Using monodromy to recover symmetries of polynomial systems

Autor:	Duff, Timothy, Korotynskiy, Viktor, Pajdla, Tomas, Regan, Margaret
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Computer Science - Mathematical Software
Druh dokumentu:	Working Paper
Popis:	Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of existence, one would like to compute formulas for these symmetries, towards the eventual goal of solving the systems more efficiently. We describe and implement one possible approach to this task using numerical homotopy continuation and multivariate rational function interpolation. We describe additional methods that detect and exploit a priori unknown quasi-homogeneous structure in symmetries. These methods extend the range of interpolation to larger examples, including applications with nonlinear symmetries drawn from vision and robotics. Comment: Extended journal version of conference paper published at ISSAC 2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.12685 Zobrazit plný text záznamu View this record from Arxiv