[with patch, positive review] order function not defined for ideal classes

[cremona]

In 3.1 you can't ask for the order of an ideal class. Example:

sage: K.<w>=QuadraticField(-23)
sage: OK=K.ring_of_integers()
sage: C=OK.class_group()
sage: h=C.order()
sage: P2a,P2b=[P for P,e in (2*OK).factor()]
sage: c=C(P2a); c
Fractional ideal class (2, 1/2*w - 1/2)
sage: c.order()
#boom

This is easily provided:

sage: sage.groups.generic.order_from_multiple(c,c.parent().order(),operation='*')
3

Patch coming up.

[cremona]

The patch implements this, and adds doctests to some other functions. Based on 3.1.1, and all doctests in sage/rings/number_fields pass.

[AlexGhitza]

Looks good and passes doctests. Also, when this gets merged, #1400 should be closed as a duplicate (note btw that John's patch addresses precisely Nick's objection on #1400).

[mabshoff]

Merged in Sage 3.1.2.alpha1

[cremona]

Replying to AlexGhitza:

Looks good and passes doctests. Also, when this gets merged, #1400 should be closed as a duplicate (note btw that John's patch addresses precisely Nick's objection on #1400).

Thanks -- sorry to have opened a new ticket unnecessarily (I did look, honest). In any case this patch is more efficient, and shows how useful the generic algorithms I implemented are!