Opened 3 years ago

Last modified 3 years ago

## #23260 new defect

# Implement a "small_residue" method on Ideal_1poly_field

Reported by: | nbruin | Owned by: | |
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Priority: | minor | Milestone: | sage-8.1 |

Component: | linear algebra | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

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

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

As this question on ask.sagemath shows, presently we have:

sage: R.<x>=QQ[] sage: M=matrix(2,2,[x,x,0,x]); sage: M.hermite_form() [x x] [0 x]

we see that the pivot column doesn't get further reduced. According to `M._echelon_form_PID`

this would be done if the relevant ideals have a `small_residue`

method.

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The implementation should be something like