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 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 |