MathAction SandBoxTensorPower

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fricas n:=5000

whatever PI

$\label{eq1}5000$

Type: PositiveInteger?

fricas

B:=OrderedVariableList [e[i] for i in 1..3]

$\label{eq2}\hbox{\axiomType{OrderedVariableList}\ } ([ e [ 1 ] , e [ 2 ] , e [ 3 ] ])$

(2)

Type: Type

fricas

e:=enumerate()$B

$\label{eq3}\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]$

(3)

Type: List(OrderedVariableList([e[1],e[2],e[3]]))

fricas

--List(Symbol) has OrderedSet
B has OrderedSet

$\label{eq4} \mbox{\rm true}$

(4)

Type: Boolean

fricas

R:=Expression Integer

$\label{eq5}\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ })$

(5)

Type: Type

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R has CommutativeRing

$\label{eq6} \mbox{\rm true}$

(6)

Type: Boolean

fricas

M:=FreeModule(R, B)

$\label{eq7}\hbox{\axiomType{FreeModule}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ }) , \hbox{\axiomType{OrderedVariableList}\ } ([ e [ 1 ] , e [ 2 ] , e [ 3 ] ]))$

(7)

Type: Type

fricas

TP:=TensorPower(n,R,B,M)

$\label{eq8}\hbox{\axiomType{TensorPower}\ } (5000, \hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ }) , \hbox{\axiomType{OrderedVariableList}\ } ([ e [ 1 ] , e [ 2 ] , e [ 3 ] ]) , \hbox{\axiomType{FreeModule}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ }) , \hbox{\axiomType{OrderedVariableList}\ } ([ e [ 1 ] , e [ 2 ] , e [ 3 ] ])))$

(8)

Type: Type

fricas

t1:=tensor([e.1,e.2,e.3,e.1,e.2])$TP

$\label{eq9}{{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{1}}}\otimes{e_{2}}$

(9)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

fricas

t2:=tensor([e.1,e.2,e.3,e.1])$TP

$\label{eq10}{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{1}}$

(10)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

fricas

t3:=tensor([e.1,e.2,e.3,e.2])$TP

$\label{eq11}{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{2}}$

(11)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

fricas

t4:=tensor([e.1,e.2,e.3])$TP

$\label{eq12}{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}$

(12)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

fricas

T:=x*t1+y^2*t2+z^3*t3-u*t4

$\label{eq13}\begin{array}{@{}l} \displaystyle {x \ {{{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{1}}}\otimes{e_{2}}}}+ \ \ \displaystyle {{{y}^{2}}\ {{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{1}}}}+ \ \ \displaystyle {{{z}^{3}}\ {{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{2}}}}-{u \ {{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}}$

(13)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

fricas

support T

$\label{eq14}\left[{\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}, \:{e_{1}}, \:{e_{2}}\right]}, \:{\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}, \:{e_{1}}\right]}, \:{\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}, \:{e_{2}}\right]}, \:{\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right]$

(14)

Type: List(Vector(OrderedVariableList([e[1],e[2],e[3]])))

fricas

numberOfMonomials T

$\label{eq15}4$

(15)

Type: PositiveInteger?

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leadingTerm T

$\label{eq16}\left[{k ={\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}, \:{e_{1}}, \:{e_{2}}\right]}}, \:{c = x}\right]$

(16)

Type: Record(k: Vector(OrderedVariableList([e[1],e[2],e[3]])),c: Expression(Integer))

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leadingCoefficient T

$\label{eq17}x$

(17)

Type: Expression(Integer)

fricas

reductum T

$\label{eq18}\begin{array}{@{}l} \displaystyle {{{y}^{2}}\ {{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{1}}}}+ \ \ \displaystyle {{{z}^{3}}\ {{{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}\otimes{e_{2}}}}-{u \ {{{e_{1}}\otimes{e_{2}}}\otimes{e_{3}}}}$

(18)

Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]])))

Subject: Be Bold !!

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