Complementary Decompositions of Monomial Ideals and Involutive Bases

Co-author(s): Amir Hashemi and Matthias Orth

Reference: Applicable Algebra in Engineering, Communication and Computing, 33 (2022) 791--821

Description: We discuss and compare different algorithms for the construction of complementary decompositions. We relate the classical algorithm by Janet to Janet trees and extend the underlying ideas to Janet-like bases to obtain an optimised algorithm. We also consider a construction presented by Hironaka and show that it produces a finite result, if and only if the input is a quasi-stable ideal, in which case it produces the same result as Janet's algorithm. Finally, we briefly apply our results to the computation of irreducible and primary decompositions.

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