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SandBoxTensorPower

Edit detail for SandBoxTensorPower revision 1 of 1

	1
Editor: pagani Time: 2020/01/30 18:28:27 GMT+0
Note:

changed:
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\begin{axiom}
n:=5000  -- whatever PI

B:=OrderedVariableList [e[i] for i in 1..3]
e:=enumerate()$B

--List(Symbol) has OrderedSet
B has OrderedSet

R:=Expression Integer
R has CommutativeRing

M:=FreeModule(R, B)

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

t1:=tensor([e.1,e.2,e.3,e.1,e.2])$TP
t2:=tensor([e.1,e.2,e.3,e.1])$TP
t3:=tensor([e.1,e.2,e.3,e.2])$TP
t4:=tensor([e.1,e.2,e.3])$TP

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

support T
numberOfMonomials T
leadingTerm T
leadingCoefficient T
reductum T
\end{axiom}

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

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

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

(5)

Type: Type

fricas

R has CommutativeRing

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

(6)

Type: Boolean

fricas

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

fricas

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

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?

fricas

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))

fricas

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]])))