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-- Category: XFreeAlgebra(vl : OrderedSet, R : Ring) : Category
++ Author: Michel Petitot petitot@lifl.fr -- ++ Date Created: 91 -- should be enough to impl TensorAlgebra(R-Module), R comm. ? -- see also SandBoxFreeProduct by B.P.
B:=OrderedVariableList [b[i] for i in 1..5]
 (1)
Type: Type
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R:=Expression Integer
 (2)
Type: Type
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X:=XDistributedPolynomial(B,R)
 (3)
Type: Type
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b:=[a::X for a in enumerate()$B]  (4) Type: List(XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))) fricas t0:=0$X
 (5)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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t1:=1\$X
 (6)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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t2:=b.1*b.2
 (7)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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t3:=b.3*t2 - t2*b.3
 (8)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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vl:=varList t3
 (9)
Type: List(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]))
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leadingMonomial t3
 (10)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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reductum t3
 (11)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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degree t3
 (12)
Type: PositiveInteger?
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t4:=x*t3+y^2*t2+z^3*t1
 (13)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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degree t4
 (14)
Type: PositiveInteger?
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leadingMonomial t4
 (15)
Type: XDistributedPolynomial(OrderedVariableList([b[1],b[2],b[3],b[4],b[5]]),Expression(Integer))
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degree t4
 (16)
Type: PositiveInteger?
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leadingCoefficient t4
 (17)
Type: Expression(Integer)
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coefficients t4
 (18)
Type: List(Expression(Integer))
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X has XFreeAlgebra(B,R)
 (19)
Type: Boolean

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