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Normaliz :: intclMonIdeal(Ideal,Thing)

intclMonIdeal(Ideal,Thing) -- normalization of Rees algebra

Synopsis

Description

The leading monomials of the elements of I are considered as generators of a monomial ideal. This function computes the integral closure of I⊂R in the polynomial ring R[t] and the normalization of its Rees algebra. If f1,...,fm are the monomial generators of I, then the normalization of the Rees algebra is the integral closure of K[f1t,...,fnt] in R[t]. For a definition of the Rees algebra (or Rees ring) see Bruns and Herzog, Cohen-Macaulay rings, Cambridge University Press 1998, p. 182. The function returns a sequence containing the integral closure of the ideal I and the normalization of its Rees algebra. If there is a free variable in the original ring (i.e. a variable that does not appear in any of the generators of I), you can give the function that variable as second input. The function then uses it instead of creating a new one. Note that in this case the input ideal is considered as ideal in the smaller polynomial ring.

R=ZZ/37[x,y,t];
I=ideal(x^3, x^2*y, y^3, x*y^2);
(intCl,normRees)=intclMonIdeal(I,t);
intCl
normRees