Mobius matrices of posets are integer matrices

[fchapoton]

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

Depends on #10998

CC: @fchapoton @sagetrac-sage-combinat

Component: combinatorics

Keywords: poset, matrix, Cernay2012

Author: Frédéric Chapoton, Florent Hivert

Reviewer: Florent Hivert, Nicolas M. Thiéry

Merged: sage-5.0.beta5

Issue created by migration from https://trac.sagemath.org/ticket/10670

[fchapoton]

Author: chapoton

[hivert]

comment:6

Hi Frédéric,

Thanks for taking care of this problem.

Here are a few remarks:

• The field Author below is used to give credits after each release. You
  should put your real name here and not your login.

• If you think returning a matrix over QQ is a bug, then you should
  make sure by a doctest that the bug is indeed fixed, indicating in comment
  the ticket number for this bug.

• I can easily imagine use cases where the Moebius function is needed over a
  different ring (eg: Z2 or a polynomial field). What about having an
  optional argument ring with a default value ZZ to avoid
  changing the ring twice ? In this case for consistency,
  .mobius_function_matrix() should also take this optional parameter too.
  What do you think ?

Right now, I'm having lunch, but I'll probably find the time to post a review
patch this evening if you don't beat me. If you start working on it please put
a message here so that we avoid doing it twice. Of course I'll do the same. In
any case one of us will have to do some review and the other to write some
code.

Florent

[hivert]

Reviewer: Florent Hivert

[hivert]

Changed author from chapoton to Frédéric Chapoton

[hivert]

comment:7

Right now, I'm having lunch, but I'll probably find the time to post a review
patch this evening if you don't beat me. If you start working on it please put
a message here so that we avoid doing it twice. Of course I'll do the same. In
any case one of us will have to do some review and the other to write some
code.

I'm on It. Please don't touch anything !

[hivert]

Dependencies: #10998

[hivert]

Changed author from Frédéric Chapoton to Frédéric Chapoton, Florent Hivert

[hivert]

comment:8

I reworked the patch. Unfortunately on the way I got a dependency on #10998

Florent

[fchapoton]

comment:9

Trying to help the build bot to do its job

Apply trac_10670_integral_mobius_matrix_for_posets-fh.patch

[hivert]

Changed keywords from poset, matrix to poset, matrix, Cernay2012

[nthiery]

Changed reviewer from Florent Hivert to Florent Hivert, Nicolas M. Thiéry

[nthiery]

comment:13

We finalized the patch together with Florent.
Positive review on the version I just uploaded, assuming the test pass (I am running them).

[nthiery]

comment:14

Except for a timeout in sage/sandpiles/sandpile.py, all tests passed on sage-5.0.beta2 with the following patches applied::

trac_11003-folded.patch
trac_10998-categories-posets-nt.patch
trac_10670_integral_mobius_matrix_for_posets-fh.patch
trac_11382-subposet_to_vertex_speedup-fh.patch
trac_12476-lattice_join_matrix_speedup-fh.patch
trac_11118-finite_enumset_list_cache-fh.patch

Setting a positive review. Thanks Frédéric and Florent!

[jdemeyer]

comment:15

Attachment: trac_10670_integral_mobius_matrix_for_posets-fh.patch.gz

[jdemeyer]

Merged: sage-5.0.beta5