Invited Speaker : Bruno Buchberger , Johannes Kepler University, Austria
Teaching Math to Lady M
I stopped teaching logic and math to humans. Instead I started to teach logic / math to Lady M, a machine. She (or he or it) has absolutely no insight and I enjoy that she does not expect that what I am telling her has any meaning (semantics). For certain input expressions she produces certain output. Very reliably, for the same input the same output. By certain input, her inner state changes and she her input / output behavior changes. Recently, after many layers of communication, I managed to make her behave the way I behaved when, as a PhD student, I invented the Gröbner bases algorithm. I.e. I taught her to invent mathematical algorithms and proofs. Of course, she does not know.
I am not sure how far I managed to carry this approach consistently through. In the talk, I will display certain stages of this program for discussion.
Invited Speaker : Dongming Wang , Beihang University and Guangxi University for Nationalities, China & CNRS, France
Characteristic Decomposition of Polynomial Sets
Let G be a reduced lexicographic Groebner basis. A polynomial g in G is said to be minimal if g has
the lowest order among all those polynomials in G which have the same leading variable as g. The
minimal polynomials in G form a triangular set, called the W-characteristic set of G or of the
ideal generated by G. G is said to be normal if for every minimal polynomial g in G, the initial
of g does not involve the leading variable of any other polynomial in G. We show that
– there are inherent connections between Ritt characteristic sets and lexicographic Groebner
– normal Groebner bases and their W-characteristic sets possess a number of interesting properties, and
– any polynomial set can be decomposed into finitely many normal Groebner bases with associated zero relations.
The decomposition algorithm is based on the structural properties we have established and the computation of lexicographic Groebner bases. We discuss briefly the implementation of our decomposition algorithm with some experiments. Part of the work presented in this talk was done jointly with Rina Dong and Chenqi Mou.
, Wilfrid Laurier University, Canada
All kinds a new Maple Packages, remind me of You
Maple 2017 encompasses a significant amount of new functionalities in more that 150 different packages. We will present an overview of new functionalities in Maple 2017, with an emphasis on the Group Theory and Physics packages. We will illustrate these functionalities with fully worked out examples.