Computations modulo regular chains
Xin Li, Marc Moreno Maza, Wei Pan · 2009
The computation of triangular decompositions involve two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations based on modular methods and fast polynomial arithmetic. We rely on new results connecting polynomial subresultants and GCDs modulo regular chains. 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.