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fricas
n:=2

\label{eq1}2(1)
fricas
T:=CartesianTensor(1,n,FRAC POLY INT)

\label{eq2}\hbox{\axiomType{CartesianTensor}\ } (1, 2, \hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Polynomial}\ } (\hbox{\axiomType{Integer}\ })))(2)
Type: Type
fricas
Y:T := unravel concat concat
  [[[script(y,[[i,j],[k]])
    for i in 1..n]
      for j in 1..n]
        for k in 1..n]

\label{eq3}\begin{array}{@{}l}
\displaystyle
\left[{\left[ 
\begin{array}{cc}
{y_{1, \: 1}^{1}}&{y_{2, \: 1}^{1}}
\
{y_{1, \: 2}^{1}}&{y_{2, \: 2}^{1}}
(3)
Type: CartesianTensor(1,2,Fraction(Polynomial(Integer)))
fricas
A:T := unravel(concat concat
  [[[script(a,[[k],[i,j]])
    for k in 1..n]
      for i in 1..n]
        for j in 1..n]
          )

\label{eq4}\begin{array}{@{}l}
\displaystyle
\left[{\left[ 
\begin{array}{cc}
{a_{1}^{1, \: 1}}&{a_{2}^{1, \: 1}}
\
{a_{1}^{2, \: 1}}&{a_{2}^{2, \: 1}}
(4)
Type: CartesianTensor(1,2,Fraction(Polynomial(Integer)))
fricas
YA:=contract(reindex(Y,[1,3,2])*A,2,3)

\label{eq5}\left[ 
\begin{array}{cc}
{{{a_{1}^{2, \: 2}}\ {y_{2, \: 2}^{1}}}+{{a_{1}^{2, \: 1}}\ {y_{2, \: 1}^{1}}}+{{a_{1}^{1, \: 2}}\ {y_{1, \: 2}^{1}}}+{{a_{1}^{1, \: 1}}\ {y_{1, \: 1}^{1}}}}&{{{a_{2}^{2, \: 2}}\ {y_{2, \: 2}^{1}}}+{{a_{2}^{2, \: 1}}\ {y_{2, \: 1}^{1}}}+{{a_{2}^{1, \: 2}}\ {y_{1, \: 2}^{1}}}+{{a_{2}^{1, \: 1}}\ {y_{1, \: 1}^{1}}}}
\
{{{a_{1}^{2, \: 2}}\ {y_{2, \: 2}^{2}}}+{{a_{1}^{2, \: 1}}\ {y_{2, \: 1}^{2}}}+{{a_{1}^{1, \: 2}}\ {y_{1, \: 2}^{2}}}+{{a_{1}^{1, \: 1}}\ {y_{1, \: 1}^{2}}}}&{{{a_{2}^{2, \: 2}}\ {y_{2, \: 2}^{2}}}+{{a_{2}^{2, \: 1}}\ {y_{2, \: 1}^{2}}}+{{a_{2}^{1, \: 2}}\ {y_{1, \: 2}^{2}}}+{{a_{2}^{1, \: 1}}\ {y_{1, \: 1}^{2}}}}
(5)
Type: CartesianTensor(1,2,Fraction(Polynomial(Integer)))
fricas
B:T := unravel concat
  [[script(b,[[i],[j]])
    for i in 1..n]
      for j in 1..n]

\label{eq6}\left[ 
\begin{array}{cc}
{b_{1}^{1}}&{b_{2}^{1}}
\
{b_{1}^{2}}&{b_{2}^{2}}
(6)
Type: CartesianTensor(1,2,Fraction(Polynomial(Integer)))
fricas
YAB:=concat [[YA[i,j]=B[i,j] for i in 1..n] for j in 1..n]

\label{eq7}\begin{array}{@{}l}
\displaystyle
\left[{{{{a_{1}^{2, \: 2}}\ {y_{2, \: 2}^{1}}}+{{a_{1}^{2, \: 1}}\ {y_{2, \: 1}^{1}}}+{{a_{1}^{1, \: 2}}\ {y_{1, \: 2}^{1}}}+{{a_{1}^{1, \: 1}}\ {y_{1, \: 1}^{1}}}}={b_{1}^{1}}}, \right.
\
\
\displaystyle
\left.\: \right.
\
\
\displaystyle
\left.{{{{a_{1}^{2, \: 2}}\ {y_{2, \: 2}^{2}}}+{{a_{1}^{2, \: 1}}\ {y_{2, \: 1}^{2}}}+{{a_{1}^{1, \: 2}}\ {y_{1, \: 2}^{2}}}+{{a_{1}^{1, \: 1}}\ {y_{1, \: 1}^{2}}}}={b_{1}^{2}}}, \right.
\
\
\displaystyle
\left.\: \right.
\
\
\displaystyle
\left.{{{{a_{2}^{2, \: 2}}\ {y_{2, \: 2}^{1}}}+{{a_{2}^{2, \: 1}}\ {y_{2, \: 1}^{1}}}+{{a_{2}^{1, \: 2}}\ {y_{1, \: 2}^{1}}}+{{a_{2}^{1, \: 1}}\ {y_{1, \: 1}^{1}}}}={b_{2}^{1}}}, \right.
\
\
\displaystyle
\left.\: \right.
\
\
\displaystyle
\left.{{{{a_{2}^{2, \: 2}}\ {y_{2, \: 2}^{2}}}+{{a_{2}^{2, \: 1}}\ {y_{2, \: 1}^{2}}}+{{a_{2}^{1, \: 2}}\ {y_{1, \: 2}^{2}}}+{{a_{2}^{1, \: 1}}\ {y_{1, \: 1}^{2}}}}={b_{2}^{2}}}\right] 
(7)
Type: List(Equation(Fraction(Polynomial(Integer))))




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