Dear friends,
P.<x0, x1, x2, x3, x4, y1, y2,y3> = LaurentPolynomialRing(QQ)
Can we make rich algebraic structure using the above P?
The variables *x0, x1, x2, x3, x4 are commutative *
and *y1, y2,y3 are non commutative.*
if we ask for relation y1*y2 = -y2*y1 it gives
SyntaxError: can't assign to operator.
Can we get something like: sage: P multivariate Laurent polynomial Ring in
x0, x1, x2, x3, x4, y1, y2,y3 over Rational Field, nc→relations: {y1*y2:
-y2*y1,y2*y3:-y3*y2,y1*
y3:-y3*y1,x1*x2:-x2*x1}
For example: Can we extend the below code to above information
sage: A. = FreeAlgebra(QQ, 3)
sage: P. = A.g_algebra(relations={y*x:-x*y}, order = 'lex')
sage: P Noncommutative Multivariate Polynomial Ring in x, y, z over
Rational Field, nc- ˓→relations: {y*x: -x*y}
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