Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials
Algebraic Geometry
2015-05-21 v1 Mathematical Software
Numerical Analysis
Abstract
We give a Descartes'-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition is satisfied. This was discovered while developing algorithms and software for computing the Gale transform of a fewnomial system, which is our main goal. This software is a component of a package we are developing for Khovanskii-Rolle continuation, which is a numerical algorithm to compute the real solutions to a system of fewnomials.
Keywords
Cite
@article{arxiv.1505.05241,
title = {Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials},
author = {Daniel J. Bates and Jonathan D. Hauenstein and Matthew E. Niemerg and Frank Sottile},
journal= {arXiv preprint arXiv:1505.05241},
year = {2015}
}
Comments
22 pages, 4 figures