Modular Cohomology Rings of Finite p-Groups

simon-king-jena commented 15 years ago

I suggest to distribute our package for the computation of modular cohomology rings of finite p-groups as an optional package.

Authors

Simon A. King (Since recently at National University of Ireland, Galway)
David J. Green (Friedrich-Schiller-Universität Jena)

Installation

The package can be installed by

sage -i http://sage.math.washington.edu/home/SimonKing/Cohomology/p_group_cohomology-1.0.spkg

Since William has put it into the experimental package repository, you can now also do

sage -i p_group_cohomology-1.0.spkg

Purpose

Given any group of order p^n (where p is prime), compute the cohomology ring (in terms of minimal generators and relations and also providing various ring theoretic invariants) of the group with coeffients in the finite field of order p. Of course, induced homomorphisms can be computed as well.

Documentation

An extensive documentation can be found at http://sage.math.washington.edu/home/SimonKing/Cohomology/.

Features

The package includes the cohomology rings of all groups of order 64. These are actually quite challenging for other software (e.g., the Hap package for Gap, or the Magma programs of Jon F. Carlson with which these cohomology rings were first computed).

On sage.math, there are the cohomology rings for all groups of order 128, and the package can download them. Sage is the only CAS that can currently provide such data. Similarly, the cohomology of the groups of order 243 is available, but six of them are still not completely computed yet.

Sources

The package comprises

a modified old version of the Aachen C-MeatAxe,
C-routines and Gap functions of David J. Green for the computation of minimal projective resolutions, and
various Cython extension modules and Singular functions written by myself, computing the structure of the cohomology ring according to algorithms of Dave Benson and David J. Green.
Data for the cohomology of all groups of order 64.

The C-MeatAxe is considerably modified, the rest of the sources has never been published yet. Therefore we included all of the sources into the Mercurial repository.

Dependencies

It is required that the SmallGroups library is installed.

Since I too often had to work around bugs in the non-commutative part of Singular 3-0-4, it is required that Singular 3-1-0 is available when dealing with a finite p-Group and p>2.

Testing

I am afraid that there is no separate test suite for the C-sources. The package includes two scripts spkg-check and spkg-check-details, that both walk through all doc tests. spkg-check-details is slower, but in case of errors provides more direct pointers to the failing tests than spkg-check. The scripts also verify the presence of doc test in any method.

Note that some tests require internet connection, as data will be downloaded.

Known issues

It is not clear to me how one properly works with Licences. I did my very best. But could please some more experienced person check whether everything is alright with the licence?
A couple of months ago, I tried to build an earlier version of the package on OS X. It failed, which was very likely due to C-MeatAxe, which in fact does not seem to support OS X (even in the most recent version). But this was without distutils. Perhaps someone can test it, as I do not have access to OS X.
By the way of saving matrices in the MeatAxe format, it is very likely that the porting between big and little endian machines will be impossible. In particular, it could turn out to be impossible to use the data bases with a motorola processor.

CC: @jhpalmieri david.green@uni-jena.de

Component: packages: optional

Keywords: cohomology ring finite p-group

Author: Simon King, David J. Green

Reviewer: David Joyner, William Stein

Merged: Sage 4.1.1.rc1

Issue created by migration from https://trac.sagemath.org/ticket/6491

simon-king-jena commented 15 years ago

comment:52

William reported (off list) that the package builds on all platforms that he tested (I don't know which these are exactly).

wdjoyner commented 15 years ago

comment:53

That is good new. But here is some bad news:

All my computers shut down this afternoon due to a big thunder storm which took out all the power. This happened in the middle of a sage -testall. I will have to retest my intel macbook OS 10.4.11 again, if you think it is necessary. Note that in one month Apple will release 10.6, so if 10.5 was already tested, we can probably skip 10.4.11 anyway. In any case, it did pass the spkg-check part of the test on 10.4.11.

simon-king-jena commented 15 years ago

comment:54

Replying to @wdjoyner:

That is good new. But here is some bad news:

All my computers shut down this afternoon due to a big thunder storm which took out all the power.

Too bad! I hope that at least you are safe!

This happened in the middle of a sage -testall. I will have to retest my intel macbook OS 10.4.11 again, if you think it is necessary. Note that in one month Apple will release 10.6, so if 10.5 was already tested, we can probably skip 10.4.11 anyway. In any case, it did pass the spkg-check part of the test on 10.4.11.

Well, if it passed spkg-check (showing the bottom line "All tests passed!"), then the work is done, and a retest wouldn't be needed. sage -testall would test all of Sage, not just our package.

I don't know if William's tests also included Macbook OS 10.4.11; I think it did include PowerPC OS X 10.4.

Thanks to both you and William for the help on getting the project finally finished!

Cheers, Simon

wdjoyner commented 15 years ago

comment:55

Sounds like this can be changed to "positive review" as far as including this as an optional package is concerned. Agreed?

simon-king-jena commented 15 years ago

comment:56

Replying to @wdjoyner:

Sounds like this can be changed to "positive review" as far as including this as an optional package is concerned. Agreed?

This time I would not oppose :)

I am currently not aware of serious issues that should be fixed. And everything else should be done in a forthcoming version, on a different ticket.

Cheers, Simon

williamstein commented 15 years ago

comment:57

This sucker works and passes tests everywhere.

williamstein commented 15 years ago

comment:58

Oh, and I posted it to the optional spkg repo.

simon-king-jena commented 15 years ago

comment:59

Replying to @williamstein:

This sucker works and passes tests everywhere.

Thanks again!

I inserted David Joyner and William Stein in the "Reviewer" form. I hope you both agree.

simon-king-jena commented 15 years ago

Reviewer: David Joyner, William Stein

7c09a680-e216-4024-bb8e-9bfd4aa7f313 commented 15 years ago

Merged: Sage 4.1.1.rc1

7c09a680-e216-4024-bb8e-9bfd4aa7f313 commented 15 years ago

Changed author from Simon King to Simon King, David J. Green

sagemath / sage