Harmony of Gröbner bases and the modern industrial society

Pure Mathematics Group

Takayuki HIBI	(Group Leader/Osaka University)
Hidefumi OHSUGI	(Rikkyo University)

Gröbner bases of toric ideals arising in pure mathematics such as computational commutative algebra, enumerative combinatorics on convex polytopes, happen to be useful for analyzing phenomenon in real world statistically. With such experiences, we will make a "dictionary" of Gröbner bases which can be computed by "hands" and construct theoretical foundations toward practical applications to, e.g., clinical testing. On the other hand, if we can implement theoretical and abstract techniques to seek for Gröbner bases of toric ideals, it is not a dream to invent software which computes Gröbner bases of complicated toric ideals without relying on Buchberger algorithm. We will promote the activity on establishing the basic research theoretically toward an invention of such a software of our dream.