#15245: Pfaffian of a skew-symmetric matrix
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Reporter: darij | Owner:
Type: enhancement | Status:
Priority: major | positive_review
Component: combinatorics | Milestone: sage-5.13
Keywords: matrix, sage-combinat, | Resolution:
pfaffian | Merged in:
Authors: Darij Grinberg | Reviewers: Travis
Report Upstream: N/A | Scrimshaw
Branch: | Work issues:
Dependencies: #14117 | Commit:
| Stopgaps:
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Comment (by nbruin):
Replying to [comment:20 darij]:
> Not sure about it. {{{is_skewsymmetric}}} should be a tad slower than
{{{is_alternating}}} (not seriously so -- it just calls diagonal elements
twice rather than once).
If that matters people can always implement both.
> What we probably cannot do is ask whether the characteristic is not 2;
uh ...
{{{
sage: GF(2).characteristic() !=2
False
sage: ZZ.characteristic() != 2
True
}}}
> if anything, we should ask for 2 to be invertible.
No, that's not the correct check. In ZZ and (ZZ/6ZZ), 2 is not invertible
and yet skew symmetric is the same as alternating.
You could check whether 1+1==0, but that's more expensive.
--
Ticket URL: <http://trac.sagemath.org/ticket/15245#comment:21>
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