On the maximum rank of a real binary form

被引：16

作者：

Causa, A. ^{[1
]}

Re, R. ^{[1
]}

机构：

[1] Univ Catania, Dipartimento Matemat & Informat, I-95125 Catania, Italy

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2011年 / 190卷 / 01期

关键词：

Typical rank; Waring rank; Real roots;

D O I：

10.1007/s10231-010-0137-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that a real binary form f of degree n has n distinct real roots if and only if for any (alpha, beta) is an element of R(2)\{0} all the forms alpha f(x) + beta f(y) have n - 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909.4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has a distinct real roots.

引用

页码：55 / 59

页数：5