Algorithms for zero-dimensional ideals using linear recurrent sequences

TL;DR

This paper introduces a novel approach leveraging linear recurrent multi-dimensional sequences to perform algebraic operations like primary decomposition of zero-dimensional ideals, inspired by sparse FGLM algorithms.

Contribution

It presents a new method using linear recurrent sequences to compute ideal decompositions, extending the capabilities of existing algorithms.

Findings

Demonstrates how to compute the annihilator of sequences for ideal decomposition

Extends sparse FGLM algorithm techniques to multi-dimensional sequences

Provides a framework for algebraic operations on zero-dimensional ideals

Abstract

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.