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 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 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 Factoring analytic multivariate polynomials and non-standard Cauchy–Riemann conditions

2014 ◽  
Vol 104 ◽  
pp. 43-57 ◽  
Author(s):  
Tomas Recio ◽  
J.-Rafael Sendra ◽  
Luis-Felipe Tabera ◽  
Carlos Villarino
Keyword(s):  
Multivariate Polynomials ◽  
Cauchy Riemann

scholarly journals Estimation of Norms of Multivariate Polynomials with Integral Coefficients

1999 ◽  
Vol 96 (2) ◽  
pp. 378-398
Author(s):  
Francisco Luquin ◽  
Concepción Besga
Keyword(s):  
Multivariate Polynomials

On Stability and Robust Stability of Multivariate Polynomials l

2000 ◽  
Vol 33 (16) ◽  
pp. 479-484
Author(s):  
Jorge A. Torres Muñoz ◽  
Vladimir L. Kharitonov
Keyword(s):  
Robust Stability ◽  
Multivariate Polynomials
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