#10670: Mobius matrices of posets are integer matrices
-------------------------------------------------+--------------------------
Reporter: chapoton | Owner: hivert
Type: defect | Status:
needs_review
Priority: minor | Milestone:
Component: combinatorics | Keywords: poset,
matrix, Cernay2012
Work_issues: | Upstream: N/A
Reviewer: Florent Hivert, Nicolas M. Thiéry | Author: Frédéric
Chapoton, Florent Hivert
Merged: | Dependencies: #10998
-------------------------------------------------+--------------------------
Changes (by nthiery):
* reviewer: Florent Hivert => Florent Hivert, Nicolas M. Thiéry
Old description:
> I have noticed the following problem.
>
> {{{
> P=Posets.PentagonPoset()
> P.mobius_function_matrix().parent()
> Full MatrixSpace of 5 by 5 sparse matrices over Rational Field
> }}}
> The Mobius function of a poset should really be an '''integer matrix'''.
> This can be achieved by using change_ring :
>
> {{{
> P.mobius_function_matrix().change_ring(ZZ).parent()
> Full MatrixSpace of 5 by 5 sparse matrices over Integer Ring
> }}}
> The patch just does this by default.
>
> Apply:
>
> * [attachment:trac_10670_integral_mobius_matrix_for_posets-fh.patch]
New description:
I have noticed the following problem.
{{{
P=Posets.PentagonPoset()
P.mobius_function_matrix().parent()
Full MatrixSpace of 5 by 5 sparse matrices over Rational Field
}}}
The Mobius function of a poset should really be an '''integer matrix'''.
This can be achieved by using change_ring :
{{{
P.mobius_function_matrix().change_ring(ZZ).parent()
Full MatrixSpace of 5 by 5 sparse matrices over Integer Ring
}}}
The patch does this by default. It also adds optional arguments to choose
sparse/dense and the base ring. Same thing for lequal_matrix.
It also makes sure those matrices are immutable, and improves a bit the
redefinition of .mobius_function when the mobius function has been
calculated.
Apply:
* [attachment:trac_10670_integral_mobius_matrix_for_posets-fh.patch]
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10670#comment:12>
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