Opened 2 years ago
Last modified 2 years ago
#24808 new defect
Equality in quotient of a free algebra is broken
Reported by: | tmonteil | Owned by: | |
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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: |
Description (last modified by )
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
See also:
sage: R.<x,y,z> = 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
Change History (4)
comment:1 Changed 2 years ago by
comment:2 Changed 2 years ago by
I don't know about simplification, i did not dig into the code of FreeAlgebra
. Sometimes Sage is lazy and shows simplified result only when it knows it already, so that representation does not cost possibly useless computation, e.g.
sage: a = sqrt(QQbar(3))^2 sage: a 3.000000000000000? sage: a == 3 True sage: a 3
comment:3 Changed 2 years ago by
- Cc alec.edgington added
comment:4 Changed 2 years ago by
- Cc tscrim SimonKing added
- Description modified (diff)
- Keywords mathexp2018 added
This bug just reappeared at mathexp2018:
sage: R.<x,y,z> = 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
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Is this just a bug with equality, or is it a bug with elements of quotient algebras in general? I would hope that either
xbar * ybar
orybar * xbar
would be simplified, but neither is:As you might expect,
xbar * ybar + ybar * xbar
does not simplify to 0, either.