id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
24808,Equality in quotient of a free algebra is broken,tmonteil,,"As reported in [https://ask.sagemath.org/question/41219/calculations-in-quotient-of-a-free-algebra/ this ask question]:
{{{
sage: A. = FreeAlgebra(QQbar)
sage: I = A.ideal([x*x - 1, y*y, x*y + y*x])
sage: I
Twosided Ideal (-1 + x^2, y^2, x*y + y*x) of Free Algebra on 2 generators (x, y) over Algebraic Field
sage: H = A.quotient(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)
sage: H.inject_variables()
Defining xbar, ybar
sage: xbar.lift()
x
sage: xbar*xbar
xbar^2
sage: xbar*xbar == 1
False
}}}
See also:
{{{
sage: R. = FreeAlgebra(QQ, 3)
sage: Q = R.quotient(z-x*y)
sage: Q
Quotient of Free Algebra on 3 generators (x, y, z) over Rational Field by the ideal (z - x*y)
sage: Q(x*y) == Q(z)
False
}}}
",defect,new,major,sage-8.2,algebra,,mathexp2018,alec.edgington tscrim SimonKing,,,,N/A,,,,,