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
numbers)
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.

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! Volkmar Welker             ! E-Mail : welker@math.tu-berlin. de    !
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