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arXiv · 0903.3690

Computations modulo regular chains

Xin Li·Marc Moreno Maza·Wei Pan
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Abstract

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

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Xin Li, Marc Moreno Maza, Wei Pan. 2009-07-25. Computations modulo regular chains. https://arxiv.org/abs/0903.3690

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