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\subset R in the polynomial ring R[t] and the normalization of its Rees algebra. If f_1,\ldots,f_m are the monomial generators of I, then the normalization of the Rees algebra is the integral closure of K[f_1t,\ldots,f_nt] in R[t]. For a definition of the Rees algebra (or Rees ring) see Bruns and Herzog, CohenMacaulay 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.
i1 : R=ZZ/37[x,y];

i2 : I=ideal(x^3, x^2*y, y^3, x*y^2);
o2 : Ideal of R

i3 : (intCl,normRees)=intclMonIdeal I;

i4 : intCl
3 2 2 3
o4 = ideal (y , x*y , x y, x )
ZZ
o4 : Ideal of [x..y, a]
37

i5 : normRees
o5 = MonomialSubalgebra{cache => CacheTable{...1...} }
3 2 2 3
generators => {y, y a, x, x*y a, x y*a, x a}
ZZ
ring => [x..y, a]
37
ZZ
o5 : MonomialSubalgebra of [x..y, a]
37
