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Algorithms for finding hypergeometric solutions of scalar linear difference equations with rational-function coefficients are known in computer algebra. We propose an algorithm for the case of a first-order system of such equations. The algorithm is ...

Recently, the authors presented a novel approach to computing resolutions and Betti numbers using Pommaret bases. For Betti numbers, this algorithm is for most examples much faster than the classical methods typically by orders of magnitude. As the ...

Given a regular chain, we are interested in questions like computing the limit points of its quasi-component, or equivalently, computing the variety of its saturated ideal. We propose techniques relying on linear changes of coordinates and we consider ...

We outline a method for computing the tangent cone of a space curve at any of its points. We rely on the theory of regular chains and Puiseux series expansions. Our approach is novel in that it explicitly constructs the tangent cone at arbitrary and ...

The conditions on parameters of the system ensuring stability or instability of relative equilibria of the orbital girostat mentioned in the title were found. The parametrical analysis of conditions of gyroscopic stabilization of the unstable equilibria ...

In this paper, we provide a new approach for computing regular solutions of first-order linear difference systems. We use the setting of factorial series known to be very well suited for dealing with difference equations and we introduce a sequence of ...

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the ...

This paper introduces a definition of polynomial first integrals in the differential algebra context and an algorithm for computing them. The method has been coded in the Maple computer algebra system and is illustrated on the pendulum and the Lotka-...

For a set S of cells in a cylindrical algebraic decomposition of ℝn, we introduce the notion of generalized cylindrical algebraic formula GCAF associated with S. We propose a multi-level heuristic algorithm for simplifying the cylindrical algebraic ...

This survey of mathematical approaches to quasi-steady state QSS phenomena provides an analytical foundation for an algorithmic-algebraic treatment of the associated parameter-dependent ordinary differential systems, in particular for reaction networks. ...

A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.

A differential polynomial G is called a divisor of a differential polynomial F if any solution of the differential equation G=0 is a solution of the equation F=0. We design an algorithm which for a class of quasi-linear partial differential polynomials ...

A symbolic algorithm which can be implemented in computer algebra systems for generating bases for irreducible representations of the laboratory and intrinsic point symmetry groups acting in the rotor space is presented. The method of generalized ...

We present new symbolic-numeric algorithms for solving the Schrödinger equation describing the scattering problem and resonance states. The boundary-value problems are formulated and discretized using the finite element method with interpolating Hermite ...

Methods of computer algebra are used to study the properties of a nonlinear algebraic system that determines equilibrium orientations of a satellite moving along a circular orbit under the action of gravitational and constant torques. An algorithm for ...

Polynomial systems of equations are a central object of study in computer algebra. Among the many existing algorithms for solving polynomial systems, perhaps the most successful numerical ones are the homotopy algorithms. The number of operations that ...

On the basis of the Routh---Lyapunov method and its generalizations, we study the structure of the phase space of the conservative system which describes the motion of a rigid body in gravitational and magnetic fields. Within the framework of this study,...

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian stochastic forces. It ...

In this paper, we present a symbolic algorithm to compute the topology of a plane curve. The algorithm mainly involves resultant computations and real root isolation for univariate polynomials. The novelty of this paper is that we use a technique of ...

This paper tackles the problem of interpolating reduced data $Q_m=\{q_i\}_{i=0}^m$ obtained by sampling an unknown curve γ in arbitrary euclidean space. The interpolation knots ${\cal T}_m= \{t_i\}_{i=0}^m$ satisfying γti=qi are assumed to be unknown ...

We recall definitions and properties of parametric solvable polynomial rings and variants. For recursive solvable polynomial rings, i.e. solvable polynomial rings with coefficients from a solvable polynomial ring, also commutator relations between main ...

Deterministic recursive algorithms for the computation of matrix triangular decompositions with permutations like LU and Bruhat decomposition are presented for the case of commutative domains. This decomposition can be considered as a generalization of ...

In this paper, we present the computer-supported theory exploration, including both formalization and verification, of a theory in commutative algebra, namely the theory of reduction rings. Reduction rings, introduced by Bruno Buchberger in 1984, are ...

We derive a combined analytical and numerical scheme to solve the 1+1-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the ...

A new effective algorithm for computing a set of algebraic local cohomology classes is presented. The key ingredient of the proposed algorithm is to utilize a standard basis. As the application, an algorithm is given for the conversion of a standard ...

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial and is challenged to approximate them faster. The challenge is known for long time,...

Circulant matrices have been extensively applied in Symbolic and Numerical Computations, but we study their new application, namely, to randomized pre-processing that supports Gaussian elimination with no pivoting, hereafter referred to as GENP. We ...

During the past few decades there have been many examples where computer algebra methods have been applied successfully in the analysis and construction of numerical schemes, including the computation of approximate solutions to partial differential ...

A quantum Fourier transform and its application to a quantum algorithm for phase estimation is discussed. It has been shown that the approximate quantum Fourier transform can be successfully used for the phase estimation instead of the full one. The ...

We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic approach, with ...