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: | |
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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

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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