Rational(3)%Rational(-1) fails

[haraldschilly]

This is inconsistent

sage: Rational(3)%Rational(-1)
ZeroDivisionError: Inverse does not exist.

but

sage: 3%(-1)
0

Component: basic arithmetic

Author: André Apitzsch

Reviewer: John Cremona

Merged: sage-4.6.2.alpha4

Issue created by migration from https://trac.sagemath.org/ticket/9955

[JohnCremona]

comment:1

This is caused by the following simpler bug:

sage: a=Integer(3)
sage: b=Integer(-1)
sage: a.inverse_mod(b)
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
...

ZeroDivisionError: Inverse does not exist.

which is easy to fix. In sage.rings.integer.Integer.inverse_mod there is special case for modulus n=1 but not for -1. Either ass this special case, or replace n by abs(n).

[JohnCremona]

comment:3

The patch looks right and I tested that it works (but did not yet test the whole library).

BUT you need to add a doctest to show that the bug has been fixed. There's a similar doctest in the same function, so just add something similar.

Then I'll look at it again.

[a-andre]

Attachment: trac_9955.patch.gz

[a-andre]

comment:4

doctest added

[a-andre]

Author: André Apitzsch

[JohnCremona]

Reviewer: John Cremona

[JohnCremona]

comment:5

Replying to @a-andre:

doctest added

Thanks! Positive review.

[jdemeyer]

Merged: sage-4.6.2.alpha4