Counting Real Roots in Polynomial-Time for Systems Supported on Circuits

Autor:	Rojas, J. Maurice
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Computer Science - Computational Complexity Computer Science - Symbolic Computation
Druh dokumentu:	Working Paper
Popis:	Suppose $A=\{a_1,\ldots,a_{n+2}\}\subset\mathbb{Z}^n$ has cardinality $n+2$, with all the coordinates of the $a_j$ having absolute value at most $d$, and the $a_j$ do not all lie in the same affine hyperplane. Suppose $F=(f_1,\ldots,f_n)$ is an $n\times n$ polynomial system with generic integer coefficients at most $H$ in absolute value, and $A$ the union of the sets of exponent vectors of the $f_i$. We give the first algorithm that, for any fixed $n$, counts exactly the number of real roots of $F$ in in time polynomial in $\log(dH)$. Comment: 29 pages, 1 figure, accepted for presentation at MEGA (Effective Methods in Algebraic Geometry) 2021. You can see a recording of my talk at MEGA 2021 (June 9, 2021) at this YouTube link: https://www.youtube.com/watch?v=KKKmTctxbs4
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.04868 Zobrazit plný text záznamu View this record from Arxiv