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Normaliz :: intclMonIdeal(Ideal)

intclMonIdeal(Ideal) -- 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 the integral closure of the ideal I and the normalization of its Rees algebra. Since the Rees algebra is defined in a polynomial ring with an additional variable, the function creates a new polynomial ring with an additional variable.

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