xgcd incorrect for padic polynomials

[saraedum]

xgcd is broken for padics:

sage: R.<x> = Qp(3,3)[]
sage: f = 3*x + 7
sage: g = 5*x + 9
sage: f.xgcd(f*g)[0].is_one()
True

sage: R.<x> = Qp(3)[]
sage: f = 490473657*x + 257392844/729
sage: g = 225227399/59049*x - 8669753175
sage: f.xgcd(f*g)[0].is_one()
True

The algorithm used is the standard Euclidean algorithm which is afaik not correct for inexact fields. Or are my examples somehow incorrect?

Depends on #13630
Depends on #13619
Depends on #13620

Component: padics

Keywords: gcd

Stopgaps: #13537

Branch/Commit: u/saraedum/ticket/13439 @ fb269f6

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/13439

[saraedum]

Description changed:

--- 
+++ 
@@ -14,4 +14,4 @@
 True
 ```
 
-The algorithm used is the standard Euclidean algorithm which is afaik not correct for inexact fields.
+The algorithm used is the standard Euclidean algorithm which is afaik not correct for inexact fields. Or are my examples somehow incorrect?

[saraedum]

comment:1

The only place where the doctests called that xgcd was in the padic L-series. I disabled the calls there until we have a working xgcd for padics.

[saraedum]

Stopgaps: #13537

[saraedum]

comment:2

Replying to @saraedum:

The only place where the doctests called that xgcd was in the padic L-series. I disabled the calls there until we have a working xgcd for padics.

Just found out about stopgaps. A stopgap makes of course much more sense than just removing functionality.

[saraedum]

Dependencies: #13630

[saraedum]

Changed dependencies from #13630 to #13630, #13619

[saraedum]

Changed dependencies from #13630, #13619 to #13630, #13619, #13620

[saraedum]

Attachment: trac_13439.patch.gz

[roed314]

comment:7

This is great. I could never get up the motivation to fix this since I always wanted to fix so many other things about p-adic polynomials first. I'll review it once the prerequisites are finished.