Multiregeneration for polynomial system solving
Colin Crowley, Jose Israel Rodriguez, Jacob Weiker, and Jacob Zoromski
TL;DR
This paper presents 'multiregeneration', a software tool implementing a continuation method for solving polynomial systems, capable of handling various polynomial structures with parallelization and strategic options.
Contribution
The paper introduces a new implementation of a continuation method for polynomial system solving, supporting diverse polynomial structures and parallel computation.
Findings
Successfully computes degrees and partial degrees for various polynomial systems.
Supports parallelization and multiple solving strategies.
Demonstrates effectiveness on structured polynomial systems.
Abstract
We demonstrate our implementation of a continuation method as described in \cite{HR2015} for solving polynomials systems. Given a sequence of (multi)homogeneous polynomials, the software "multiregeneration" outputs the respective (multi)degree in a wide range of cases and partial multidegree in all others. We use Python for the file processing, while Bertini is needed for the continuation. Moreover, parallelization options and several strategies for solving structured polynomial systems are available.
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