univariate polynomial _xgcd only over fields

[saraedum]

sage.rings.polynomial.polynomial_element.Polynomial provides an implementation for _xgcd. This implementation is not correct for polynomials over arbitrary rings. Therefore it should be moved to sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_field.

The way it currently is, doesn't cause any bugs (except for one which already has a stopgap warning) because only elements of a PID call the _xgcd method.

---

Apply: attachment: trac_13438_header.patch​

Component: basic arithmetic

Keywords: gcd, xgcd, beginner sd51

Author: Julian Rueth

Reviewer: Travis Scrimshaw, Michiel Kosters

Merged: sage-5.12.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13438

[saraedum]

Changed keywords from xgcd to gcd, xgcd

[saraedum]

Author: Julian Rueth

[saraedum]

Dependencies: #13439

[saraedum]

Changed dependencies from #13439 to none

[saraedum]

Attachment: trac_13438.patch.gz

[tscrim]

comment:8

Two minor things I'd like to see changed:

• The INPUT: bullet is indented one to many times
• Change the OUTPUT: to

Polynomials ``g``, ``u``, and ``v`` such that ``g = u * self + v * other``. 

Thanks.

[sagetrac-mkosters]

comment:9

Attachment: trac_13438_beta.patch.gz

Beta patch should replace original patch. Original patch fails due to intermediate changes in sage (as of 5.10). Beta patch also includes tscrim's suggested doc changes.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:10

The patch is missing the header information. You'll need to run

sage -hg qrefresh -e
sage -hg export trac_13438_beta.patch > path/to/sage/devel/sage/.hg/patches/trac_13438_beta.patch

(or save it to wherever you'd like to upload the patch from). You should also add yourself as a reviewer of the patch with your real name.

Thanks,

Travis

[sagetrac-mkosters]

comment:11

Attachment: trac_13438_header.patch.gz

The new patch (trac_13438_header.patch​) includes header and commit.

[sagetrac-mkosters]

Changed reviewer from Travis Scrimshaw to Travis Scrimshaw, Michiel Kosters

[tscrim]

comment:12

Looks good to me. Thank you.

For patchbot:

Apply: trac_13438_header.patch​

[mstreng]

Changed keywords from gcd, xgcd to gcd, xgcd, beginner sd51

[jdemeyer]

Merged: sage-5.12.beta2