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SandBoxTensorPower
last edited 5 years ago by pagani

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fricas (1) -> n:=5000

whatever PI

\label{eq1}5000 (1)

Type: PositiveInteger?

fricas

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

\label{eq2}\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\right]}\right) (2)

Type: Type

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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

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R:=Expression Integer

\label{eq5}\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right) (5)

Type: Type

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R has CommutativeRing

\label{eq6} \mbox{\rm true} (6)

Type: Boolean

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M:=FreeModule(R, B)

\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

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

\label{eq8}\hbox{\axiomType{TensorPower}\ } \left({{5000}, \:{\hbox{\axiomType{Expression}\ } \left({\hbox{\axiomType{Integer}\ }}\right)}, \:{\hbox{\axiomType{OrderedVariableList}\ } \left({\left[{e_{1}}, \:{e_{2}}, \:{e_{3}}\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)}}\right) (8)

Type: Type

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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]])))

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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]])))

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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]])))

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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)

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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]])))