Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772905 | Journal of Pure and Applied Algebra | 2017 | 11 Pages |
Abstract
Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if n=2 or d=1 or (n,2d)=(3,4), where n is the number of variables and 2d the degree of the form. We study the analogue for even symmetric forms. We establish that an even symmetric n-ary 2d-ic psd form is sos if and only if n=2 or d=1 or (n,2d)=(n,4)nâ¥3 or (n,2d)=(3,8).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Charu Goel, Salma Kuhlmann, Bruce Reznick,