Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library

We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our experiments show that, for difficult input systems, the computing time for removing redundant components can be reduced to a small portion of the total time needed for solving these systems. Since testing the inclusion between two quasi-components can be as expensive as a radical membership test, and many pairs of quasi-components may need to be compared, we believe that we have obtained an efficient solution.