#17671: Implement gcd for fraction fields
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Reporter: vdelecroix | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/17671 | d8a03d7fa1dd0e401adbae8e2a16ccbfb1902392
Dependencies: #17673 | Stopgaps:
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Description changed by vdelecroix:
Old description:
> As reported on [https://groups.google.com/forum/#!topic/sage-
> support/AYDqdxy5fTw sage-support], gcd and xgcd disagree on fraction
> fields
> {{{
> sage: gcd(6/1,2/1)
> 2
> sage: xgcd(6/1,2/1)
> (1, 1/6, 0)
> }}}
>
> We implement a `xgcd` for the `QuotientFields` category in order to fix
> that (there was a `gcd` here without a `xgcd`).
New description:
As reported on [https://groups.google.com/forum/#!topic/sage-
support/AYDqdxy5fTw sage-support], gcd and xgcd disagree on fraction
fields
{{{
sage: gcd(6/1,2/1)
2
sage: xgcd(6/1,2/1)
(1, 1/6, 0)
}}}
We implement a `xgcd` for the `QuotientFields` category in order to fix
that (there was a `gcd` here without a `xgcd`). We also check that for PID
the `gcd` and `xgcd` agree by implementing a `_test_gcd_vs_xgcd`. With
that branch
{{{
sage: xgcd(6/1,2/1)
(2, 0, 1)
sage: xgcd(5/2, 3/4)
(1/4, -1/2, 2)
}}}
which is consistent with `gcd`.
QUESTIONS:
1. In the previous implementation of gcd in `sage.categories.fields` there
is a backward compatibility weirdness
{{{
sage: gcd(2.0, 4.0)
2
sage: gcd(2.0, 4.0).parent()
Integer Ring
}}}
For the moment, I propagated this to `lcm` and `xgcd`.
2. There is a method `xgcd` implemented for univariate polynomial over ZZ.
This is not a proper name since it has nothing to do with `gcd` (see
[https://groups.google.com/forum/#!topic/sage-devel/JV8fCPUqTzo this sage-
devel thread])
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17671#comment:4>
Sage <http://www.sagemath.org>
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