Algorithms for Computing Triangular Decompositions of Polynomial Systems [article]

Changbo Chen, Marc Moreno Maza
2011 arXiv   pre-print
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the library in ,
more » ... rforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.
arXiv:1104.0689v1 fatcat:ez5kkazvrrgpdjpstb5iosqorm