A Symbolic Algorithm For Computing Critical Values Of Algebraic Functions Under SAS Restrictions

In this paper, we propose a complete symbolic algorithm for computing an alge-braic function's all critical values under the restriction of a semi-algebraic system. Itcan be applied to solve global optimization problems. We give proofs to every stepsof the algorithm to ensure the correctness. It has been programmed on Maple systemusing the well known packages such as Groebner, RegularChains and DISCOVERER.The demonstration of the automated computing procedure is included.