#16603: permanental_minor_vector, matching polynomial
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Reporter: pernici | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.4
Component: linear algebra | Resolution:
Keywords: | Merged in:
Authors: Mario Pernici | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pernici/ticket/16603 | 19350a4574f4caa2e0b5ad08f66e51930b647a42
Dependencies: | Stopgaps:
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Comment (by pernici):
Hello Vincent,
> Do you know an adaptation of your method to compute only a specific
permanental minor? (I guess that to compute the k-th permanental minor it
is just enough to ignore the terms t^l^ with l > k)
I adapted the algorithm to compute fastly k-th permanental minor for small
`k`;
testing on `A = matrix(n, k, range(n)` using this algorithm
`A.permanent_minor(k)` is faster for `2 <= k <= n-2
>does your algorithm have a name? I used Butera-Pernici (see the item just
below, it has some importance).
No, it did not have a name.
> Right now, in all methods except matrix.rook_vector, the default choice
for algorithm is Ryser (what was before). Where do you think we should put
yours in first?
In the example above, for n x n matrices in `permanental_minor`
the Ryser algorithm is generally faster for `k=n` (permanent), slightly
faster for
`k=1,n-1`; maybe one could make a default option which uses the Ryser
algorithm in those cases, the new algorithm in the other cases.
> why matrix.rook_vector is only defined for {0,1} matrices... it is well
defined for any matrix, isn't it?
Usually `rook vector` is defined only on {0,1} matrices; I added the
"Godsil" algorithm which
is faster than the "Ryser" algorithm.
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Ticket URL: <http://trac.sagemath.org/ticket/16603#comment:24>
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