Gröbner Bases for Complete Uniform Families
نویسندگان
چکیده
We describe (reduced) Gröbner bases of the ideal of polynomials over a field, which vanish on the set of characterisic vectors of the complete unifom families ([n] d ). An interesting feature of the results is that they are largely independent of the monomial order selected. The bases depend only on the ordering of the variables. We can thus use past results related to the lex order in the presence of degree-compatible orders, such as deglex. As applications, we give simple proofs of some known results on incidence matrices.
منابع مشابه
Applying Gröbner Bases to Solve Reduction Problems for Feynman Integrals
We describe how Gröbner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators...
متن کاملGröbner Bases and Systems Theory
We present the basic concepts and results of Gröbner bases theory for readers working or interested in systems theory. The concepts and methods of Gröbner bases theory are presented by examples. No prerequisites, except some notions of elementary mathematics, are necessary for reading this paper. The two main properties of Gröbner bases, the elimination property and the linear independence prop...
متن کاملMATH536A Paper: Gröbner Bases
An introduction to Gröbner bases and some of their uses in affine algebraic geometry.
متن کامل