Abstract:

In this talk, I will first demonstrate how Wu’s method beautifully apply to automated geometric theorem proving. Then I will present the algorithm of computing a characteristic set. Such set may contain more zeros than the original one, but the idea here is to decompose zeros by repeatly computing many characteristic sets. Since it seems there are no “specialization” issues as naturally encountered in computing Groebner basis with parameters, Wu’s method may be a good tool in dealing with parametric polynomial systems. Moreover, I will also discuss the possibility of using the pseudodivision in obtaining upper bounds of a zero dimensional variety in the hope of dealing with some finiteness problems of central configurations.