Opened 5 years ago

Last modified 4 years ago

#24808 new defect

Equality in quotient of a free algebra is broken — at Initial Version

Reported by: Thierry Monteil Owned by:
Priority: major Milestone: sage-8.2
Component: algebra Keywords: mathexp2018
Cc: Alec Edgington, ​tscrim, ​SimonKing Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

As reported in this ask question:

sage: A.<x,y> = 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

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