Related papers: Integral D-Finite Functions
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…
We present a prototypical linear algebra compiler that automatically exploits domain-specific knowledge to generate high-performance algorithms. The input to the compiler is a target equation together with knowledge of both the structure of…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
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…
In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions originally considered by Dales and Davie. For many compact plane sets the classical…
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
We present a new open source implementation in the SageMath computer algebra system of algorithms for the numerical solution of linear ODEs with polynomial coefficients. Our code supports regular singular connection problems and provides…
The aim of this paper is to give two new algorithms, which are elimination free, to find polynomial and rational solutions for a given holonomic system associated to a set of linear differential operators in the Weyl algebra D = k<x_1, ...,…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…
In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions…
This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of…
We give a geometric interpretation of the reciprocal complement of an integral domain $D$ in the case $D$ is a one-dimensional finitely generated algebra over an algebraically closed field.
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…