相关论文: The generic Groebner walk
Computing Gr\"obner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gr\"obner bases through the Gr\"obner fan, one can attempt an…
We outline a generalization of the Groebner fan of a homogeneous ideal with maximal cells parametrizing truncated Groebner bases. This "truncated" Groebner fan is usually much smaller than the full Groebner fan and offers the natural…
The theory of Groebner Bases originated in the work of Buchberger and is now considered to be one of the most important and useful areas of symbolic computation. A great deal of effort has been put into improving Buchberger's algorithm for…
We show the power of Bruno Buchberger's seminal Groebner Basis algorithm, interfaced, seamlessly, with what we call symbolic dynamical programming, to automatically generate algebraic equations satisfied by the generating functions…
This paper presents algorithms for computing the Groebner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Groebner bases of the ideal. Our algorithms are based on a uniform definition of the…
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$…
In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
We describe how Groebner 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…
This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals…
We show that a circuit walk from a given feasible point of a given linear program to an optimal point can be computed in polynomial time using only linear algebra operations and the solution of the single given linear program. We also show…
In this paper we outline the most general and universal algorithmic approach to reduction of loop integrals to basic integrals. The approach is based on computation of Groebner bases for recurrence relations derived from the integration by…
In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
We present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties…
We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively…
We present an algorithm which converts a given Sagbi basis of a polynomial $K$-subalgebra $\mathcal{A}$ to a Sagbi basis of $\mathcal{A}$ in a polynomial ring with respect to another term ordering, under the assumption that subalgebra…
This paper shows that Gr\"obner walks aiming for the elimination of variables from a polynomial ideal can be terminated much earlier than previously known. To this end we provide an improved stopping criterion for a known Gr\"obner walk…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…