Usage:
<l_from_dual I' I
Compute the ideal I which is dual to the inverse system I'.
I' is generated by the dual polynomials of the 1xn matrix I'.
Parameters:
I' = 1xn matrix, over a base ring S.
Output values:
I = 1xm matrix, over the same base ring S.
Let R be the localization of S at the homogeneous maximal ideal.
Let E be the R-module generated by {1/x^A}, for all monomials x^A, with
R action defined by x^A.(1/x^B) = 0 (if A-B has a positive component)
1/x^(B-A) otherwise.
E is the injective envelope of the base field k in R. It is not
finitely generated.
Given an ideal I of R, its inverse system I' is defined to be
Hom_R(R/I, E)
which is naturally identified as a submodule of E.
If R/I is Artinian, then I' is finitely generated. If
I' is finitely generated, then R/I is Artinian.
Similarly, given a submodule I' of E, define an ideal I of R by
I = {g in R : g.h = 0, for all h in I'} = Ann I'
Caveats: The base ring S should not be a quotient ring.