#6491: [with spkg, needs review] Modular Cohomology Rings of Finite p-Groups
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Reporter: SimonKing | Owner: tbd
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1.1
Component: optional packages | Keywords: cohomology ring finite p-group
Reviewer: | Author: Simon King
Merged: |
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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
}}}
== 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 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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6491>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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