2026-09-20T06:26:27Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/593102026-09-18T13:52:03Zcom_10339_14934col_10339_38132

Henderson, Kenneth Terrell 2016-05-21T08:35:49Z 2016-05-21T08:35:49Z 2016 https://wakespace.lib.wfu.edu/handle/10339/59310 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. en Wake Forest University Algebraic Geometry Commutative Algebra Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem Thesis Moore, William F Kirkman, Ellen Robinson, Stephen Mathematics open.access