#14666: Test if a weight function is generic for a given matroid
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Reporter: Stefan | Owner: Stefanf
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-7.2
Component: matroid theory | Resolution:
Keywords: matroid, weight | Merged in:
function | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | 059b6d3816eae7412bc5e6570c17888fa2b75678
public/ticket/14666 | Stopgaps:
Dependencies: |
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Comment (by tara):
The algorithm follows from the idea that whenever we apply the greedy
algorithm, we get a maximal basis, and we can get each maximal basis by
using the greedy algorithm. A maximal weighted basis `B` is unique if and
only if for every `e\in E(M)-B`, we have `e` is in the closure of `{b\in
B|w(b)>w(e)}`. In other words, `B` is unique, if when using the greedy
algorithm, we never were able to choose an element of `E(M)-B`.
We don't need an array for `smres` in the weights is None case. I had
originally put both cases in one for loop, until I realized that that was
gross, and I didn't notice, when I changed it, that `smres` is now
pointless in that case.
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Ticket URL: <http://trac.sagemath.org/ticket/14666#comment:16>
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