منابع مشابه
CertiVed Numerical Root Finding
Root isolation of univariate polynomials is one of the fundamental problems in computational algebra. It aims to find disjoint regions on the real line or complex plane, each containing a single root of a given polynomial, such that the union of the regions comprises all roots. For root solving over the field of complex numbers, numerical methods are the de facto standard. They are known to be ...
متن کاملGeometric Invariant Theory via Cox Rings
We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox ring all maximal open subsets such that the quotient is quasiprojective or embeddable into a toric variety. As applications, we obtain an explicit description...
متن کاملQuasipolynomial root-finding: A numerical homotopy method∗
Quasipolynomials arise in a number of applications, and in particular as the characteristic equation associated with systems of delay differential equations. Quasipolynomial equations are generally difficult to solve, and most often must be solved numerically. In the non-trivial case, quasipolynomials have an infinite number of roots in the complex plane. We present a new numerical method for f...
متن کاملDivisorial rings and Cox rings
1 Preliminaries on monoids Definition 1.1. An Abelian monoid is a set with a binary, associative, and commutative operation which has a neutral element. It will often be called just a monoid in this manuscript because we will not deal with non-commutative monoids. A monoid M is called • finitely generated if there is a finite set of generators, or equivalently if there is a surjection of monoid...
متن کاملOn Factoriality of Cox Rings
Generalized Cox’s construction associates with an algebraic variety a remarkable invariant – its total coordinate ring, or Cox ring. In this note we give a new proof of factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on a notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ri...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2020
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2020.106367