On Jan 18, 10:46 pm, William Stein <wst...@gmail.com> wrote:
> On Sun, Jan 18, 2009 at 10:40 PM, John H Palmieri
>
>
>
> <jhpalmier...@gmail.com> wrote:
>
> > I have a first draft of a module which implements simplicial
> > complexes, chain complexes, and their homology. It isn't perfect: it
> > is limited by Sage's abilities to deal with modules over arbitrary
> > commutative rings, or at least by my knowledge of Sage's abilities.
> > Thus for example, you can define a chain complex over a polynomial
> > ring on one or several variables, but you probably can't compute its
> > homology very reliably.
>
> > I would appreciate comments, and eventually I hope to submit it to the
> > trac server.
>
> > (I tried searching the various Sage groups to see if anyone was
> > working on similar stuff and didn't find anything. I hope I'm not
> > stepping on any toes.)
>
> If you are it is a surprise to me. The only time in my entire life
> that I have heard of anybody implementing computation of generic
> simplical homology in any math software system is right now from you.
Macaulay2 has this, although I've never used it (just looked at the
documentation and a little of the source code, which I found rather
opaque). See
<http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.1/share/doc/
Macaulay2/SimplicialComplexes/html/___Simplicial__Complex.htm>
> I've never heard of anybody doing a single real thing in this
> direction in Sage or Magma ever (I'm not saying nothing was done in
> Magma, but I don't know about it). So I'm very enthusiastic about
> this! I also think this is great motivation to finally implement
> general finitely generated modules over ZZ, so, e.g., cokernels are
> defined.
John
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