{{ \Gamma} _i} _j} _k} = {{-{{{{ d} _i} _j} _k}} + {{{{ d} _j} _i} _k} + {{{{ d} _k} _i} _j}}$
${{{{ \Gamma} ^i} _j} _k} = {{{{{ \gamma} ^i} ^l}} {{\left({{{{{ d} _j} _l} _k} + {{{{{ d} _k} _l} _j} - {{{{ d} _l} _j} _k}}}\right)}}}$
${\gamma^{ij}}_{,k}$ wrt aux vars
${{{{ \gamma} ^i} ^j} _{,k}} = { {-{{{ \gamma} ^i} ^l}} {{{{{ \gamma} _l} _m} _{,k}}} {{{{ \gamma} ^m} ^j}}}$
${{{{ \gamma} ^i} ^j} _{,k}} = {-{{{2}} {{{{ \gamma} ^i} ^l}} {{{{ \gamma} ^m} ^j}} {{{{{ d} _k} _l} _m}}}}$
Ricci wrt aux vars
${{{ R} _i} _j} = {{{{{{{{ \Gamma} ^k} _i} _j} _{,k}} - {{{{{ \Gamma} ^k} _i} _k} _{,j}}} + {{{{{{ \Gamma} ^k} _l} _k}} {{{{{ \Gamma} ^l} _i} _j}}}} - {{{{{{ \Gamma} ^k} _l} _j}} {{{{{ \Gamma} ^l} _i} _k}}}}$
${{{ R} _i} _j} = {{{{{\left( {{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}\right)} _{,k}} - {{\left( {{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _k} + {{{{{ d} _k} _a} _i} - {{{{ d} _a} _i} _k}}}\right)}}\right)} _{,j}}} + {{{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _l} _a} _k} + {{{{{ d} _k} _a} _l} - {{{{ d} _a} _l} _k}}}\right)}}}} {{{{{{ \gamma} ^l} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}}}}} - {{{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _l} _a} _j} + {{{{{ d} _j} _a} _l} - {{{{ d} _a} _l} _j}}}\right)}}}} {{{{{{ \gamma} ^l} ^a}} {{\left({{{{{ d} _i} _a} _k} + {{{{{ d} _k} _a} _i} - {{{{ d} _a} _i} _k}}}\right)}}}}}}$
${{{ R} _i} _j} = {{{{{{{ \gamma} ^k} ^a} _{,k}}} {{{{{ d} _i} _a} _j}}} + {{{{{{{ \gamma} ^k} ^a} _{,k}}} {{{{{ d} _j} _a} _i}}} - {{{{{{ \gamma} ^k} ^a} _{,k}}} {{{{{ d} _a} _i} _j}}}} + {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _i} _a} _j} _{,k}}}} + {{{{{{{{ \gamma} ^k} ^a}} {{{{{{ d} _j} _a} _i} _{,k}}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _a} _i} _j} _{,k}}}}} - {{{{{{ \gamma} ^k} ^a} _{,j}}} {{{{{ d} _i} _a} _k}}}} - {{{{{{ \gamma} ^k} ^a} _{,j}}} {{{{{ d} _k} _a} _i}}}} + {{{{{{{{ \gamma} ^k} ^a} _{,j}}} {{{{{ d} _a} _i} _k}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _i} _a} _k} _{,j}}}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _k} _a} _i} _{,j}}}}} + {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _a} _i} _k} _{,j}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _j}} {{{{{ d} _l} _a} _k}}} + {{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _j}} {{{{{ d} _k} _a} _l}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _k}} {{{{{ d} _i} _a} _j}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _i}} {{{{{ d} _l} _a} _k}}} + {{{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _i}} {{{{{ d} _k} _a} _l}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _k}} {{{{{ d} _j} _a} _i}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _l} _a} _k}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _k} _a} _l}}}} + {{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _l} _k}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _k}} {{{{{ d} _l} _a} _j}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _k} _a} _i}} {{{{{ d} _l} _a} _j}}}} + {{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _k}} {{{{{ d} _l} _a} _j}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _k}} {{{{{ d} _j} _a} _l}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _l}} {{{{{ d} _k} _a} _i}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _k}} {{{{{ d} _j} _a} _l}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _i} _a} _k}}} + {{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _k} _a} _i}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _a} _i} _k}}}}}$
${{{ R} _i} _j} = {{{-{{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _a} _j}} {{{{{ d} _k} _b} _c}}}} - {{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _j} _a} _i}} {{{{{ d} _k} _b} _c}}}} + {{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _a} _i} _j}} {{{{{ d} _k} _b} _c}}} + {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _i} _a} _j} _{,k}}}} + {{{{{{ \gamma} ^k} ^a}} {{{{{{ d} _j} _a} _i} _{,k}}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _a} _i} _j} _{,k}}}}} + {{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _a} _k}} {{{{{ d} _j} _b} _c}}} + {{{{{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _j} _b} _c}} {{{{{ d} _k} _a} _i}}} - {{{2}} {{{{ \gamma} ^c} ^a}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _a} _i} _k}} {{{{{ d} _j} _b} _c}}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _i} _a} _k} _{,j}}}}} - {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _k} _a} _i} _{,j}}}}} + {{{{{ \gamma} ^k} ^a}} {{{{{{ d} _a} _i} _k} _{,j}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _j}} {{{{{ d} _l} _a} _k}}} + {{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _j}} {{{{{ d} _k} _a} _l}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _k}} {{{{{ d} _i} _a} _j}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _i}} {{{{{ d} _l} _a} _k}}} + {{{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _i}} {{{{{ d} _k} _a} _l}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _k}} {{{{{ d} _j} _a} _i}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _l} _a} _k}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _k} _a} _l}}}} + {{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _l} _k}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _k}} {{{{{ d} _l} _a} _j}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _k} _a} _i}} {{{{{ d} _l} _a} _j}}}} + {{{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _k}} {{{{{ d} _l} _a} _j}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _i} _a} _k}} {{{{{ d} _j} _a} _l}}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _j} _a} _l}} {{{{{ d} _k} _a} _i}}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _i} _k}} {{{{{ d} _j} _a} _l}}} + {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _i} _a} _k}}} + {{{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _k} _a} _i}}} - {{{{{ \gamma} ^k} ^a}} {{{{ \gamma} ^l} ^a}} {{{{{ d} _a} _l} _j}} {{{{{ d} _a} _i} _k}}}}}$
symmetrizing
${{{ R} _i} _j} = {{{-{{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _b} _c} _k}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _b} _c} _k}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _a} _i} _j}} {{{{{ d} _b} _c} _k}}} + {{{{{ \gamma} ^a} ^k}} {{{{{{ d} _i} _a} _j} _{,k}}}} + {{{{{{ \gamma} ^a} ^k}} {{{{{{ d} _j} _a} _i} _{,k}}}} - {{{{{ \gamma} ^a} ^k}} {{{{{{ d} _a} _i} _j} _{,k}}}}} + {{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _i} _a} _k}} {{{{{ d} _j} _b} _c}}} + {{{{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _j} _b} _c}} {{{{{ d} _k} _a} _i}}} - {{{2}} {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^b} ^k}} {{{{{ d} _a} _i} _k}} {{{{{ d} _j} _b} _c}}}} - {{{{{ \gamma} ^a} ^k}} {{{{{{ d} _i} _a} _k} _{,j}}}}} + {{{{{ \gamma} ^a} ^l}} {{{{ \gamma} ^a} ^k}} {{{{{ d} _a} _k} _l}} {{{{{ d} _i} _a} _j}}} + {{{{{{{ \gamma} ^a} ^k}} {{{{ \gamma} ^a} ^l}} {{{{{ d} _a} _k} _l}} {{{{{ d} _j} _a} _i}}} - {{{{{ \gamma} ^a} ^k}} {{{{ \gamma} ^a} ^l}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _k} _l}}}} - {{{{{ \gamma} ^a} ^k}} {{{{ \gamma} ^a} ^l}} {{{{{ d} _i} _a} _k}} {{{{{ d} _j} _a} _l}}}}}$
${{{ R} _i} _j} = {{{{{ \gamma} ^a} ^b}} {{\left({{{{-{{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _b} _c}}}} - {{{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{{{ d} _a} _i} _j} _{,b}}} + {{{{{ d} _b} _a} _i} _{,j}} + {{{{{{ d} _b} _a} _j} _{,i}} - {{{{{ d} _i} _a} _b} _{,j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}}}\right)}}}$
${{{ R} _i} _j} = {{{{{ \gamma} ^a} ^b}} {{\left({{{{-{{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _b} _c}}}} - {{{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{{{ d} _a} _i} _j} _{,b}}} + {{{{{ d} _b} _a} _i} _{,j}} + {{{{{{ d} _b} _a} _j} _{,i}} - {{{{{ d} _i} _a} _b} _{,j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}}}\right)}}}$
${{{ R} _i} _j} = {{{{{ \gamma} ^a} ^b}} {{\left({{{{-{{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _b} _c}}}} - {{{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{{{ d} _a} _i} _j} _{,b}}} + {{{{{ d} _b} _a} _i} _{,j}} + {{{{{{ d} _b} _a} _j} _{,i}} - {{{{{ d} _i} _a} _b} _{,j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}}}\right)}}}$
${{{ R} _i} _j} = {{{{{{{ d} ^a} _i} _j}} {{{{{ d} ^b} _a} _b}}} + {{{{{{{{{ d} _i} ^a} _b}} {{{{{ d} _j} _a} ^b}}} - {{{2}} {{{{{ d} ^a} _b} _i}} {{{{{ d} _j} _a} ^b}}}} - {{{{{{ d} ^b} _a} _b}} {{{{{ d} _i} ^a} _j}}}} - {{{{{{ d} ^b} _a} _b}} {{{{{ d} _j} ^a} _i}}}} + {{{{2}} {{{{{ d} _a} ^b} _i}} {{{{{ d} _j} ^a} _b}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}}}$
${{{ R} _i} _j} = {{{{{ e} _a}} {{{{{ d} ^a} _i} _j}}} + {{{{{{{{{ d} _i} ^a} _b}} {{{{{ d} _j} _a} ^b}}} - {{{2}} {{{{{ d} ^a} _b} _i}} {{{{{ d} _j} _a} ^b}}}} - {{{{ e} _a}} {{{{{ d} _i} ^a} _j}}}} - {{{{ e} _a}} {{{{{ d} _j} ^a} _i}}}} + {{{{2}} {{{{{ d} _a} ^b} _i}} {{{{{ d} _j} ^a} _b}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}}}$
${{{ R} _i} _j} = {{{{{ e} _a}} {{{{{ d} ^a} _i} _j}}} + {{{{{{{{{ d} _i} ^a} _b}} {{{{{ d} _j} _a} ^b}}} - {{{{ e} _a}} {{{{{ d} _i} ^a} _j}}}} - {{{{ e} _a}} {{{{{ d} _j} ^a} _i}}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} - {{{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}}}$
${{{ R} _i} _j} = {{{{{ \gamma} ^a} ^b}} {{\left({{{{{{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _b} _d}} {{{{{ d} _c} _i} _j}}} - {{{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _b} _d}} {{{{{ d} _i} _c} _j}}}} - {{{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _b} _d}} {{{{{ d} _j} _c} _i}}}} + {{{{{ d} _a} _b} _i} _{,j}} + {{{{{{{ d} _a} _b} _j} _{,i}} - {{{{{ d} _a} _i} _j} _{,b}}} - {{{{{ d} _i} _a} _b} _{,j}}} + {{{{{{ d} _i} _a} _c}} {{{{{ d} _j} _b} ^c}}}}\right)}}}$
time derivative of $\alpha_{,t}$
${{ \alpha} _{,t}} = {{-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {{{{ \beta} ^i}} {{{{\alpha}} \cdot {{{ a} _i}}}}}}$
time derivative of $\gamma_{ij,t}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{{{{ \gamma} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ \gamma} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{ \gamma} _i} _k}} {{{{ \beta} ^k} _{,j}}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{{ \beta} ^k}} {{{{2}} {{{{{ d} _k} _i} _j}}}}} + {{{{{ \gamma} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{ \gamma} _i} _k}} {{{{ \beta} ^k} _{,j}}}}}$
time derivative of $a_{k,t}$
${{{ a} _k} _{,t}} = {\frac{{{{\alpha}} \cdot {{{{ \alpha} _{,k}} _{,t}}}} - {{{{ \alpha} _{,k}}} {{{ \alpha} _{,t}}}}}{{\alpha}^{2}}}$
${{{ a} _k} _{,t}} = {\frac{{{{\alpha}} \cdot {{{\left( {-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {{{{ \beta} ^i}} {{{{\alpha}} \cdot {{{ a} _i}}}}}\right)} _{,k}}}} - {{{{ \alpha} _{,k}}} {{\left({{-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {{{{ \beta} ^i}} {{{{\alpha}} \cdot {{{ a} _i}}}}}}\right)}}}}{{\alpha}^{2}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{\alpha}} \cdot {{{ f} _{,k}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ f} _{,k}}}} + {{{{2}} {{\Theta}} \cdot {{f}} {{{ \alpha} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{{ \gamma} ^i} ^l} _{,k}}}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{f}} {{{ \alpha} _{,k}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{\alpha}} \cdot {{{ f} _{,k}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ f} _{,k}}}} + {{{{2}} {{\Theta}} \cdot {{f}} {{{ \alpha} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{{ \gamma} ^i} ^l} _{,k}}}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{f}} {{{ \alpha} _{,k}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{\alpha}} \cdot {{{{f'}} \cdot {{\alpha}} \cdot {{{ a} _k}}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{f'}} \cdot {{\alpha}} \cdot {{{ a} _k}}}}} + {{{{2}} {{\Theta}} \cdot {{f}} {{{{\alpha}} \cdot {{{ a} _k}}}}} - {{{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{{ \gamma} ^i} ^l} _{,k}}}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{f}} {{{{\alpha}} \cdot {{{ a} _k}}}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f'}} \cdot {{{ a} _k}} {{{\alpha}^{2}}}} + {{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}} {{{ a} _k}}} - {{{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{{ \gamma} ^i} ^l} _{,k}}}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f'}} \cdot {{{ a} _k}} {{{\alpha}^{2}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}} {{{ a} _k}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^i} ^a}} {{{{{ d} _k} _a} _b}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f'}} \cdot {{{ a} _k}} {{{\alpha}^{2}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}} {{{ a} _k}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^i} ^a}} {{{{{ d} _k} _a} _b}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
time derivative of $d_{kij,t}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\frac{1}{2}} {{{{{ \gamma} _i} _j} _{,k}} _{,t}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\frac{1}{2}} {{\left( {{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{{ \beta} ^l}} {{{{2}} {{{{{ d} _l} _i} _j}}}}} + {{{{{ \gamma} _l} _j}} {{{{ \beta} ^l} _{,i}}}} + {{{{{ \gamma} _i} _l}} {{{{ \beta} ^l} _{,j}}}}\right)} _{,k}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{-{{{2}} {{{ \alpha} _{,k}}} {{{{ K} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}}} + {{{2}} {{{{ \beta} ^l} _{,k}}} {{{{{ d} _l} _i} _j}}} + {{{2}} {{{ \beta} ^l}} {{{{{{ d} _l} _i} _j} _{,k}}}} + {{{{{ \gamma} _l} _j}} {{{{{ \beta} ^l} _{,i}} _{,k}}}} + {{{{{ \beta} ^l} _{,i}}} {{{{{ \gamma} _l} _j} _{,k}}}} + {{{{{ \gamma} _i} _l}} {{{{{ \beta} ^l} _{,j}} _{,k}}}} + {{{{{ \beta} ^l} _{,j}}} {{{{{ \gamma} _i} _l} _{,k}}}}}\right)}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{-{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ K} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}}} + {{{2}} {{{{ \beta} ^l} _{,k}}} {{{{{ d} _l} _i} _j}}} + {{{2}} {{{ \beta} ^l}} {{{{{{ d} _l} _i} _j} _{,k}}}} + {{{{{ \gamma} _l} _j}} {{{{{ \beta} ^l} _{,i}} _{,k}}}} + {{{2}} {{{{ \beta} ^l} _{,i}}} {{{{{ d} _k} _l} _j}}} + {{{{{ \gamma} _i} _l}} {{{{{ \beta} ^l} _{,j}} _{,k}}}} + {{{2}} {{{{ \beta} ^l} _{,j}}} {{{{{ d} _k} _i} _l}}}}\right)}}$
$K_{ij,t}$ with hyperbolic terms
${{{{ K} _i} _j} _{,t}} = {{-{{{ \alpha} _{,i}} _{,j}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{ \alpha} _{,k}}}} + {{{\alpha}} \cdot {{\left({{{{{{{{{ R} _i} _j} + {{{ Z} _j} _{,i}}} - {{{{{{ \Gamma} ^k} _j} _i}} {{{ Z} _k}}}} + {{{ Z} _i} _{,j}}} - {{{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}}} + {{{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {{{2}} {{\Theta}}}}\right)}} {{{{ K} _i} _j}}}} - {{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _j} _l}}}}\right)}}} + {{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{4}} {{\pi}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S} - {\rho}}\right)}}} - {{{2}} {{{{ S} _i} _j}}}}\right)}}}}$
${{{{ K} _i} _j} _{,t}} = {{-{{{\frac{1}{2}}} {{\left({{{\left( {{\alpha}} \cdot {{{ a} _i}}\right)} _{,j}} + {{\left( {{\alpha}} \cdot {{{ a} _j}}\right)} _{,i}}}\right)}}}} + {{{{{{ \Gamma} ^k} _i} _j}} {{{{\alpha}} \cdot {{{ a} _k}}}}} + {{{\alpha}} \cdot {{\left({{{{{{{{{ R} _i} _j} + {{{ Z} _j} _{,i}}} - {{{{{{ \Gamma} ^k} _j} _i}} {{{ Z} _k}}}} + {{{ Z} _i} _{,j}}} - {{{{{{ \Gamma} ^k} _i} _j}} {{{ Z} _k}}}} + {{{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {{{2}} {{\Theta}}}}\right)}} {{{{ K} _i} _j}}}} - {{{2}} {{{{ K} _i} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _j} _l}}}}\right)}}} + {{{{{{ K} _i} _j} _{,k}}} {{{ \beta} ^k}}} + {{{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{4}} {{\pi}} \cdot {{\alpha}} \cdot {{\left({{{{{{ \gamma} _i} _j}} {{\left({{S} - {\rho}}\right)}}} - {{{2}} {{{{ S} _i} _j}}}}\right)}}}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{{ \Gamma} ^k} _i} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{ \Gamma} ^k} _j} _i}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{ \Gamma} ^k} _i} _j}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _k}} {{{{ K} _j} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{2}} {{{ \beta} ^k}} {{{{{ K} _i} _j} _{,k}}}} + {{{2}} {{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{2}} {{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{{ \alpha} _{,j}}} {{{ a} _i}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{{ \alpha} _{,i}}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{{ \Gamma} ^k} _i} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{ \Gamma} ^k} _j} _i}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{ \Gamma} ^k} _i} _j}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _k}} {{{{ K} _j} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{2}} {{{ \beta} ^k}} {{{{{ K} _i} _j} _{,k}}}} + {{{2}} {{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{2}} {{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}}}} + {{{2}} {{\alpha}} \cdot {{{{ R} _i} _j}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _j} _a} _i} + {{{{{ d} _i} _a} _j} - {{{{ d} _a} _j} _i}}}\right)}}}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _k}} {{{{ K} _j} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{2}} {{{ \beta} ^k}} {{{{{ K} _i} _j} _{,k}}}} + {{{2}} {{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{2}} {{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}}}} + {{{2}} {{\alpha}} \cdot {{{{{{ \gamma} ^a} ^b}} {{\left({{{{-{{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _b} _c}}}} - {{{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{2}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{{{ d} _a} _i} _j} _{,b}}} + {{{{{ d} _b} _a} _i} _{,j}} + {{{{{{ d} _b} _a} _j} _{,i}} - {{{{{ d} _i} _a} _b} _{,j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}}}\right)}}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _j} _a} _i} + {{{{{ d} _i} _a} _j} - {{{{ d} _a} _j} _i}}}\right)}}}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{{{ \gamma} ^k} ^a}} {{\left({{{{{ d} _i} _a} _j} + {{{{{ d} _j} _a} _i} - {{{{ d} _a} _i} _j}}}\right)}}}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _k}} {{{{ K} _j} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{2}} {{{ \beta} ^k}} {{{{{ K} _i} _j} _{,k}}}} + {{{2}} {{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{2}} {{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _i} _a} _j}}} + {{{{{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _j} _a} _i}}} - {{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _a} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _i} _j}} {{{{{ d} _a} _b} _c}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _b} _a} _i} _{,j}}}} + {{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _b} _a} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}} + {{{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _j} _a} _i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _i} _a} _j}}}} + {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _a} _j} _i}}} + {{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^k} ^a}} {{{{{ d} _a} _i} _j}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _k}} {{{{ K} _j} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{2}} {{{ \beta} ^k}} {{{{{ K} _i} _j} _{,k}}}} + {{{2}} {{{{ K} _k} _i}} {{{{ \beta} ^k} _{,j}}}} + {{{2}} {{{{ K} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}} + {{{{{{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}} - {{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _a} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}} + {{{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}}} + {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _a} _b}} {{{{ K} _i} _j}} {{{{ \gamma} ^a} ^b}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _a}} {{{{ K} _j} _b}} {{{{ \gamma} ^a} ^b}}}} + {{{2}} {{{ \beta} ^a}} {{{{{ K} _i} _j} _{,a}}}} + {{{2}} {{{{ K} _a} _i}} {{{{ \beta} ^a} _{,j}}}} + {{{2}} {{{{ K} _a} _j}} {{{{ \beta} ^a} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
Z4 terms
${{ \Theta} _{,t}} = {{\frac{1}{2}}{\left({{-{{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}}}} + {{{{2}} {{{ \Theta} _{,k}}} {{{ \beta} ^k}}} - {{{2}} {{{ \alpha} _{,k}}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}}} + {{{2}} {{{ \alpha} _{,k}}} {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{ d} _j} _d} _e}}} + {{{{{{2}} {{{ Z} _a}} {{{ \alpha} _{,k}}} {{{{ \gamma} ^k} ^a}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^k} ^b}} {{{{{ \gamma} ^j} ^c} _{,k}}} {{{{{ d} _b} _c} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{{ \gamma} ^k} ^b} _{,k}}} {{{{{ d} _b} _c} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{{ d} _b} _c} _j} _{,k}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^e} ^k}} {{{{{ \gamma} ^d} ^j} _{,k}}} {{{{{ d} _j} _d} _e}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{{ \gamma} ^e} ^k} _{,k}}} {{{{{ d} _j} _d} _e}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{{ d} _j} _d} _e} _{,k}}}} + {{{2}} {{\alpha}} \cdot {{{{ Z} _a} _{,k}}} {{{{ \gamma} ^k} ^a}}} + {{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{{ \gamma} ^k} ^a} _{,k}}}} + {{{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} - {{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{ d} _j} _d} _e}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{ a} _k}} {{{{ \gamma} ^k} ^a}}}} + {{{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{{ \Gamma} ^k} _r} _s}} {{{{{ d} _k} _d} _e}}} - {{{\alpha}} \cdot {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _l} _f}}}} + {{{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} - {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}}}} + {{{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^m} ^n}}} - {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}}}\right)}}$
${{ \Theta} _{,t}} = {{\frac{1}{2}}{\left({{-{{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}}}} + {{{{2}} {{{ \Theta} _{,k}}} {{{ \beta} ^k}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{ a} _k}} {{{{ \gamma} ^k} ^a}}}} + {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^c}} {{{{ \gamma} ^j} ^g}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} + {{{{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^b}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{{ d} _b} _c} _j} _{,k}}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^g}} {{{{ \gamma} ^e} ^k}} {{{{ \gamma} ^h} ^j}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^g}} {{{{ \gamma} ^h} ^k}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{{ d} _j} _d} _e} _{,k}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _a} _{,k}}} {{{{ \gamma} ^k} ^a}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^h} ^a}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _k} _g} _h}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _r} _i} _s}}} + {{{{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _s} _i} _r}}} - {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _i} _r} _s}} {{{{{ d} _k} _d} _e}}}} - {{{\alpha}} \cdot {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _l} _f}}}} + {{{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} - {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}}}} + {{{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^m} ^n}}} - {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}}}\right)}}$
${{{ Z} _i} _{,t}} = {{{{{{{\left( {{{ \beta} ^k}} {{{ Z} _i}}\right)} _{,k}} + {{\left( {{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}}\right)} _{,k}}} - {{\left( {{\alpha}} \cdot {{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {\Theta}}\right)}}\right)} _{,i}}} - {{{{ Z} _i}} {{{{ b} ^k} _k}}}} + {{{{ Z} _k}} {{{{ b} ^k} _i}}} + {{{\alpha}} \cdot {{\left({{{{{{{ a} _i}} {{\left({{{{{{ \gamma} ^k} ^l}} {{{{ K} _k} _l}}} - {{{2}} {{\Theta}}}}\right)}}} - {{{{ a} _k}} {{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}}}} - {{{{{ \gamma} ^k} ^l}} {{{{ K} _l} _r}} {{{{{ \Gamma} ^r} _k} _i}}}} + {{{{{ \gamma} ^k} ^l}} {{{{ K} _l} _i}} {{\left({{{{{ d} _k} _m} ^m} - {{{2}} {{{ Z} _k}}}}\right)}}}}\right)}}}} - {{{8}} {{\pi}} \cdot {{\alpha}} \cdot {{{ S} _i}}}}$
${{{ Z} _i} _{,t}} = {{{{{ \beta} ^k}} {{{{ Z} _i} _{,k}}}} + {{{{ Z} _i}} {{{{ \beta} ^k} _{,k}}}} + {{{{ \alpha} _{,k}}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _l} _i} _{,k}}}} + {{{{\alpha}} \cdot {{{{ K} _l} _i}} {{{{{ \gamma} ^k} ^l} _{,k}}}} - {{{{ \alpha} _{,i}}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{{{\Theta}} \cdot {{{ \alpha} _{,i}}}} - {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _k} _l} _{,i}}}}} - {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{{ \gamma} ^k} ^l} _{,i}}}}} + {{{{\alpha}} \cdot {{{ \Theta} _{,i}}}} - {{{{ Z} _i}} {{{{ b} ^k} _k}}}} + {{{{ Z} _k}} {{{{ b} ^k} _i}}} + {{{{{{\alpha}} \cdot {{{ a} _i}} {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}} - {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{ a} _i}}}} - {{{\alpha}} \cdot {{{ a} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} - {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{{ \Gamma} ^r} _k} _i}}}} + {{{{{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^k} ^l}} {{{{{ d} _k} _m} _a}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{{ S} _i}}}}}$
${{{ Z} _i} _{,t}} = {{{{{ \beta} ^k}} {{{{ Z} _i} _{,k}}}} + {{{{ Z} _i}} {{{{ \beta} ^k} _{,k}}}} + {{{{{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _l} _i} _{,k}}}} - {{{2}} {{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _k} _b} _c}}}} - {{{\Theta}} \cdot {{\alpha}} \cdot {{{ a} _i}}}} - {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _k} _l} _{,i}}}}} + {{{2}} {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _b} _c}}} + {{{{\alpha}} \cdot {{{ \Theta} _{,i}}}} - {{{{ Z} _i}} {{{{ b} ^k} _k}}}} + {{{{{{ Z} _k}} {{{{ b} ^k} _i}}} - {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _k} _d} _i}}}} - {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _i} _d} _k}}}} + {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _d} _k} _i}}} + {{{{{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^k} ^l}} {{{{{ d} _k} _m} _a}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{{ S} _i}}}}}$
partial derivatives
${{ \alpha} _{,t}} = {{-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {{{{ \beta} ^i}} {{{{\alpha}} \cdot {{{ a} _i}}}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}} + {{{{ \beta} ^k}} {{{{2}} {{{{{ d} _k} _i} _j}}}}} + {{{{{ \gamma} _k} _j}} {{{{ \beta} ^k} _{,i}}}} + {{{{{ \gamma} _i} _k}} {{{{ \beta} ^k} _{,j}}}}}$
${{{ a} _k} _{,t}} = {{{{{ \beta} ^i}} {{{{ a} _i} _{,k}}}} + {{{{{ a} _i}} {{{{ \beta} ^i} _{,k}}}} - {{{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}} + {{{2}} {{\Theta}} \cdot {{f'}} \cdot {{{ a} _k}} {{{\alpha}^{2}}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}} {{{ a} _k}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^i} ^a}} {{{{{ d} _k} _a} _b}}} + {{{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} - {{{\alpha}} \cdot {{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{-{{{2}} {{\alpha}} \cdot {{{ a} _k}} {{{{ K} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}}} + {{{2}} {{{{ \beta} ^l} _{,k}}} {{{{{ d} _l} _i} _j}}} + {{{2}} {{{ \beta} ^l}} {{{{{{ d} _l} _i} _j} _{,k}}}} + {{{{{ \gamma} _l} _j}} {{{{{ \beta} ^l} _{,i}} _{,k}}}} + {{{2}} {{{{ \beta} ^l} _{,i}}} {{{{{ d} _k} _l} _j}}} + {{{{{ \gamma} _i} _l}} {{{{{ \beta} ^l} _{,j}} _{,k}}}} + {{{2}} {{{{ \beta} ^l} _{,j}}} {{{{{ d} _k} _i} _l}}}}\right)}}$
${{{{ K} _i} _j} _{,t}} = {{\frac{1}{2}}{\left({{{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}} + {{{{{{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}} - {{{2}} {{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _a} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}} + {{{{{2}} {{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}}} + {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}} + {{{2}} {{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{{{2}} {{\alpha}} \cdot {{{{ K} _a} _b}} {{{{ K} _i} _j}} {{{{ \gamma} ^a} ^b}}} - {{{4}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} - {{{4}} {{\alpha}} \cdot {{{{ K} _i} _a}} {{{{ K} _j} _b}} {{{{ \gamma} ^a} ^b}}}} + {{{2}} {{{ \beta} ^a}} {{{{{ K} _i} _j} _{,a}}}} + {{{2}} {{{{ K} _a} _i}} {{{{ \beta} ^a} _{,j}}}} + {{{2}} {{{{ K} _a} _j}} {{{{ \beta} ^a} _{,i}}}} + {{{{{{{{8}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}} - {{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{2}} {{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} - {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}} - {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}\right)}}$
${{ \Theta} _{,t}} = {{\frac{1}{2}}{\left({{-{{{16}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}}}} + {{{{2}} {{{ \Theta} _{,k}}} {{{ \beta} ^k}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{ a} _k}} {{{{ \gamma} ^k} ^a}}}} + {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^c}} {{{{ \gamma} ^j} ^g}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} + {{{{{{4}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^b}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} - {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{{ d} _b} _c} _j} _{,k}}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^g}} {{{{ \gamma} ^e} ^k}} {{{{ \gamma} ^h} ^j}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} - {{{4}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^g}} {{{{ \gamma} ^h} ^k}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{{ d} _j} _d} _e} _{,k}}}} + {{{{2}} {{\alpha}} \cdot {{{{ Z} _a} _{,k}}} {{{{ \gamma} ^k} ^a}}} - {{{4}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^h} ^a}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _k} _g} _h}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _r} _i} _s}}} + {{{{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _s} _i} _r}}} - {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _i} _r} _s}} {{{{{ d} _k} _d} _e}}}} - {{{\alpha}} \cdot {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _l} _f}}}} + {{{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} - {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}}}} + {{{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^m} ^n}}} - {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}}}\right)}}$
${{{ Z} _i} _{,t}} = {{{{{ \beta} ^k}} {{{{ Z} _i} _{,k}}}} + {{{{ Z} _i}} {{{{ \beta} ^k} _{,k}}}} + {{{{{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _l} _i} _{,k}}}} - {{{2}} {{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _k} _b} _c}}}} - {{{\Theta}} \cdot {{\alpha}} \cdot {{{ a} _i}}}} - {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _k} _l} _{,i}}}}} + {{{2}} {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _b} _c}}} + {{{{\alpha}} \cdot {{{ \Theta} _{,i}}}} - {{{{ Z} _i}} {{{{ b} ^k} _k}}}} + {{{{{{ Z} _k}} {{{{ b} ^k} _i}}} - {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _k} _d} _i}}}} - {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _i} _d} _k}}}} + {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _d} _k} _i}}} + {{{{{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^k} ^l}} {{{{{ d} _k} _m} _a}}} - {{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} - {{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{{ S} _i}}}}}$
neglecting shift
${{ \alpha} _{,t}} = {{{{2}} {{\Theta}} \cdot {{f}} {{{\alpha}^{2}}}} + {-{{{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}}}$
${{{{ \gamma} _i} _j} _{,t}} = {{{-2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}$
${{{ a} _k} _{,t}} = {{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f}} {{{ a} _k}}} + {{{2}} {{\Theta}} \cdot {{f'}} \cdot {{{ a} _k}} {{{\alpha}^{2}}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^i} ^a}} {{{{{ d} _k} _a} _b}}} + {{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} + {-{{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}} + {-{{{\alpha}} \cdot {{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} + {-{{{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}} {{{\alpha}^{2}}}}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{-{{{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}}} + {-{{{\alpha}} \cdot {{{ a} _k}} {{{{ K} _i} _j}}}}}$
${{{{ K} _i} _j} _{,t}} = {{{{4}} {{S}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ \gamma} _i} _j}}} + {-{{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _i} _j}}}} + {{{\alpha}} \cdot {{{{ K} _a} _b}} {{{{ K} _i} _j}} {{{{ \gamma} ^a} ^b}}} + {-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _a}} {{{{ K} _j} _b}} {{{{ \gamma} ^a} ^b}}}} + {{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}} + {-{{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}}} + {-{{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}}} + {{{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} + {-{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} + {-{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} + {-{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _a} _i} _j}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} + {-{{{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}}} + {{{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}} + {{{\alpha}} \cdot {{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}}} + {-{{{\alpha}} \cdot {{{ a} _i}} {{{ a} _j}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}} + {-{{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{{{ S} _i} _j}}}} + {-{{{4}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}}}$
${{ \Theta} _{,t}} = {{-{{{\Theta}} \cdot {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}} + {{\frac{1}{2}} {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^m} ^n}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}}}}} + {{{\alpha}} \cdot {{{{ Z} _a} _{,k}}} {{{{ \gamma} ^k} ^a}}} + {-{{{2}} {{\alpha}} \cdot {{{ Z} _a}} {{{{ \gamma} ^h} ^a}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _k} _g} _h}}}} + {-{{{\alpha}} \cdot {{{ Z} _a}} {{{ a} _k}} {{{{ \gamma} ^k} ^a}}}} + {{{\alpha}} \cdot {{{ Z} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} + {-{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^g}} {{{{ \gamma} ^e} ^k}} {{{{ \gamma} ^h} ^j}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} + {-{{{2}} {{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^g}} {{{{ \gamma} ^h} ^k}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{{ d} _j} _d} _e} _{,k}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _i} _r} _s}} {{{{{ d} _k} _d} _e}}}}} + {{\frac{1}{2}} {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _r} _i} _s}}}} + {{\frac{1}{2}} {{{\alpha}} \cdot {{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _s} _i} _r}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _l} _f}}}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^b}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} + {{{2}} {{\alpha}} \cdot {{{{ \gamma} ^h} ^c}} {{{{ \gamma} ^j} ^g}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{{ d} _b} _c} _j} _{,k}}}}} + {-{{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{\rho}}}}}$
${{{ Z} _i} _{,t}} = {{-{{{\Theta}} \cdot {{\alpha}} \cdot {{{ a} _i}}}} + {{{2}} {{\alpha}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _b} _c}}} + {{{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^k} ^l}} {{{{{ d} _k} _m} _a}}} + {-{{{2}} {{\alpha}} \cdot {{{{ K} _l} _i}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _k} _b} _c}}}} + {{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _d} _k} _i}}} + {-{{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _i} _d} _k}}}} + {-{{{\alpha}} \cdot {{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _k} _d} _i}}}} + {-{{{2}} {{\alpha}} \cdot {{{ Z} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} + {{{\alpha}} \cdot {{{ \Theta} _{,i}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _k} _l} _{,i}}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _l} _i} _{,k}}}} + {-{{{8}} {{\alpha}} \cdot {{\pi}} \cdot {{{ S} _i}}}}}$
neglecting source terms
${{ \alpha} _{,t}} = {0}$
${{{{ \gamma} _i} _j} _{,t}} = {0}$
${{{ a} _k} _{,t}} = {{{{2}} {{\alpha}} \cdot {{f}} {{{ \Theta} _{,k}}}} + {-{{{\alpha}} \cdot {{f}} {{{{ \gamma} ^i} ^l}} {{{{{ K} _i} _l} _{,k}}}}}}$
${{{{{ d} _k} _i} _j} _{,t}} = {{{-1}} {{\alpha}} \cdot {{{{{ K} _i} _j} _{,k}}}}$
${{{{ K} _i} _j} _{,t}} = {{{{\alpha}} \cdot {{{{ Z} _i} _{,j}}}} + {{{\alpha}} \cdot {{{{ Z} _j} _{,i}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _i} _{,j}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _b} _j} _{,i}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _a} _i} _j} _{,b}}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^a} ^b}} {{{{{{ d} _i} _a} _b} _{,j}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ a} _i} _{,j}}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{{{ a} _j} _{,i}}}}}}}$
${{ \Theta} _{,t}} = {{{{\alpha}} \cdot {{{{ Z} _a} _{,k}}} {{{{ \gamma} ^k} ^a}}} + {{{\alpha}} \cdot {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^k}} {{{{{{ d} _j} _d} _e} _{,k}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{{ d} _b} _c} _j} _{,k}}}}}}$
${{{ Z} _i} _{,t}} = {{{{\alpha}} \cdot {{{ \Theta} _{,i}}}} + {-{{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _k} _l} _{,i}}}}} + {{{\alpha}} \cdot {{{{ \gamma} ^k} ^l}} {{{{{ K} _l} _i} _{,k}}}}}$
...and those source terms are...
${ \alpha} _{,t}$$ + \dots = $${{f}} {{{\alpha}^{2}}} {{\left({{{{2}} {{\Theta}}} - {{{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}}\right)}}$
${{{ \gamma} _i} _j} _{,t}$$ + \dots = $$-{{{2}} {{\alpha}} \cdot {{{{ K} _i} _j}}}$
${{ a} _k} _{,t}$$ + \dots = $${{\alpha}} \cdot {{\left({{{{2}} {{\Theta}} \cdot {{f}} {{{ a} _k}}} + {{{2}} {{\Theta}} \cdot {{\alpha}} \cdot {{f'}} \cdot {{{ a} _k}}} + {{{{{2}} {{f}} {{{{ K} _i} _l}} {{{{ \gamma} ^b} ^l}} {{{{ \gamma} ^i} ^a}} {{{{{ d} _k} _a} _b}}} - {{{f}} {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}} - {{{\alpha}} \cdot {{f'}} \cdot {{{ a} _k}} {{{{ K} _i} _l}} {{{{ \gamma} ^i} ^l}}}}}\right)}}$
${{{{ d} _k} _i} _j} _{,t}$$ + \dots = $$-{{{\alpha}} \cdot {{{ a} _k}} {{{{ K} _i} _j}}}$
${{{ K} _i} _j} _{,t}$$ + \dots = $${{\alpha}} \cdot {{\left({{{{{4}} {{S}} {{\pi}} \cdot {{{{ \gamma} _i} _j}}} - {{{2}} {{\Theta}} \cdot {{{{ K} _i} _j}}}} + {{{{{{ K} _a} _b}} {{{{ K} _i} _j}} {{{{ \gamma} ^a} ^b}}} - {{{2}} {{{{ K} _i} _a}} {{{{ K} _j} _b}} {{{{ \gamma} ^a} ^b}}}} + {{{{{2}} {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}} - {{{2}} {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}}} - {{{2}} {{{ Z} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}}} + {{{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _i} _a} _j}}} + {{{{{{ \gamma} ^a} ^c}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _a} _b} _c}} {{{{{ d} _j} _a} _i}}} - {{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _d} _i}} {{{{{ d} _j} _b} _c}}}} + {{{{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _a} _i} _j}} {{{{{ d} _c} _b} _d}}} - {{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _i} _a} _j}}}} - {{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _c} _b} _d}} {{{{{ d} _j} _a} _i}}}} + {{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _d} _a} _i}} {{{{{ d} _j} _b} _c}}} + {{{{{{2}} {{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^c} ^d}} {{{{{ d} _i} _a} _d}} {{{{{ d} _j} _b} _c}}} - {{{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _a} _b} _c}} {{{{{ d} _a} _i} _j}}}} - {{{{{ \gamma} ^a} ^b}} {{{{ \gamma} ^a} ^c}} {{{{{ d} _i} _a} _c}} {{{{{ d} _j} _a} _b}}}} - {{{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _b} _i} _j}}}} + {{{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _i} _b} _j}}} + {{{{{{{ a} _a}} {{{{ \gamma} ^a} ^b}} {{{{{ d} _j} _b} _i}}} - {{{{ a} _i}} {{{ a} _j}}}} - {{{8}} {{\pi}} \cdot {{{{ S} _i} _j}}}} - {{{4}} {{\pi}} \cdot {{\rho}} \cdot {{{{ \gamma} _i} _j}}}}}\right)}}$
${ \Theta} _{,t}$$ + \dots = $${\frac{1}{2}} {{{\alpha}} \cdot {{\left({{-{{{2}} {{\Theta}} \cdot {{{{ K} _k} _l}} {{{{ \gamma} ^k} ^l}}}} + {{{{{{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^m} ^n}}} - {{{{{ K} _k} _l}} {{{{ K} _m} _n}} {{{{ \gamma} ^k} ^m}} {{{{ \gamma} ^l} ^n}}}} - {{{4}} {{{ Z} _a}} {{{{ \gamma} ^h} ^a}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _k} _g} _h}}}} - {{{2}} {{{ Z} _a}} {{{ a} _k}} {{{{ \gamma} ^k} ^a}}}} + {{{{{{2}} {{{ Z} _k}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}}} - {{{4}} {{{{ \gamma} ^d} ^g}} {{{{ \gamma} ^e} ^k}} {{{{ \gamma} ^h} ^j}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} - {{{4}} {{{{ \gamma} ^d} ^j}} {{{{ \gamma} ^e} ^g}} {{{{ \gamma} ^h} ^k}} {{{{{ d} _j} _d} _e}} {{{{{ d} _k} _g} _h}}}} - {{{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _i} _r} _s}} {{{{{ d} _k} _d} _e}}}} + {{{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _r} _i} _s}}} + {{{{{{ \gamma} ^d} ^r}} {{{{ \gamma} ^e} ^s}} {{{{ \gamma} ^k} ^i}} {{{{{ d} _k} _d} _e}} {{{{{ d} _s} _i} _r}}} - {{{{{ \gamma} ^f} ^l}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _l} _f}}}} + {{{4}} {{{{ \gamma} ^h} ^b}} {{{{ \gamma} ^j} ^c}} {{{{ \gamma} ^k} ^g}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} + {{{{4}} {{{{ \gamma} ^h} ^c}} {{{{ \gamma} ^j} ^g}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _b} _c} _j}} {{{{{ d} _k} _g} _h}}} - {{{16}} {{\pi}} \cdot {{\rho}}}}}\right)}}}$
${{ Z} _i} _{,t}$$ + \dots = $${{\alpha}} \cdot {{\left({{-{{{\Theta}} \cdot {{{ a} _i}}}} + {{{2}} {{{{ K} _k} _l}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _i} _b} _c}}} + {{{{{{ K} _l} _i}} {{{{ \gamma} ^a} ^m}} {{{{ \gamma} ^k} ^l}} {{{{{ d} _k} _m} _a}}} - {{{2}} {{{{ K} _l} _i}} {{{{ \gamma} ^c} ^l}} {{{{ \gamma} ^k} ^b}} {{{{{ d} _k} _b} _c}}}} + {{{{{{{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _d} _k} _i}}} - {{{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _i} _d} _k}}}} - {{{{{ K} _l} _r}} {{{{ \gamma} ^k} ^l}} {{{{ \gamma} ^r} ^d}} {{{{{ d} _k} _d} _i}}}} - {{{2}} {{{ Z} _k}} {{{{ K} _l} _i}} {{{{ \gamma} ^k} ^l}}}} - {{{8}} {{\pi}} \cdot {{{ S} _i}}}}}\right)}}$
spelled out
mismatch
${ {K_{xy}}_{,{{t}}}} = {{{{\alpha}} \cdot {{ {Z_y}_{,{{x}}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{ {a_y}_{,{{x}}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{yxx}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{xyy}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yxy}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{yxz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}}$
difference
${-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{yxx}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yxy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{yxz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yyy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}}}$

mismatch
${ {K_{xz}}_{,{{t}}}} = {{{{\alpha}} \cdot {{ {Z_z}_{,{{x}}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{ {a_z}_{,{{x}}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{zxx}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{zxy}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{xzz}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zxz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}}}$
difference
${-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{zxx}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{zxy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zxz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zzz}}_{,{{x}}}}}}}$

${ \alpha_{,{{t}}}} = {0}$
${ {\gamma_{xx}}_{,{{t}}}} = {0}$
${ {\gamma_{xy}}_{,{{t}}}} = {0}$
${ {\gamma_{xz}}_{,{{t}}}} = {0}$
${ {\gamma_{yy}}_{,{{t}}}} = {0}$
${ {\gamma_{yz}}_{,{{t}}}} = {0}$
${ {\gamma_{zz}}_{,{{t}}}} = {0}$
${ {a_x}_{,{{t}}}} = {{-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{f}} {{ {K_{xx}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{f}} {{ {K_{xy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{f}} {{ {K_{xz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{f}} {{ {K_{yy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{f}} {{ {K_{yz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{f}} {{ {K_{zz}}_{,{{x}}}}}}} + {{{2}} {{\alpha}} \cdot {{f}} {{ \Theta_{,{{x}}}}}}}$
${ {a_y}_{,{{t}}}} = {0}$
${ {a_z}_{,{{t}}}} = {0}$
${ {d_{xxx}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{xx}}_{,{{x}}}}}}$
${ {d_{xxy}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{xy}}_{,{{x}}}}}}$
${ {d_{xxz}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{xz}}_{,{{x}}}}}}$
${ {d_{xyy}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{yy}}_{,{{x}}}}}}$
${ {d_{xyz}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{yz}}_{,{{x}}}}}}$
${ {d_{xzz}}_{,{{t}}}} = {{{-1}} {{\alpha}} \cdot {{ {K_{zz}}_{,{{x}}}}}}$
${ {d_{yxx}}_{,{{t}}}} = {0}$
${ {d_{yxy}}_{,{{t}}}} = {0}$
${ {d_{yxz}}_{,{{t}}}} = {0}$
${ {d_{yyy}}_{,{{t}}}} = {0}$
${ {d_{yyz}}_{,{{t}}}} = {0}$
${ {d_{yzz}}_{,{{t}}}} = {0}$
${ {d_{zxx}}_{,{{t}}}} = {0}$
${ {d_{zxy}}_{,{{t}}}} = {0}$
${ {d_{zxz}}_{,{{t}}}} = {0}$
${ {d_{zyy}}_{,{{t}}}} = {0}$
${ {d_{zyz}}_{,{{t}}}} = {0}$
${ {d_{zzz}}_{,{{t}}}} = {0}$
${ {K_{xx}}_{,{{t}}}} = {{{{2}} {{\alpha}} \cdot {{ {Z_x}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{ {a_x}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yxx}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zxx}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{xyy}}_{,{{x}}}}}}} + {{{2}} {{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yxy}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}}} + {{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yxz}}_{,{{x}}}}}} + {{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zxy}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{xzz}}_{,{{x}}}}}}} + {{{2}} {{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zxz}}_{,{{x}}}}}}}$
${ {K_{xy}}_{,{{t}}}} = {{{{\alpha}} \cdot {{ {Z_y}_{,{{x}}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{ {a_y}_{,{{x}}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{xyy}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yyy}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}}$
${ {K_{xz}}_{,{{t}}}} = {{{{\alpha}} \cdot {{ {Z_z}_{,{{x}}}}}} + {-{{\frac{1}{2}} {{{\alpha}} \cdot {{ {a_z}_{,{{x}}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{xzz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zzz}}_{,{{x}}}}}}}$
${ {K_{yy}}_{,{{t}}}} = {{-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{xyy}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yyy}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}}}}$
${ {K_{yz}}_{,{{t}}}} = {{-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}}}$
${ {K_{zz}}_{,{{t}}}} = {{-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {d_{xzz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zzz}}_{,{{x}}}}}}}}$
${ \Theta_{,{{t}}}} = {{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {Z_x}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{xyy}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yxy}}_{,{{x}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yxz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zxy}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{xzz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zxz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {Z_y}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{{\gamma^{xy}}}^{2}}} {{ {d_{xyy}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{{\gamma^{xy}}}^{2}}} {{ {d_{yxy}}_{,{{x}}}}}}} + {{{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{xyz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{yxz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{ {d_{zxy}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {Z_z}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{{\gamma^{xz}}}^{2}}} {{ {d_{xzz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{{\gamma^{xz}}}^{2}}} {{ {d_{zxz}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{yyz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{ {d_{zyy}}_{,{{x}}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{yzz}}_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}} \cdot {{ {d_{zyz}}_{,{{x}}}}}}}}$
${ {Z_x}_{,{{t}}}} = {{{{\alpha}} \cdot {{ \Theta_{,{{x}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {K_{xy}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {K_{xz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{ {K_{yy}}_{,{{x}}}}}}} + {-{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{ {K_{yz}}_{,{{x}}}}}}} + {-{{{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{ {K_{zz}}_{,{{x}}}}}}}}$
${ {Z_y}_{,{{t}}}} = {{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {K_{xy}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {K_{yy}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {K_{yz}}_{,{{x}}}}}}}$
${ {Z_z}_{,{{t}}}} = {{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{ {K_{xz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{ {K_{yz}}_{,{{x}}}}}} + {{{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{ {K_{zz}}_{,{{x}}}}}}}$

as C code:

real tmp1 = Dx.K_ll.xy * gamma_uu.xy;
real tmp2 = Dx.K_ll.xz * gamma_uu.xz;
real tmp3 = Dx.K_ll.yz * gamma_uu.yz;
real tmp4 = Dx.K_ll.zz * gamma_uu.zz;
real tmp6 = 2. * tmp3;
real tmp8 = Dx.K_ll.yy * gamma_uu.yy;
real tmp107 = gamma_uu.xx * gamma_uu.yy;
real tmp108 = gamma_uu.xy * gamma_uu.xy;
real tmp111 = gamma_uu.xx * gamma_uu.yz;
real tmp113 = gamma_uu.xy * gamma_uu.xz;
real tmp117 = gamma_uu.xx * gamma_uu.zz;
real tmp118 = gamma_uu.xz * gamma_uu.xz;
real tmp129 = gamma_uu.xy * gamma_uu.yz;
real tmp130 = gamma_uu.xz * gamma_uu.yy;
real tmp133 = gamma_uu.xy * gamma_uu.zz;
real tmp134 = gamma_uu.xz * gamma_uu.yz;
F.alpha = 0.;
F.gamma_ll.xx = 0.;
F.gamma_ll.xy = 0.;
F.gamma_ll.xz = 0.;
F.gamma_ll.yy = 0.;
F.gamma_ll.yz = 0.;
F.gamma_ll.zz = 0.;
F.a_l.x = f_alpha * (tmp8 + tmp6 + tmp4 - 2. * Dx.Theta + 2. * tmp2 + 2. * tmp1 + Dx.K_ll.xx * gamma_uu.xx);
F.a_l.y = 0.;
F.a_l.z = 0.;
F.d_lll.x.xx = Dx.K_ll.xx * alpha;
F.d_lll.x.xy = Dx.K_ll.xy * alpha;
F.d_lll.x.xz = Dx.K_ll.xz * alpha;
F.d_lll.x.yy = Dx.K_ll.yy * alpha;
F.d_lll.x.yz = Dx.K_ll.yz * alpha;
F.d_lll.x.zz = Dx.K_ll.zz * alpha;
F.d_lll.y.xx = 0.;
F.d_lll.y.xy = 0.;
F.d_lll.y.xz = 0.;
F.d_lll.y.yy = 0.;
F.d_lll.y.yz = 0.;
F.d_lll.y.zz = 0.;
F.d_lll.z.xx = 0.;
F.d_lll.z.xy = 0.;
F.d_lll.z.xz = 0.;
F.d_lll.z.yy = 0.;
F.d_lll.z.yz = 0.;
F.d_lll.z.zz = 0.;
F.K_ll.xx = alpha * (Dx.a_l.x + Dx.d_lll.x.zz * gamma_uu.zz - Dx.d_lll.y.xx * gamma_uu.xy - 2. * Dx.d_lll.y.xy * gamma_uu.yy - 2. * Dx.d_lll.y.xz * gamma_uu.yz - Dx.d_lll.z.xx * gamma_uu.xz - 2. * Dx.d_lll.z.xy * gamma_uu.yz - 2. * Dx.d_lll.z.xz * gamma_uu.zz + 2. * Dx.d_lll.x.yz * gamma_uu.yz + Dx.d_lll.x.yy * gamma_uu.yy + -2. * Dx.Z_l.x);
F.K_ll.xy = (alpha * (Dx.a_l.y - 2. * Dx.d_lll.x.yy * gamma_uu.xy - 2. * Dx.d_lll.x.yz * gamma_uu.xz - 2. * Dx.d_lll.y.yy * gamma_uu.yy - 2. * Dx.d_lll.y.yz * gamma_uu.yz - 2. * Dx.d_lll.z.yy * gamma_uu.yz - 2. * Dx.d_lll.z.yz * gamma_uu.zz + -2. * Dx.Z_l.y)) / 2.;
F.K_ll.xz = (alpha * (Dx.a_l.z - 2. * Dx.d_lll.x.yz * gamma_uu.xy - 2. * Dx.d_lll.x.zz * gamma_uu.xz - 2. * Dx.d_lll.y.yz * gamma_uu.yy - 2. * Dx.d_lll.y.zz * gamma_uu.yz - 2. * Dx.d_lll.z.yz * gamma_uu.yz - 2. * Dx.d_lll.z.zz * gamma_uu.zz + -2. * Dx.Z_l.z)) / 2.;
F.K_ll.yy = alpha * (Dx.d_lll.z.yy * gamma_uu.xz + Dx.d_lll.y.yy * gamma_uu.xy + Dx.d_lll.x.yy * gamma_uu.xx);
F.K_ll.yz = alpha * (Dx.d_lll.z.yz * gamma_uu.xz + Dx.d_lll.y.yz * gamma_uu.xy + Dx.d_lll.x.yz * gamma_uu.xx);
F.K_ll.zz = alpha * (Dx.d_lll.z.zz * gamma_uu.xz + Dx.d_lll.y.zz * gamma_uu.xy + Dx.d_lll.x.zz * gamma_uu.xx);
F.Theta = alpha * (Dx.d_lll.z.yz * tmp134 + Dx.d_lll.z.yy * tmp130 - Dx.d_lll.z.yz * tmp133 + Dx.d_lll.z.xz * tmp118 - Dx.d_lll.z.yy * tmp129 + Dx.d_lll.z.xy * tmp113 - Dx.d_lll.z.xz * tmp117 + Dx.d_lll.y.zz * tmp133 - Dx.d_lll.y.zz * tmp134 - Dx.d_lll.z.xy * tmp111 + Dx.d_lll.y.yz * tmp129 - Dx.d_lll.y.yz * tmp130 + Dx.d_lll.y.xz * tmp113 + Dx.d_lll.y.xy * tmp108 - Dx.d_lll.y.xz * tmp111 + Dx.d_lll.x.zz * tmp117 - Dx.d_lll.x.zz * tmp118 - Dx.d_lll.y.xy * tmp107 + 2. * Dx.d_lll.x.yz * tmp111 - 2. * Dx.d_lll.x.yz * tmp113 + Dx.d_lll.x.yy * tmp107 - Dx.d_lll.x.yy * tmp108 + -Dx.Z_l.x * gamma_uu.xx - Dx.Z_l.y * gamma_uu.xy - Dx.Z_l.z * gamma_uu.xz);
F.Z_l.x = alpha * (tmp1 + tmp2 + tmp8 + tmp6 + tmp4 - Dx.Theta);
F.Z_l.y = -alpha * (Dx.K_ll.yz * gamma_uu.xz + Dx.K_ll.yy * gamma_uu.xy + Dx.K_ll.xy * gamma_uu.xx);
F.Z_l.z = -alpha * (Dx.K_ll.zz * gamma_uu.xz + Dx.K_ll.yz * gamma_uu.xy + Dx.K_ll.xz * gamma_uu.xx);

${{\left[ \begin{matrix} \alpha_{,{{t}}} \\ {\gamma_{xx}}_{,{{t}}} \\ {\gamma_{xy}}_{,{{t}}} \\ {\gamma_{xz}}_{,{{t}}} \\ {\gamma_{yy}}_{,{{t}}} \\ {\gamma_{yz}}_{,{{t}}} \\ {\gamma_{zz}}_{,{{t}}} \\ {a_x}_{,{{t}}} \\ {a_y}_{,{{t}}} \\ {a_z}_{,{{t}}} \\ {d_{xxx}}_{,{{t}}} \\ {d_{xxy}}_{,{{t}}} \\ {d_{xxz}}_{,{{t}}} \\ {d_{xyy}}_{,{{t}}} \\ {d_{xyz}}_{,{{t}}} \\ {d_{xzz}}_{,{{t}}} \\ {d_{yxx}}_{,{{t}}} \\ {d_{yxy}}_{,{{t}}} \\ {d_{yxz}}_{,{{t}}} \\ {d_{yyy}}_{,{{t}}} \\ {d_{yyz}}_{,{{t}}} \\ {d_{yzz}}_{,{{t}}} \\ {d_{zxx}}_{,{{t}}} \\ {d_{zxy}}_{,{{t}}} \\ {d_{zxz}}_{,{{t}}} \\ {d_{zyy}}_{,{{t}}} \\ {d_{zyz}}_{,{{t}}} \\ {d_{zzz}}_{,{{t}}} \\ {K_{xx}}_{,{{t}}} \\ {K_{xy}}_{,{{t}}} \\ {K_{xz}}_{,{{t}}} \\ {K_{yy}}_{,{{t}}} \\ {K_{yz}}_{,{{t}}} \\ {K_{zz}}_{,{{t}}} \\ \Theta_{,{{t}}} \\ {Z_x}_{,{{t}}} \\ {Z_y}_{,{{t}}} \\ {Z_z}_{,{{t}}}\end{matrix} \right]} + { {\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{f}} & {{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{f}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{f}} & -{{{2}} {{\alpha}} \cdot {{f}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{yy}}}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{2}} {{\alpha}}} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{2}} {\alpha} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\alpha} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{2}} {\alpha} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\alpha} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}\right)}} & {{2}} {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}} - {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}\right)}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & {{\alpha}} \cdot {{{\gamma^{xz}}}} & {{\alpha}} \cdot {{{\gamma^{yy}}}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} & -{\alpha} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0\end{matrix} \right]} {\left[ \begin{matrix} \alpha_{,{{x}}} \\ {\gamma_{xx}}_{,{{x}}} \\ {\gamma_{xy}}_{,{{x}}} \\ {\gamma_{xz}}_{,{{x}}} \\ {\gamma_{yy}}_{,{{x}}} \\ {\gamma_{yz}}_{,{{x}}} \\ {\gamma_{zz}}_{,{{x}}} \\ {a_x}_{,{{x}}} \\ {a_y}_{,{{x}}} \\ {a_z}_{,{{x}}} \\ {d_{xxx}}_{,{{x}}} \\ {d_{xxy}}_{,{{x}}} \\ {d_{xxz}}_{,{{x}}} \\ {d_{xyy}}_{,{{x}}} \\ {d_{xyz}}_{,{{x}}} \\ {d_{xzz}}_{,{{x}}} \\ {d_{yxx}}_{,{{x}}} \\ {d_{yxy}}_{,{{x}}} \\ {d_{yxz}}_{,{{x}}} \\ {d_{yyy}}_{,{{x}}} \\ {d_{yyz}}_{,{{x}}} \\ {d_{yzz}}_{,{{x}}} \\ {d_{zxx}}_{,{{x}}} \\ {d_{zxy}}_{,{{x}}} \\ {d_{zxz}}_{,{{x}}} \\ {d_{zyy}}_{,{{x}}} \\ {d_{zyz}}_{,{{x}}} \\ {d_{zzz}}_{,{{x}}} \\ {K_{xx}}_{,{{x}}} \\ {K_{xy}}_{,{{x}}} \\ {K_{xz}}_{,{{x}}} \\ {K_{yy}}_{,{{x}}} \\ {K_{yz}}_{,{{x}}} \\ {K_{zz}}_{,{{x}}} \\ \Theta_{,{{x}}} \\ {Z_x}_{,{{x}}} \\ {Z_y}_{,{{x}}} \\ {Z_z}_{,{{x}}}\end{matrix} \right]}}} = {\left[ \begin{matrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0\end{matrix} \right]}$
characteristic polynomial:
${{{\lambda}^{24}}} {{\left({{{{15}} {{{\alpha}^{4}}} {{{{\gamma^{xx}}}^{2}}} {{{\lambda}^{10}}}} + {{{{{\alpha}^{12}}} {{{{\gamma^{xx}}}^{6}}} {{{\lambda}^{2}}}} - {{{6}} {{{\alpha}^{10}}} {{{{\gamma^{xx}}}^{5}}} {{{\lambda}^{4}}}}} + {{{{{{15}} {{{\alpha}^{8}}} {{{{\gamma^{xx}}}^{4}}} {{{\lambda}^{6}}}} - {{{20}} {{{\alpha}^{6}}} {{{{\gamma^{xx}}}^{3}}} {{{\lambda}^{8}}}}} - {{{6}} {{{\gamma^{xx}}}} \cdot {{{\alpha}^{2}}} {{{\lambda}^{12}}}}} - {{{{\gamma^{xx}}}} \cdot {{f}} {{{\alpha}^{2}}} {{{\lambda}^{12}}}}} + {{{{\lambda}^{14}} - {{{15}} {{f}} {{{\alpha}^{10}}} {{{{\gamma^{xx}}}^{5}}} {{{\lambda}^{4}}}}} - {{{15}} {{f}} {{{\alpha}^{6}}} {{{{\gamma^{xx}}}^{3}}} {{{\lambda}^{8}}}}} + {{{6}} {{f}} {{{\alpha}^{4}}} {{{{\gamma^{xx}}}^{2}}} {{{\lambda}^{10}}}} + {{{6}} {{f}} {{{\alpha}^{12}}} {{{{\gamma^{xx}}}^{6}}} {{{\lambda}^{2}}}} + {{{{20}} {{f}} {{{\alpha}^{8}}} {{{{\gamma^{xx}}}^{4}}} {{{\lambda}^{6}}}} - {{{f}} {{{\alpha}^{14}}} {{{{\gamma^{xx}}}^{7}}}}}}\right)}}$
simplified...
${{{\lambda}^{24}}} {{\left({{{{15}} {{{\alpha}^{4}}} {{{{\gamma^{xx}}}^{2}}} {{{\lambda}^{10}}}} + {{{{{15}} {{{\alpha}^{8}}} {{{{\gamma^{xx}}}^{4}}} {{{\lambda}^{6}}}} - {{{20}} {{{\alpha}^{6}}} {{{{\gamma^{xx}}}^{3}}} {{{\lambda}^{8}}}}} - {{{6}} {{{\alpha}^{10}}} {{{{\gamma^{xx}}}^{5}}} {{{\lambda}^{4}}}}} + {{{{{{\alpha}^{12}}} {{{{\gamma^{xx}}}^{6}}} {{{\lambda}^{2}}}} - {{{6}} {{{\gamma^{xx}}}} \cdot {{{\alpha}^{2}}} {{{\lambda}^{12}}}}} - {{{{\gamma^{xx}}}} \cdot {{f}} {{{\alpha}^{2}}} {{{\lambda}^{12}}}}} + {{\lambda}^{14}} + {{{6}} {{f}} {{{\alpha}^{12}}} {{{{\gamma^{xx}}}^{6}}} {{{\lambda}^{2}}}} + {{{20}} {{f}} {{{\alpha}^{8}}} {{{{\gamma^{xx}}}^{4}}} {{{\lambda}^{6}}}} + {{{{{{6}} {{f}} {{{\alpha}^{4}}} {{{{\gamma^{xx}}}^{2}}} {{{\lambda}^{10}}}} - {{{15}} {{f}} {{{\alpha}^{10}}} {{{{\gamma^{xx}}}^{5}}} {{{\lambda}^{4}}}}} - {{{15}} {{f}} {{{\alpha}^{6}}} {{{{\gamma^{xx}}}^{3}}} {{{\lambda}^{8}}}}} - {{{f}} {{{\alpha}^{14}}} {{{{\gamma^{xx}}}^{7}}}}}}\right)}}$
simplified:
$\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{xy}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{xz}}}} \cdot {{f}} & {{\alpha}} \cdot {{{\gamma^{yy}}}} \cdot {{f}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} \cdot {{f}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} \cdot {{f}} & -{{{2}} {{\alpha}} \cdot {{f}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & \alpha & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{yy}}}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{2}} {{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{2}} {{\alpha}}} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{2}} {\alpha} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\alpha} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{2}} {\alpha} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{yz}}}}} & -{{{\alpha}} \cdot {{{\gamma^{zz}}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\alpha} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}\right)}} & {{2}} {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}} - {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}\right)}} & 0 & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}}\right)}} & {{\alpha}} \cdot {{\left({{-{{{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}\right)}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {{\alpha}} \cdot {{{\gamma^{xy}}}} & {{\alpha}} \cdot {{{\gamma^{xz}}}} & {{\alpha}} \cdot {{{\gamma^{yy}}}} & {{2}} {{\alpha}} \cdot {{{\gamma^{yz}}}} & {{\alpha}} \cdot {{{\gamma^{zz}}}} & -{\alpha} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & -{{{\alpha}} \cdot {{{\gamma^{xy}}}}} & -{{{\alpha}} \cdot {{{\gamma^{xz}}}}} & 0 & 0 & 0 & 0\end{matrix} \right]$
$\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & \frac{{\gamma^{yy}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & \frac{{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{2}} {{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} - {{{{\gamma^{yz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}}\right)}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{-{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}}} + {{{2}} {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{2}} {{{\gamma^{yy}}}}}{{{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2}{\alpha} & 0 & \frac{{{2}} {{{\gamma^{xy}}}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & \frac{{{2}} {{{\gamma^{xz}}}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2}{\alpha} & 0 & \frac{{{2}} {{{\gamma^{xy}}}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & \frac{{{2}} {{{\gamma^{xz}}}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\alpha}} \cdot {{{\gamma^{xx}}}}} & \frac{{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}{{{\alpha}} \cdot {{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{1}{{{\alpha}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\frac{1}{{{2}} {{\alpha}} \cdot {{f}}}} & 0 & 0 & \frac{{\gamma^{xx}}}{{{2}} {{\alpha}}} & {\frac{1}{\alpha}} {{\gamma^{xy}}} & {\frac{1}{\alpha}} {{\gamma^{xz}}} & \frac{{\gamma^{yy}}}{{{2}} {{\alpha}}} & {\frac{1}{\alpha}} {{\gamma^{yz}}} & \frac{{\gamma^{zz}}}{{{2}} {{\alpha}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 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& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\frac{1}{{{2}} {{f}}}} & 0 & 0 & {\frac{1}{2}} {{\gamma^{xx}}} & 0 & 0 & -{{\frac{1}{2}} {{\gamma^{yy}}}} & -{{\gamma^{yz}}} & -{{\frac{1}{2}} {{\gamma^{zz}}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\gamma^{xx}} & 0 & {\gamma^{xy}} & {\gamma^{xz}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\gamma^{xx}} & 0 & {\gamma^{xy}} & {\gamma^{xz}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{matrix} \right]$
$\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{\gamma^{xy}}} & 0 & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & {\frac{1}{{\gamma^{xx}}}} {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}}} & \frac{{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{{\gamma^{yy}}}^{2}}}}} + {{{{2}} {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{{\gamma^{yz}}}} \cdot {{{{\gamma^{xy}}}^{3}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{-{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{3}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}} - {{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{2}} {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & -{{\gamma^{xz}}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{2}} {{\left({{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}} - {{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\left({{-{{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} + {{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}}} + {{{{2}} {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}}} - {{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{2}} {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\frac{{{2}} {{{{\gamma^{xy}}}^{2}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{2}} {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{2}} {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{2} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{2} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}} & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}} & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}} & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & \frac{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & {\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}} & \frac{{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{2}} {{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & 0 & \frac{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}} + {{{2}} {{{\gamma^{xy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{\frac{{\gamma^{xx}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{xy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{xz}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 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eigenvalue: 0
eigenvector:
$\left[ \begin{matrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\gamma^{xy}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & -{{\frac{1}{{\gamma^{xx}}}} {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}}}} & \frac{{{2}} {{\left({{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{{\gamma^{yy}}}^{2}}}} - {{{2}} {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{{\gamma^{yz}}}} \cdot {{{{\gamma^{xy}}}^{3}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{3}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}}} + {{{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{yz}}}}} - {{{2}} {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & {\gamma^{xz}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{2}} {{\left({{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}} + {{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\left({{{{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} - {{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}} - {{{2}} {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{{\gamma^{zz}}}}} + {{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{2}} {{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{2}} {{{{\gamma^{xy}}}^{2}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{2}} {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}} & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & 0 & 0 & 0 & 0 & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}} & {\frac{1}{{\gamma^{xx}}}} {{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}} & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}}} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & 0 & 0 & 0 & 0 & 0 & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}}} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} - {{{2}} {{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & 0 & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{zz}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yz}}}}} - {{{2}} {{{\gamma^{xy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{\gamma^{xx}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xz}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{matrix} \right]$
eigenvalue: ${-{\alpha}} {{\sqrt{{\gamma^{xx}}}}}$
eigenvector:
$\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{{{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} - {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{f}}}}\right)}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}} & \frac{{{{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}} - {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xz}}}^{2}}}}} - {{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{{\gamma^{zz}}}} \cdot {{f}} {{{{\gamma^{xy}}}^{2}}}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{1} - {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{2}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} + {{{2}} {{f}} {{{{\gamma^{xy}}}^{2}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{{{\gamma^{xy}}}^{2}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}}\right)}}} & \frac{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} \\ \frac{{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} - {{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & \frac{{\gamma^{xy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{yy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} \\ \frac{{\gamma^{xy}}}{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}} & \frac{{\gamma^{xz}}}{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}} & 0 & 0 & 0 & -{\frac{1}{{\gamma^{xx}}}} \\ \frac{{{2}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{{{\gamma^{xz}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{\sqrt{{\gamma^{xx}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & -{\frac{{\gamma^{xx}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{xy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{xz}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} \\ -{\frac{1}{\sqrt{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & -{\frac{1}{\sqrt{{\gamma^{xx}}}}} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \frac{{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} + {{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{f}}}}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xx}}}} \cdot {{\left({{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xz}}}^{2}}}} + {{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{{\gamma^{zz}}}} \cdot {{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{{{{{\gamma^{xy}}}^{2}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} & \frac{{{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{{{{2}} {{{{\gamma^{xy}}}^{2}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{2}} {{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{1} - {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{1} - {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} \\ \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}} + {{{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{\gamma^{xy}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{yy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} \\ -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}}} & 0 & 0 & 0 & \frac{1}{\sqrt{{\gamma^{xx}}}} \\ \frac{{{2}} {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & -{\frac{{\gamma^{xx}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}}} & \frac{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}}} \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1\end{matrix} \right]$
eigenvalue: ${{\alpha}} \cdot {{\sqrt{{\gamma^{xx}}}}}$
eigenvector:
$\left[ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \frac{{{2}} {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} + {{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{f}}}}}\right)}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}} & \frac{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xz}}}^{2}}}} + {{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{{\gamma^{zz}}}} \cdot {{f}} {{{{\gamma^{xy}}}^{2}}}}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{-{1}} + {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{2}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} + {{{2}} {{f}} {{{{\gamma^{xy}}}^{2}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{{{{{\gamma^{xy}}}^{2}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}}\right)}}} & \frac{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} \\ \frac{{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} - {{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{-{{{\gamma^{xy}}}^{2}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} {{\left({{-{{{\gamma^{xy}}}^{2}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{xy}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{\gamma^{yy}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{-{{{\gamma^{xy}}}^{2}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}}} \\ -{\frac{{\gamma^{xy}}}{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} & -{\frac{{\gamma^{xz}}}{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}} & 0 & 0 & 0 & -{\frac{1}{{\gamma^{xx}}}} \\ \frac{{{2}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}}\right)}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{{{\gamma^{xz}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}}\right)}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{\sqrt{{\gamma^{xx}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xx}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xy}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xz}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} \\ \frac{1}{\sqrt{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{\sqrt{{\gamma^{xx}}}} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \frac{{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{\left({{-{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} + {{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}} - {{{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}} \cdot {{f}}}}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xx}}}} \cdot {{\left({{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xz}}}^{2}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xz}}}^{2}}}} + {{{{{\gamma^{zz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}} - {{{{\gamma^{zz}}}} \cdot {{f}} {{{{\gamma^{xy}}}^{2}}}}}}\right)}}}{{-{{{{\gamma^{yy}}}} \cdot {{{{\gamma^{xx}}}^{3}}}}} + {{{{\gamma^{yy}}}} \cdot {{f}} {{{{\gamma^{xx}}}^{3}}}} + {{{{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}} - {{{f}} {{{{\gamma^{xx}}}^{2}}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{yy}}}} \cdot {{\left({{-{1}} + {f}}\right)}}}{{{{{{\gamma^{xy}}}^{2}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} & \frac{{{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{-{{{2}} {{{{\gamma^{xy}}}^{2}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}}} + {{{2}} {{f}} {{{{\gamma^{xy}}}^{2}}}}}\right)}}}{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{\gamma^{xy}}}^{2}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{-{1}} + {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} & \frac{{{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}} {{\left({{-{1}} + {f}}\right)}}}{{{{{\gamma^{xy}}}^{2}} - {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}} + {{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}} \cdot {{f}}} - {{{f}} {{{{\gamma^{xy}}}^{2}}}}}} \\ \frac{{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{xz}}}} \cdot {{{\gamma^{yy}}}}}} - {{{{\gamma^{xz}}}} \cdot {{{{\gamma^{xy}}}^{2}}}}} + {{{2}} {{{\gamma^{xx}}}} \cdot {{{\gamma^{xy}}}} \cdot {{{\gamma^{yz}}}}}}{{{{\gamma^{xx}}}} \cdot {{\left({{-{{{\gamma^{xy}}}^{2}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\left({{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}} - {{{\gamma^{xz}}}^{2}}}\right)}}}{{{{\gamma^{xx}}}} \cdot {{\left({{-{{{\gamma^{xy}}}^{2}}} + {{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}}}\right)}}} & -{\frac{{\gamma^{xy}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{yy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} & -{\frac{{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}} \cdot {{\frac{1}{\sqrt{{\gamma^{xx}}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}}} \\ -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xy}}}} & -{{\frac{1}{{\gamma^{xx}}}} {{\gamma^{xz}}}} & 0 & 0 & 0 & -{\frac{1}{\sqrt{{\gamma^{xx}}}}} \\ \frac{{{2}} {{\left({{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yz}}}}}} + {{{{\gamma^{xy}}}} \cdot {{{\gamma^{xz}}}}}}\right)}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{-{{{{\gamma^{xx}}}} \cdot {{{\gamma^{zz}}}}}} + {{{\gamma^{xz}}}^{2}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{\gamma^{xx}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xx}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xy}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} & \frac{{{{\gamma^{xz}}}} \cdot {{\sqrt{{\gamma^{xx}}}}}}{{{{{\gamma^{xx}}}} \cdot {{{\gamma^{yy}}}}} - {{{\gamma^{xy}}}^{2}}} \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1\end{matrix} \right]$
eigenvalue: ${-{\alpha}} {{\sqrt{{{f}} {{{\gamma^{xx}}}}}}}$