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.
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页码：87 / 100
页数：14
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