Good morning! I have been trolling through the manuals trying to understand
how to construct a basis for a hom-space but I keep going around in
circles. Can anyone help me out?
I have two CombinatorialFreeModules G and H which are modules for some
algebra A. (The algebra A is not implemented in sage, although its action
on G and H is.) The module G is cyclic, generated by z say, so every
homomorphism f:G->H is determined by f(z). The basis of G takes the form
{G(t) = z.psi( t )}, where t runs through a set of tableaux. (In case you
are interested, G and H are Specht modules.) That is, the psi method tells
me how to write G(t)=z*\phi_t so that f(G(t))=f(z).psi(t) as H also has a
psi method.
I can construct a set of elements {h_1,...,h_d} in H such that the maps
{f_1,....,f_d} determined by f_i(z)=h_i, for 1\le i\le d, is a basis for
Hom_A(G,H).
My questions are: how do I construct the maps f_i in sage and how do I tell
sage that these maps are a basis of Hom_A(G,H)?
Cheers,
Andrew
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