D.4.9 reesclos_lib

Library:

reesclos.lib

Purpose:

procedures to compute the int. closure of an ideal

Author:

Tobias Hirsch, email: hirsch@math.tu-cottbus.de

Overview:

A library to compute the integral closure of an ideal I in a polynomial ring R=K[x(1),...,x(n)] using the Rees Algebra R[It] of I. It computes the integral closure of R[It] (in the same manner as done in the library ’normal.lib’), which is a graded subalgebra of R[t]. The degree-k-component is the integral closure of the k-th power of I.
These procedures can also be used to compute the integral closure R^ of an integral domain R=k[x(1),...,x(n)]/ker, ker a prime ideal, in its quotient field K=Q(R), as an affine ring R^=k[T(1),...,T(s)]]/J and to get representations of elements of R^ as fractions of elements of R.

Procedures:

D.4.9.1 ReesAlgebra		computes the Rees Algebra of an ideal I
D.4.9.2 normalI		computes the integral closure of an ideal I using R[It]
D.4.9.3 primeClosure		computes the integral closure of the int. domain R
D.4.9.4 closureRingtower		defines the rings in the list L as global objects R(i)
D.4.9.5 closureFrac		computes fractions representing elements of R^=L[n]