Hello Martin Am 03.07.2016 um 09:45 schrieb Martin Baker:
> So I have added homology functions to DeltaComplex, > FiniteSimplicialComplex and FiniteCubicalComplex just so end users can > avoid having to explicitly do these steps. > > But I think this is not what you are saying. Are you saying there is > some, more direct method, which does not go through these steps? > In a sense, yes. There is a bunch of homology theories. It's not easy to express what I have in mind in few words, however, considering that homology is just a pair (M,b) where M is a module (usually graded) and b:M->M a linear mapping such that b b = 0, we just have to compute ker(b)/image(b) to get the homology 'spaces'. Usually M is a direct sum of chain spaces (abelian groups or even vector spaces) but the 'homology' function should accept as much as possible (premises above). If for instance M is a vector space (think of polyhedral chains with rational or real coefficients) then cohomology ist just (M',b'), where M' is the conjugate space and b' the transpose of b. To cut a long story short, it might be an asset to have a package 'Co/Homology' that tries to compute the 'quotients' whenever possible (input M,b), disregarding the origin (complex, current, abstract, geometric ...). I guess it's not the goal to compete wirh all the special tools available anyway. Please, don't become confused about these remarks; just my point of view and by no means criticism. > I would like it if the Homology domain was an extension of existing > abelian group categories. Is there some way to do this that could handle > both infinite cycles and torsion? > Yes and no. See e.g. https://en.wikipedia.org/wiki/Homological_algebra Kurt > > Martin > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
