#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 tscrim):
I think what we really should be checking is if it has positive even
characteristic (see the ZZ/4 example in the patch). For example doing
something like
{{{#!python
def is_alternating(self):
if not self.is_skew_symmetric():
return False
c = self.base_ring().characteristic()
return c != 0 or c % 2 != 0 \ # If past here, we have pos. even char.
or all(self.get_unsafe(i,i) == 0 for i in range(self._ncols))
}}}
I do agree that `is_skew_symmetric()` should be the "main" method, also
because it is a larger class of matrices in positive even characteristic.
However, I don't see a way to speed up `is_skew_symmetric()` for the mod
case, so I'm happy with the two ([more] optimized) implementations.
--
Ticket URL: <http://trac.sagemath.org/ticket/15245#comment:22>
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