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Abstract: The computation of triangular decompositions are based on two fundamentaloperations: polynomial GCDs modulo regular chains and regularity test modulosaturated ideals. We propose new algorithms for these core operations relyingon modular methods and fast polynomial arithmetic. Our strategies take alsoadvantage of the context in which these operations are performed. We report onextensive experimentation, comparing our code to pre-existing Mapleimplementations, as well as more optimized Magma functions. In most cases, ournew code outperforms the other packages by several orders of magnitude.

Autor: Xin Li, Marc Moreno Maza, Wei Pan


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