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toDual(d,f) -- given a 1 by n matrix f over a polynomial ring R and an integer d such that the d-th power of each variable is in the image of f, computes Hom(R/image f, E), where E is the injective envelope of the coefficient field of R.

This function mimics the script <l_to_dual of Macaulay, and is probably going to be changed substantially.

See also:

Code:

     -- ../../../Macaulay2/m2/duals.m2:15-21
     toDual = (d, f) -> (
         R := ring f;
         g := product apply(generators R, v -> v^d);
         box := matrix table (1, numgens R, (i,j) -> R_j^(d+1));
         contract(
              transpose mingens image (generators (image box : image f) % box),
              matrix{{g}}))

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