uniformise the behaviour of gcd for rational numbers

[novoselt]

I got very confused by the first line since I used to use gcd for clearing denominators:

sage: gcd((1, 2/3, 1/6, 1/6))
1
sage: gcd((2/3, 1/6, 1/6))
1/6
sage: gcd((2/3, 1, 1/6, 1/6))
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.rings.rational.Rational, got sage.rings.integer.Integer)
sage: gcd((2/3, 2/2, 1/6, 1/6))
1/6

I'd expect all calls above to return 1/6.

CC: @robertwb @craigcitro @JohnCremona @burcin

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/3214

[sagetrac-mabshoff]

comment:1

This works now:

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| Sage Version 3.2.alpha1, Release Date: 2008-10-26                  |
| Type notebook() for the GUI, and license() for information.        |
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sage: gcd((2/3, 1, 1/6, 1/6))
1/6

Cheers,

Michael

[sagetrac-mabshoff]

comment:2

But the first case is still broken. This might not be coercion related, though.

Cheers,

Michael

[sagetrac-mabshoff]

comment:3

This seems critical enough to elevate its priority. Also CC some people who might be able and willing to fix it :)

Cheers,

Michael

[aghitza]

comment:5

It is indeed not coercion-related. The computation of the gcd is done in a loop, from which one exits as soon as a gcd of 1 is obtained (ignoring the rest of the elements). In the case of elements with denominators (such as rational numbers or rational functions) this gives rise to the wrong answers reported above.

The attached trivial patch fixes this so that correct answers are returned.