
D.4.18.5 intclMonIdeal
Procedure from library normaliz.lib (see normaliz_lib).
 Usage:
 intclMonIdeal(ideal I);
intclMonIdeal(ideal I, intvec grading);
 Return:
 The exponent vectors of the leading monomials of the elements of I
are considered as generators of a monomial ideal for which the
normalization of its Rees algebra is computed. For a Definiton of the
Rees algebra (or Rees ring) see Bruns and Herzog, CohenMacaulay
rings, Cambridge University Press 1998, p. 182.
The function returns a list of ideals:
(i) If the last ring variable is not used by the monomials, it is treated
as the auxiliary variable of the Rees algebra. The function returns two
ideals, the first containing the monomials generating the integral
closure of the monomial ideal, the second containing the algebra
generators of the normalization of the Rees algebra.
(ii) If the last ring variable is used by the monomials, the list returned
contains only one ideal, namely the monomials generating the integral
closure of the ideal.
The function returns the a list containing the input ideal I if one
of the options supp , triang , volume , or
hseries has been activated.
However, in this case some numerical invariants are computed, and
some other data may be contained in files that you can read into
Singular (see showNuminvs, exportNuminvs).
Example:
 LIB "normaliz.lib";
ring R=0,(x,y,z,t),dp;
ideal I=x^2,y^2,z^3;
list l=intclMonIdeal(I);
l[1]; // integral closure of I
==> _[1]=y2
==> _[2]=xy
==> _[3]=x2
==> _[4]=z3
==> _[5]=yz2
==> _[6]=xz2
l[2]; // monomials generating the integral closure of the Rees algebra
==> _[1]=z
==> _[2]=y2t
==> _[3]=xyt
==> _[4]=x2t
==> _[5]=z3t
==> _[6]=y
==> _[7]=x
==> _[8]=yz2t
==> _[9]=xz2t
 See also:
ehrhartRing;
intclToricRing;
normalToricRing.
