On the expected number of real roots of polynomials and exponential sums

被引：0

作者：

Malajovich, Gregorio ^{[1
]}

机构：

[1] Univ Fed Rio de Janeiro, Dept Matemat Aplicada, Inst Matemat, Caixa Postal 68530, BR-21941909 Rio De Janeiro, RJ, Brazil

来源：

JOURNAL OF COMPLEXITY | 2023年 / 76卷

关键词：

Random polynomials; Sparse polynomials; Mixed volume; Real roots;

D O I：

10.1016/j.jco.2022.101720

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The expected number of real projective roots of orthogonally invariant random homogeneous real polynomial systems is known to be equal to the square root of the Bezout number. A similar result is known for random multi-homogeneous systems, invariant through a product of orthogonal groups. In this note, those results are generalized to certain families of sparse polynomial systems, with no orthogonal invariance assumed.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：11

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