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math.OC2012★ 2 cited
A certificate for semidefinite relaxations in computing positive dimensional real varieties
Yue Ma, Chu Wang, Lihong Zhi
For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal…
math.OC2012
Certificates of Impossibility of Hilbert-Artin Representations of a Given Degree for Definite Polynomials and Functions
Feng Guo, Erich L. Kaltofen, Lihong Zhi
We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any re…