#8095: is_primitive of WordMorphism is broken
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Reporter: slabbe | Owner: slabbe
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.3.2
Component: combinatorics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by slabbe):
* cc: slabbe (removed)
* cc: abmasse (added)
* status: new => needs_review
Comment:
I just posted a patch which solves the described problem. The solution
uses the following algorithm:
{{{
ALGORITHM:
Let `m` be the incidence matrix of a endomorphism on a monoid
of `d` letters. The endomorphism is primitive if and only if
there exists `k` such that `1 \leq k \leq (d-1)^2+1` and `m^k`
contains no zero.
}}}
Are we sure this is true? Is there a proof of that somewhere?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8095#comment:2>
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