Related papers: A Recursive Method for Determining the One-Dimensi…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of…
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
We develop a $D-$module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zeros of remainder maps of such long divisions are handled by…
We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no…
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
Existential types are reconstructed in terms of small reflective subuniverses and dependent sums. The folklore decomposition detailed here gives rise to a particularly simple account of first-class modules as a mode of use of traditional…
We calculate the decomposition series of the D-module defined as the push-forward of a rank one linear system on the complement of a normal crossings hyperplane configuration and use data of a resolution of singularities to give a…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
We make a detailed analysis of the A-hypergeometric system (or GKZ system) associated with a monomial curve and integral, hence resonant, exponents. We characterize the Laurent polynomial solutions and show that these are the only rational…
The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the…
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the…
We determine the topological Euler number of certain moduli space of 1-dimensional closed subschemes in a smooth projective variety which admits a Zariski-locally trivial fibration with 1-dimensional fibers. The main approach is to use…