[with patch, positive review] Inverse modulo an ideal in a relative number field

[davidloeffler]

This adds a few lines to get inverse_mod working in the ring of integers of a relative field.

[davidloeffler]

patch against 4.1.alpha2

[ncalexan]

These doctests don't actually assert that the results are correct. Could you add the few lines verifying that you're really getting a basis and really getting an inverse?

[ncalexan]

Also, I get a doctest failure on sage.math. This could be transient -- this is with a slightly out of date sage build. But there's no way this will work on all architectures, so testing the property will be much better.

sage -t -long devel/sage/sage/rings/number_field/number_field_element.pyx
**********************************************************************
File "/scratch/ncalexan/sage-4.0.2.alpha1/devel/sage-main/sage/rings/number_field/number_field_element.pyx", line 3436:
    sage: OE(b - a).inverse_mod(17*b)
Expected:
    (-25*b + 26)*a + 51*b - 1
Got:
    (26*b - 25)*a - 51*b - 1

[davidloeffler]

apply after previous patch

[davidloeffler]

Good point; I have uploaded a second patch that adjusts the doctests as you suggest.

[ncalexan]

Beautiful.

[mvngu]

David, the patch trac_6458-relative_ideal_inverse_mod.patch doesn't have your username. So I'm committing it in your name. Merged both patches in sage-4.1.1-alpha0. I can't close this ticket because I don't have the privilege to do so. Sorry, folks :-(