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fricas
(1) -> R ==> EXPR INT
Type: Void
fricas
e:=[subscript('e, [k]) for k in 1..3]

\label{eq1}\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right](1)
Type: List(Symbol)
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g:=[subscript('g, [k]) for k in 1..4]

\label{eq2}\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right](2)
Type: List(Symbol)
fricas
h:=[superscript('h, [k]) for k in 1..4]

\label{eq3}\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right](3)
Type: List(Symbol)
fricas
B1:=OrderedVariableList e

\label{eq4}\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)(4)
Type: Type
fricas
B2:=OrderedVariableList g

\label{eq5}\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)(5)
Type: Type
fricas
B3:=OrderedVariableList h

\label{eq6}\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)(6)
Type: Type
fricas
M1:=FreeModule(R,B1)

\label{eq7}\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}}\right)(7)
Type: Type
fricas
M2:=FreeModule(R,B2)

\label{eq8}\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)(8)
Type: Type
fricas
M3:=FreeModule(R,B3)

\label{eq9}\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)}}\right)(9)
Type: Type
fricas
M12:=TensorProduct(R,B1,B2,M1,M2)

\label{eq10}\hbox{\axiomType{TensorProduct}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)}}\right)(10)
Type: Type
fricas
M23:=TensorProduct(R,B2,B3,M2,M3)

\label{eq11}\hbox{\axiomType{TensorProduct}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)}}\right)}}\right)(11)
Type: Type
fricas
M123:=TensorProduct(R,Product(B1,B2),B3,M12,M3)

\label{eq12}\hbox{\axiomType{TensorProduct}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{Product}\ } \left({{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)}, \:{\hbox{\axiomType{TensorProduct}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right)}}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)}}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{h^{1}}, \:{h^{2}}, \:{h^{3}}, \:{h^{4}}\right]}\right)}}\right)}}\right)(12)
Type: Type
fricas
v1:=x*(e.1)::M1 - y*(e.3)::M1

\label{eq13}{x \ {e_{1}}}-{y \ {e_{3}}}(13)
Type: FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]))
fricas
v2:=q*(g.2)::M2 + r*(g.4)::M2

\label{eq14}{q \ {g_{2}}}+{r \ {g_{4}}}(14)
Type: FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]]))
fricas
v3:=3*(h.1)::M3 - z*(h.3)::M3

\label{eq15}{3 \ {h^{1}}}-{z \ {h^{3}}}(15)
Type: FreeModule(Expression(Integer),OrderedVariableList([h[;1],h[;2],h[;3],h[;4]]))
fricas
t12:=tensor(v1,v2)$M12

\label{eq16}\begin{array}{@{}l}
\displaystyle
{q \  x \ {{e_{1}}\otimes{g_{2}}}}+{r \  x \ {{e_{1}}\otimes{g_{4}}}}-{q \  y \ {{e_{3}}\otimes{g_{2}}}}- 
\
\
\displaystyle
{r \  y \ {{e_{3}}\otimes{g_{4}}}}
(16)
Type: TensorProduct?(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),OrderedVariableList([g[1],g[2],g[3],g[4]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])),FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]])))
fricas
t23:=tensor(v2,v3)$M23

\label{eq17}\begin{array}{@{}l}
\displaystyle
{3 \  q \ {{g_{2}}\otimes{h^{1}}}}-{q \  z \ {{g_{2}}\otimes{h^{3}}}}+{3 \  r \ {{g_{4}}\otimes{h^{1}}}}- 
\
\
\displaystyle
{r \  z \ {{g_{4}}\otimes{h^{3}}}}
(17)
Type: TensorProduct?(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]]),OrderedVariableList([h[;1],h[;2],h[;3],h[;4]]),FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]])),FreeModule(Expression(Integer),OrderedVariableList([h[;1],h[;2],h[;3],h[;4]])))
fricas
t123:=tensor(t12,v3)$M123

\label{eq18}\begin{array}{@{}l}
\displaystyle
{3 \  q \  x \ {{\left[{e_{1}}, \:{g_{2}}\right]}\otimes{h^{1}}}}-{q \  x \  z \ {{\left[{e_{1}}, \:{g_{2}}\right]}\otimes{h^{3}}}}+ 
\
\
\displaystyle
{3 \  r \  x \ {{\left[{e_{1}}, \:{g_{4}}\right]}\otimes{h^{1}}}}-{r \  x \  z \ {{\left[{e_{1}}, \:{g_{4}}\right]}\otimes{h^{3}}}}- 
\
\
\displaystyle
{3 \  q \  y \ {{\left[{e_{3}}, \:{g_{2}}\right]}\otimes{h^{1}}}}+{q \  y \  z \ {{\left[{e_{3}}, \:{g_{2}}\right]}\otimes{h^{3}}}}- 
\
\
\displaystyle
{3 \  r \  y \ {{\left[{e_{3}}, \:{g_{4}}\right]}\otimes{h^{1}}}}+{r \  y \  z \ {{\left[{e_{3}}, \:{g_{4}}\right]}\otimes{h^{3}}}}
(18)
Type: TensorProduct?(Expression(Integer),Product(OrderedVariableList([e[1],e[2],e[3]]),OrderedVariableList([g[1],g[2],g[3],g[4]])),OrderedVariableList([h[;1],h[;2],h[;3],h[;4]]),TensorProduct?(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),OrderedVariableList([g[1],g[2],g[3],g[4]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])),FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]]))),FreeModule(Expression(Integer),OrderedVariableList([h[;1],h[;2],h[;3],h[;4]])))
fricas
N:=TensorPower(3,R,B2,M2)

\label{eq19}\hbox{\axiomType{TensorPower}\ } \left({3, \:{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}, \:{\hbox{\axiomType{FreeModule}\ } \left({{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{g_{1}}, \:{g_{2}}, \:{g_{3}}, \:{g_{4}}\right]}\right)}}\right)}}\right)(19)
Type: Type
fricas
tt3:=tensor([(g.1)::M2,(g.2)::M2,(g.4)::M2])$N

\label{eq20}{{g_{1}}\otimes{g_{2}}}\otimes{g_{4}}(20)
Type: TensorPower?(3,Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]]),FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3],g[4]])))
fricas
-- 
construct(e.1,g.1)$Product(B1,B2)::M12
Cannot convert the value from type Product(OrderedVariableList([e[1] ,e[2],e[3]]),OrderedVariableList([g[1],g[2],g[3],g[4]])) to TensorProduct(Expression(Integer),OrderedVariableList([e[1],e[2], e[3]]),OrderedVariableList([g[1],g[2],g[3],g[4]]),FreeModule( Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])), FreeModule(Expression(Integer),OrderedVariableList([g[1],g[2],g[3 ],g[4]]))) .

Tensor product of three or more different spaces:

 U\otimes V \otimes W 
where
U=[e_1,e_2,e_3], V=[g_1,\ldots,g_4] 
and
W=[h^1,\ldots,h^4] 
. The problem can be seen in the output of equation (18).

In order to get the output correct how should B12 be set?




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