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# Edit detail for SandBoxDemoXFreeAlgebra revision 1 of 1

 1 Editor: pagani Time: 2020/01/30 21:19:46 GMT+0 Note:

changed:
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\begin{axiom}
-- 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. ?

B:=OrderedVariableList [b[i] for i in 1..5]

R:=Expression Integer
X:=XDistributedPolynomial(B,R)

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