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fricas
n:=5000
whatever PI
 (1)
Type: PositiveInteger?
fricas
B:=OrderedVariableList [e[i] for i in 1..3]
 (2)
Type: Type
fricas
e:=enumerate()$B  (3) Type: List(OrderedVariableList([e[1],e[2],e[3]])) fricas --List(Symbol) has OrderedSet B has OrderedSet  (4) Type: Boolean fricas R:=Expression Integer  (5) Type: Type fricas R has CommutativeRing  (6) Type: Boolean fricas M:=FreeModule(R, B)  (7) Type: Type fricas TP:=TensorPower(n,R,B,M)  (8) Type: Type fricas t1:=tensor([e.1,e.2,e.3,e.1,e.2])$TP
 (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])$TP  (10) Type: TensorPower?(5000,Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]),FreeModule(Expression(Integer),OrderedVariableList([e[1],e[2],e[3]]))) fricas t3:=tensor([e.1,e.2,e.3,e.2])$TP
 (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
 (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
 (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
 (14)
Type: List(Vector(OrderedVariableList([e[1],e[2],e[3]])))
fricas
numberOfMonomials T
 (15)
Type: PositiveInteger?
fricas
leadingTerm T
 (16)
Type: Record(k: Vector(OrderedVariableList([e[1],e[2],e[3]])),c: Expression(Integer))
fricas
leadingCoefficient T
 (17)
Type: Expression(Integer)
fricas
reductum T
 (18)
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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