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]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
 `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 because only elements of PID call the `_xgcd` method. Nevertheless it should imho be moved.
+The way it currently is, doesn't cause any bugs because only elements of a PID call the `_xgcd` method.

[saraedum]

Author: Julian Rueth

[saraedum]

Dependencies: #13439

[saraedum]

Changed dependencies from #13439 to none

[saraedum]

Attachment: trac_13438.patch.gz

[saraedum]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
 `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 because only elements of a PID call the `_xgcd` method.
+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.

[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.