ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 21 Feb 2018 07:44:18 -0600Calculations in quotient of a free algebrahttps://ask.sagemath.org/question/41219/calculations-in-quotient-of-a-free-algebra/I want to define (the algebra part of) Sweedler's four-dimensional Hopf algebra, which is freely generated by $x,y$ and subject to the relations
$$
x^2 = 1, \qquad y^2 = 0, \qquad x\cdot y = - y\cdot x~ ,
$$
but I don't see how to do it.
I have tried the following:
sage: A.<x,y> = FreeAlgebra(QQbar)
sage: I = A*[x*x - 1, y*y, x*y + y*x]*A
sage: H.<x,y> = A.quo(I)
sage: H
Quotient of Free Algebra on 2 generators (x, y) over Algebraic Field by the ideal (-1 + x^2, y^2, x*y + y*x)
But then I get
sage: H.one() == H(x*x)
False
So is this currently possibly using a different method?
ThanksJo BeWed, 21 Feb 2018 07:44:18 -0600https://ask.sagemath.org/question/41219/