Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem

It is a difficult problem to prove that a polynomial only takes non-negative values. One way to certify that a polynomial is non-negative is to express it as a sum of squares, however not all non-negative polynomials can be written as a sum of squares. The fundamental reason that there exist non-negative polynomials that cannot be written as sums of squares is that these polynomials satisfy linear inequalities that arise from linear relations known as the Cayley-Bacharach relations.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2016

Author dc:creator

• Henderson, Kenneth Terrell

• Algebraic Geometry

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/59310

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/59310