ylfink@water.UUCP (ylfink) (02/18/86)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES COMPUTER SCIENCE COLLOQUIUM - Thursday, February 20, 1986. Professor Scott McCallum of the University of Toronto will speak on ``Decision Methods for Algebraic Equa- tions''. TIME: 2:30 PM ROOM: MC 2034 ABSTRACT The decision problem for systems of polynomial equali- ties and inequalities in ``n'' variables with rational co-efficients is to decide whether or not a given such system has a solution in real n-space. An algorithm due to Collins for this decision problem will be presented in this talk. The algorithm has been imple- mented in the SAC-2 computer algebra system. For ``n''-fixed, the algorithm runs in polynomial time. However, the running time depends doubly-exponentially on ``n''. A recent algorithm for the decision problem due to Grigoriev runs in time singularly-exponential in ``n''.