Opened 7 years ago

Last modified 2 years ago

## #16993 closed defect

# Broken fraction field of rational polynomial ring — at Initial Version

Reported by: | SimonKing | Owned by: | |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |

Component: | commutative algebra | Keywords: | |

Cc: | tscrim, yzh, mkoeppe, etn40ff, slelievre | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

sage: P.<t> = QQ[] sage: p = 4/(-4*t) sage: p # OK, fractions are not automatically reduced 4/(-4*t) sage: p.reduce() sage: p # What the heck... 4/(-4*t) sage: p == -1/t # At least sage gets this right True

So, not only is the fraction not automatically simplified by "obvious" common factors, but also it is not simplified upon request.

Note that the fraction field of an integral polynomial ring works better.

sage: P.<t> = ZZ[] sage: p = 4/(-4*t) sage: p 1/-t

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