D.4.9 reesclos_lib
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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:
* ReesAlgebra:: computes the Rees Algebra of an ideal I
* normalI:: computes the integral closure of an ideal I using R[It]
* primeClosure:: computes the integral closure of the int. domain R
* closureRingtower:: defines the rings in the list L as global objects R(i)
* closureFrac:: computes fractions representing elements of R^=L[n]

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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