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SandBoxCoMultiplication

Edit detail for SandBoxCoMultiplication revision 1 of 1

	1
Editor: Bill Page Time: 2011/02/25 15:14:16 GMT-8
Note: 4 equations and 8 unknowns

changed:
-
\begin{axiom}
n:=2
T:=CartesianTensor(1,n,FRAC POLY INT)
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]
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]
          )
YA:=contract(reindex(Y,[1,3,2])*A,2,3)
B:T := unravel concat
  [[script(b,[[i],[j]])
    for i in 1..n]
      for j in 1..n]
YAB:=concat [[YA[i,j]=B[i,j] for i in 1..n] for j in 1..n]
\end{axiom}

fricas

(1) -> n:=2

$\label{eq1}2$

(1)

Type: PositiveInteger?

fricas

T:=CartesianTensor(1,n,FRAC POLY INT)

$\label{eq2}\hbox{\axiomType{CartesianTensor}\ } \left({1, \: 2, \:{\hbox{\axiomType{Fraction}\ } \left({\hbox{\axiomType{Polynomial}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}\right)}}\right)$

(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))))