D.4.12 modnormal_lib

Library:

modnormal.lib

Purpose:

Normalization of affine domains using modular methods

Authors:

J. Boehm boehm@mathematik.uni-kl.de
W. Decker decker@mathematik.uni-kl.de
S. Laplagne slaplagn@dm.uba.ar
G. Pfister pfister@mathematik.uni-kl.de
A. Steenpass steenpass@mathematik.uni-kl.de
S. Steidel steidel@mathematik.uni-kl.de

Overview:

Suppose A is an affine domain over a perfect field.
This library implements a modular strategy for finding the normalization of A. Following [1], the idea is to apply the normalization algorithm given in [2] over finite fields and lift the results via Chinese remaindering and rational reconstruction as described in [3]. This approch is inherently parallel.
The strategy is available both as a randomized and as a verified algorithm.

References:

[1] Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Stefan Steidel, Andreas Steenpass: Parallel algorithms for normalization, preprint, 2011.

[2] Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch: Normalization of Rings, Journal of Symbolic Computation 9 (2010), p. 887-901

[3] Janko Boehm, Wolfram Decker, Claus Fieker, Gerhard Pfister: The use of Bad Primes in Rational Reconstruction, preprint, 2012.

Procedures:

D.4.12.1 modNormal

normalization of R/I using modular methods