On Jul 2, 5:36 am, Simon King <[EMAIL PROTECTED]> wrote:
> Dear Sage team,
>
> this time i have two groups of questions.
>
> 1.
> My main project is the creation of a data base of cohomology rings of
> finite p-groups (coefficients in GF(p), of course). For each group in
> the data base, it should provide
> - a quotient of a graded-commutative ring, isomorphic to the
> cohomology ring; these are data in Singular.
Do you mean, a quotient of a "free" graded-commutative ring, or
something like that? Otherwise, why say "quotient"?
> - special subgroups, namely maximal elementary abelian subgroups and
> the greatest central elementary abelian subgroup; these are data in
> Gap.
> - the restriction map for each special subgroup; again, data in
> Singular.
>
> Question to group theorists:
> What further informations do you wish to be part of such data base?
I'm not a group theorist, but I play one in the occasional paper. How
about the action of the Steenrod operations? (I have a Sage package
which does mod 2 Steenrod operations currently under review. I am
working on adding the odd primary version, too.) For normal subgroups,
would it make sense to somehow encode the behavior of the Lyndon-
Hochschild-Serre spectral sequence? I don't know how you would do
this; maybe record some sort of minimal information about the nonzero
differentials? Barring this, if E is a subgroup (e.g., an elementary
abelian one), information about the action of the normalizer N(E) on
H^*(E): it would be nice to be able to see Quillen's theorem in
action.
What about non-trivial coefficients? Perhaps for some groups there are
naturally occurring modules M for which you should record the
cohomology H*(G;M) as a module over H*(G;k)?
>
> Question to everybody:
> What tools/packages are available for Sage that help to create and
> maintain a data base (please with hints to tutorials/manuals)?
>
> 2.
> There is a long thread about improving linear algebra (specifically
> over small fields) in
> Sage:http://groups.google.com/group/sage-devel/browse_thread/thread/aa4edc...
>
> Has this improvement become part of the Sage distribution? Or is it an
> optional package? Personally, I specifically need fast operations
> "matrix times vector", "vector times scalar", "sum/difference of
> vectors", "echelon form of a matrix".
>
> Yours
> Simon
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