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. |
PDF File: (565 kB)
|
Home,
Last update:
Sat Nov 19 16:53:13 2022
|