> < ^ Date: Fri, 19 Feb 1999 09:43:54 GMT
> ^ From: Volkmar Welker <welker@immd1.informatik.uni-erlangen.de >
^ Subject: Re: simplicial homology groups? simplicial homology groups?

is there a package which will compute them?

--> I do not know whether GAP can do that.

--> One can use Macaulay for doing it or any software
being able to do free resolutions (resolve the
Stanley-Reisner ring of the simplicial complex and use
Hochsters formula for the multi-graded betti
I myself and many others did so. But for my own
projects the complexes became too big.
This sparked code development by Frank Heckenbach. He
wrote very efficient code specifally doing simplicial homology computation.
(code available under http://www.mi.uni-erlangen.de/~heckenb).
Again this has its limitation.
In cooperation with myself, Dave Saunders (Delware) together with
Jean-Guilleaume Dumas (Grenoble) are trying to adapt
general Smith-Normal form algorithms to the specific
requirements of homology computations. This has proven to
be quite successful. But there is no software available yet.

--> If one asks for rational homology onlyone can use the approach
via combinatorial laplacians. Freedman (u british columbia)
has analyzed and probably implemented this.

! Volkmar Welker             ! E-Mail : welker@math.tu-berlin. de    !
! Fachbereich Mathematik     ! Tel.   : +49 30 314 25751             ! 
! TU-Berlin                  ! FAX    : +49 30 314 25191             !
! Strasse des 17. Juni 136   !---------------------------------------!
! D-10623 Berlin             !http://www.math.tu-berlin.de/~welker   !
! Germany                    !                                       !

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