Primary decomposition of zero-dimensional ideals: Putting Monico's algorithm into practice
Marc Moreno Maza, Éric Schost, Wenqin Zhou · 2006
Monico published in [Journal of Symbolic Computation, 34(5):451–459, 2002] an algorithm to compute the primary decomposition of a zero-dimensional ideal, that mostly relies on a characteristic polynomial computation modulo the input ideal, and its factorization. We revisit this algorithm, and discuss Maple and Magma implementations that contradict the somehow pessimistic conclusions of Monico’s original article: this algorithm provides competitive, sometimes faster alternatives to built-in functions in both systems. We also give an estimation of the probability of success of the algorithm.