Related papers: Groebner Bases in Perturbative Calculations
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Groebner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological…
In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely…
The interpolation step of Guruswami and Sudan's list decoding of Reed-Solomon codes poses the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is…
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
Gr\"{o}bner bases are nowadays central tools for solving various problems in commutative algebra and algebraic geometry. A typical use of Gr\"{o}bner bases is the multivariate polynomial system solving, which enables us to construct…
Total degree reverse lexicographic order is currently generally regarded as most often fastest for computing Groebner bases. This article describes an alternate less mysterious algorithm for computing this order using exponent subtotals and…
We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…
Standard noncommutative Gr\"obner basis procedures are used for computing ideals of free noncommutative polynomial rings over fields. This paper describes Gr\"obner basis procedures for one-sided ideals in finitely presented noncommutative…
Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…
We show herein that a pattern based on FGLM techniques can be used for computing Gr\"obner bases, or related structures, associated to linear codes. This Gr\"obner bases setting turns out to be strongly related to the combinatorics of the…
The efficiency of Gr\"obner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on…
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…
We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear…
A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld…
In this work we study five Grovers algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We report results on various techniques which allow to compute the expansion into Legendre (or in general Gegenbauer) polynomials in an efficient way. We describe in some detail the algebraic/symbolic approach already presented in Ref.1 and…