A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals. (January 2016) - Ma, Yue; Wang, Chu; Zhi, Lihong
Abstract: For an ideal I with a positive-dimensional real variety V R ( I ), based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Gröbner basis of an ideal J generated by the kernel of a truncated moment matrix and satisfying I ⊆ J ⊆ I ( V R ( I ) ), V R ( I ) = V C ( J ) ∩ R n . We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic δ -regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.