相关论文: Algorithms for integrals of holonomic functions ov…

We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis…

We present an algorithm to compute the annihilator of (i.e., the linear differential equations for) the logarithm of a polynomial in the ring of differential operators with polynomial coefficients. The algorithm consists of differentiation…

Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…

We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…

A holonomic system of linear partial differential equations is, roughly speaking, a system whose solution space is finite dimensional. A distribution that is a solution of a holonomic system is called a holonomic distribution. We give…

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

We give an approximate algorithm of computing holonomic systems of linear differential equations for definite integrals with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping…

A simple algorithm to compute all the zeros of a generic polynomial is proposed.

We present a new algorithm by which the Adomian polynomials can be determined for scalar-valued nonlinear polynomial functional in a Hilbert space. This algorithm calculates the Adomian polynomials without the complicated operations such as…

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…

We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.

Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a…

In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…

We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…

In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…