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The following functions give some fundamental basic constructions with modules.
Given compatible modules M and N (ie, embedded in the same ambient module),
return the sum of M and N; that is, the submodule of the ambient generated
by M and N.
Given compatible modules M and N (ie, embedded in the same ambient module),
return the intersection of M and N in the ambient. This uses the standard
algorithm for intersecting two modules of a free module (see Section 2.8.3 of
[GP02]). If the ambient
is the quotient of a free module F by non-trivial relations, the intersection
performed is effectively that of the inverse images of M and N in F.
M * f : ModMPol, RngElt -> ModMPol
Given an R-module M and an element f∈R, return the
submodule of M generated by { f.v: v ∈M }
or { v.f: v ∈M }, respectively.
M * I : ModMPol, RngMPol -> ModMPol
Given an R-module M and an ideal I of R, return the
submodule of M generated by { f.v: f ∈I, v ∈M }
or { v.f: f ∈I, v ∈M }, respectively.
Given compatible modules M and N (ie, embedded in the same ambient module),
return the quotient module M/(M ∩N).
This has the same effect as using the quo constructor.
Given R-modules M and N, return the direct sum D = M direct-sum N
and two sequences of corresponding homomorphisms giving the injections
into and projections from D, respectively.
DirectSum(S) : [* ModMPol *] -> ModMPol, [ModMPolHom], [ModMPolHom]
A sequence or list L of R-modules, return their direct sum D and
two sequences of corresponding homomorphisms giving the injections into
and projections from D, respectively.
Given a graded module M, and an integer d, return the Serre twist M(d)
and an isomorphism f:M -> M(d). The twisted module is simply
an isomorphic copy of M, but with the grading twisted by d (so
d is subtracted from each weight of M). f has degree -d.
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