{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/59310"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/59310","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Henderson, Kenneth Terrell"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-27T22:02:05Z","subjects":["Algebraic Geometry"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/59310","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Henderson, Kenneth Terrell"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-21T08:35:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-21T08:35:49Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Geometry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/59310"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem"]}]}],"canonical_facts":{"dc:creator":["Henderson, Kenneth Terrell"],"dc:date.accessioned":["2016-05-21T08:35:49Z"],"dc:date.available":["2016-05-21T08:35:49Z"],"dc:date.issued":["2016"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/10339/59310"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Algebraic Geometry"],"dc:title":["Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:05Z"}