Related papers: An Efficient Method for Computing Liouvillian Firs…

In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…

Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning…

This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…

We provide precise formulations and proofs of two theorems from Darboux's lectures on orthogonal systems. These results provide local existence and uniqueness of solutions to certain types of first order PDE systems where each equation…

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We compute the first explicit polynomials with Galois groups $G=P\Gamma L_3(4)$, $PGL_3(4)$, $PSL_3(4)$ and $PSL_5(2)$ over $\mathbb{Q}(t)$. Furthermore we compute the first examples of totally real polynomials with Galois groups…

Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on…

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…

We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…

Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…

The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a linear differential equation of the first order, which previously did not appear in the literature and which is satisfied…

In this paper we study linear projection methods for approximating the solution and simultaneously preserving first integrals of autonomous ordinary differential equations. We show that (linear) projection methods are a subset of discrete…

We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition…

We solve the Poincar\'e problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give an algorithm that decides whether a foliation has a rational first integral and computes it in the affirmative case. We…

In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.

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…

We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$-…

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…

We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The algorithm reduces this computation to the…

We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the necessary conditions for the existence of polynomial first…