Recursive Structures in Involutive Bases Theory

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

Reference: Journal of Symbolic Computation, 118 (2023) 32-68

Description: We discuss characterisations of Janet and Pommaret bases via recursion of the variables in the underlying polynomial ring and use them to provide novel completion algorithms. We extend the results to minimal Janet bases and Janet-like bases. We generalise the concept of Janet-like bases to arbitrary involutive divisions and study in particular Pommaret-like bases. The arising theory leads to a novel recursive characterisation of quasi-stable ideals and a novel algorithm for the deterministic construction of "good" coordinates for a polynomial ideal which is more efficient than previous ones. We also provide a syzygy theory for involutive-like bases.

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