Algorithmic Computation of Polynomial Amoebas

被引：8

作者：

Bogdanov, D. V. ^{[1
]}

Kytmanov, A. A. ^{[2
]}

Sadykov, T. M. ^{[1
]}

机构：

[1] Plekhanov Russian Univ, Stremyanny 36, Moscow 125993, Russia

[2] Siberian Fed Univ, Svobodny 79, Krasnoyarsk 660041, Russia

来源：

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2016 | 2016年 / 9890卷

关键词：

Amoebas; Newton polytope; Optimal algebraic hypersurface; The contour of an amoeba; Hypergeometric functions; MELLIN SYSTEM;

D O I：

10.1007/978-3-319-45641-6_7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present algorithms for computation and visualization of polynomial amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide a method and an algorithm for the computation of polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope. The presented algorithms are implemented in computer algebra systems Matlab 8 and Mathematica 9.

引用

页码：87 / 100

页数：14

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