#13439: padic xgcd incorrect
----------------------------+-----------------------------------------------
Reporter: saraedum | Owner: roed
Type: defect | Status: new
Priority: minor | Milestone: sage-5.4
Component: padics | Resolution:
Keywords: gcd | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
----------------------------+-----------------------------------------------
Old description:
> {{{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.
New description:
{{{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?
--
Comment (by 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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13439#comment:1>
Sage <http://www.sagemath.org>
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