scholarly journals Newton Polytopes and Witness Sets

2014 ◽  
Vol 8 (2) ◽  
pp. 235-251 ◽  
Author(s):  
Jonathan D. Hauenstein ◽  
Frank Sottile
Keyword(s):  
Newton Polytopes

scholarly journals The bifurcation set of a rational function via Newton polytopes

2021 ◽  
Author(s):  
Tat Thang Nguyen ◽  
Takahiro Saito ◽  
Kiyoshi Takeuchi
Keyword(s):  
Rational Function ◽  
Newton Polytopes ◽  
Bifurcation Set

scholarly journals Newton polytopes of invariants of additive group actions

2001 ◽  
Vol 156 (2-3) ◽  
pp. 187-197 ◽  
Author(s):  
Harm Derksen ◽  
Ofer Hadas ◽  
Leonid Makar-Limanov
Keyword(s):  
Group Actions ◽  
Additive Group ◽  
Newton Polytopes ◽  
Additive Group Actions

scholarly journals Systems of polynomials with at least one positive real zero

2019 ◽  
Vol 19 (10) ◽  
pp. 2050183 ◽  
Author(s):  
Jie Wang
Keyword(s):  
Polynomial Optimization ◽  
Real Zero ◽  
Sufficient Conditions ◽  
Combinatorial Structure ◽  
Multivariate Polynomials ◽  
Positive Real ◽  
Newton Polytopes

In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials admitting at least one positive real zero in terms of their Newton polytopes and combinatorial structure. Moreover, a class of polynomials attaining their global minimums in the first quadrant are given, which is useful in polynomial optimization.

scholarly journals Lattice Points in the Newton Polytopes of Key Polynomials

2020 ◽  
Vol 34 (2) ◽  
pp. 1281-1289
Author(s):  
Neil J. Y. Fan ◽  
Peter L. Guo ◽  
Simon C. Y. Peng ◽  
Sophie C. C. Sun
Keyword(s):  
Lattice Points ◽  
Newton Polytopes ◽  
Key Polynomials

Gcd of multivariate polynomials via Newton polytopes

2011 ◽  
Vol 217 (21) ◽  
pp. 8377-8386
Author(s):  
Luiz Emilio Allem ◽  
Vilmar Trevisan
Keyword(s):  
Multivariate Polynomials ◽  
Newton Polytopes

scholarly journals Absolute Irreducibility of Polynomials via Newton Polytopes

2001 ◽  
Vol 237 (2) ◽  
pp. 501-520 ◽  
Author(s):  
Shuhong Gao
Keyword(s):  
Newton Polytopes

Newton polytopes and the Bezout theorem

1977 ◽  
Vol 10 (3) ◽  
pp. 233-235 ◽  
Author(s):  
A. G. Kushnirenko
Keyword(s):  
Newton Polytopes ◽  
Bezout Theorem

scholarly journals Newton Polytopes of Cluster Variables of Type $A_n$

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Adam Kalman
Keyword(s):  
Type A ◽  
Laurent Expansion ◽  
Cluster Algebras ◽  
Newton Polytope ◽  
Newton Polytopes ◽  
Affine Hull ◽  
Cluster Variable ◽  
Nous Montrons ◽  
The Face ◽  
International Audience

International audience We study Newton polytopes of cluster variables in type $A_n$ cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope of the Laurent expansion of any cluster variable, with respect to any cluster. In particular, we show that every Laurent monomial in a Laurent expansion of a type $A$ cluster variable corresponds to a vertex of the Newton polytope. We also describe the face lattice of each Newton polytope via an isomorphism with the lattice of elementary subgraphs of the associated snake graph. Nous étudions polytopes de Newton des variables amassées dans les algèbres amassées de type A, dont les variables sont indexés par les diagonales et les côtés d’un polygone. Nos principaux résultats comprennent une description explicite de l’enveloppe affine et facettes du polytope de Newton du développement de Laurent de toutes variables amassées. En particulier, nous montrons que tout monôme Laurent dans un développement de Laurent de variable amassée de type A correspond à un sommet du polytope de Newton. Nous décrivons aussi le treillis des facesde chaque polytope de Newton via un isomorphisme avec le treillis des sous-graphes élémentaires du “snake graph” qui est associé.

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