extracting submodules

[Paul Zinn-Justin]

This may be obvious but here's the question:

start from R=QQ[x,y].

Define a (possible infinite-rank) module over R, e.g., of the form

S=R[a,b,c]/(x*a^2-y*b*c)

S is infinite-rank, but the graded pieces (where the degree is here in a,b,c only) are finite-rank.

The question is, how to get M2 to extract these graded pieces as modules over R?

[Frank Moore]

I believe something like this will work.  It computes the module you are after in degree d:

R = QQ[x,y]
S = R[a,b,c]
I = ideal (x*a^2 - y^2*b*c)
T = S/I

d = 3

-- the command is called 'basis' but really only returns a generating set in situations such as the two uses below:

degGenSet = sub(basis(d,T),S)

relsFromI = coefficients(gens image basis(d,I), Monomials => degGenSet)

M = coker sub(last relsFromI,R)

I haven't tried this on a more complicated example yet but perhaps this is good enough to get started?

Best,

Frank

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Dr. W. Frank Moore
Associate Professor

Department of Mathematics and Statistics

Wake Forest University

email: moo...@wfu.edu

[Paul Zinn-Justin]

Thanks Frank.

that worked!

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