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 f
1,...,f
m are the monomial generators of I, then the normalization of the Rees algebra is the integral closure of K[f
1t,...,f
nt] 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. If the option
allComputations is set to true, all data that has been computed by
Normaliz is stored in a
RationalCone in the CacheTable of the monomial subalgebra returned.
R=ZZ/37[x,y]; |
I=ideal(x^3, x^2*y, y^3, x*y^2); |
(intCl,normRees)=intclMonIdeal(allComputations=>true,I) |
normRees.cache#"cone" |