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We investigate the stability of the modified difference scheme of Kim and Moin for numerical integration of two-dimensional incompressible Navier–Stokes equations by the Fourier method and by the method of discrete perturbations. The obtained analytic-form stability condition gives the maximum time steps allowed by stability, which are by factors from 2 to 58 higher than the steps obtained from previous empirical stability conditions. The stability criteria derived with the aid of CAS Mathematica are verified by numerical solution of two test problems one of which has a closed-form analytic solution. [ABSTRACT FROM AUTHOR]

In this paper, we propose a symbolic-numerical algorithm for collision-free placement and motion of an object avoiding collisions with obstacles. The algorithm is based on the combination of configuration space and energy approaches. According to the configuration space approach, the position and orientation of the geometric object to be moved or placed is represented as an individual point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of this object. The configurations which, due to the presence of obstacles, are forbidden to the object, can be characterized as regions in this configuration space called configuration space obstacles. As will be demonstrated, configuration space obstacles can be computed symbolically using quantifier elimination over the reals and represented by polynomial inequalities. We propose to use the functional representation of semi-algebraic point sets defined by such inequalities, so-called R-functions, to describe nonlinear geometric objects in the configuration space. The potential field defined by R-functions can be used to “move” objects in such a way as to avoid collisions. Introducing the additional function, which forces the object towards the goal position, we reduce the problem of finding collision free path to a solution of the Newton’s equations, which describes the motion of a body in the field produced by the superposition of “attractive” and “repulsive” forces. These equations can be solved iteratively in a computationally efficient manner. Furthermore, we investigate the differential properties of R-functions in order to construct a suitable superposition of attractive and repulsive potentials. [ABSTRACT FROM AUTHOR]

Automatic generation of smooth, non-overlapping meshes on arbitrary regions is the well-known problem. Considered as optimization task the problem may be reduced to finding a minimizer of the weighted combination of so-called length, area, and orthogonality functionals. Unfortunately, it has been shown that on the one hand, certain weights of the individual functionals do not admit the unique optimizer on certain geometric domains. On the other hand, some combinations of these functionals lead to the lack of ellipticity of corresponding Euler-Lagrange equations, and finding the optimal grid becomes computationally too expensive for practical applications. Choosing the right functional for the particular geometric domain of interest may improve the grid generation very much, but choosing the functional parameters is usually done in the trial and error way and depends very much on the geometric domain. This makes the automatic and robust grid generation impossible. Thus, in the present paper we consider the way to compute certain approximations of minimizer of grid functionals independently of the particular domain. Namely, we are looking for the approximation of the minimizer of the individual grid functionals in the local sense. This means the functional has to be satisfied on the possible largest parts of the domain. In particular, we shall show that the so called method of envelopes, otherwise called the method of rolling circle, that has been proposed in our previous paper, guarantees the optimality with respect to the area and orthogonality functionals in this local sense. In the global sense, the grids computed with the aid of envelopes, can be considered as approximations of the optimal solution. We will give the comparison of the method of envelopes with well established Winslow generator by presenting computational results on selected domains with different mesh size. [ABSTRACT FROM AUTHOR]

The proposed in [7] uniform error estimate allows to control the accuracy of the symbolic approximate solution of the Dirichlet problem for elliptic PDE in the whole domain of the problem considered. The present paper demonstrates the techniques of finding such an approximate solution with Mathematica and the use of the uniform error estimate for a concrete example. [ABSTRACT FROM AUTHOR]

We present algorithms for parametric problems in differential algebra that can be formulated in a suitable first-order language L. The atomic L-formulas are linear ODEs of arbitrary order with parametric coefficients of arbitrary degrees. Using rather weak axioms on differential fields or differential algebras that are realized in natural function domains, we establish explicit quantifier elimination algorithms for L providing also parametric sample solutions for purely existential problems. These sample solutions are "generic" solutions of univariate parametric linear ODEs that can be realized by concrete functions in the natural function domains mentioned above. We establish upper complexity bounds for the elimination algorithms that are elementary recursive for formulas of bounded quantifier alternation, in particular doubly exponential for existential formulas. Our results are in contrast to Seidenberg's model theoretic elimination theory for non-linear problems that is non elementary recursive, requires very strong axioms that are not realizable in natural function domains, and does not provide sample solutions. [ABSTRACT FROM AUTHOR]

The standard methods for the search for the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and the search for solutions of the obtained system. It has been demonstrated by the example of the generalized Hénon-Heiles system that the use of the Laurent-series solutions of the initial differential equation assists to solve the obtained algebraic system and, thereby, simplifies the search for elliptic solutions. This procedure has been automatized with the help of the computer algebra systems Maple and REDUCE. The Laurent-series solutions also assist to solve the inverse problem: to prove the non-existence of elliptic solutions. Using the Hone's method based on the use the Laurent-series solutions and the residue theorem, we have proved that the cubic complex one-dimensional Ginzburg-Landau equation has neither elliptic standing wave nor elliptic travelling wave solutions. To find solutions of the initial differential equation in the form of the Laurent series we use the Painlevé test. [ABSTRACT FROM AUTHOR]

We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the size of the subresultant matrix drastically compared with the recursive subresultant proposed by the authors before, hence it is much more useful for investigation of the recursive PRS. Finally, we discuss usage of the reduced nested subresultant in approximate algebraic computation, which motivates the present work. [ABSTRACT FROM AUTHOR]

In original comprehensive Gröbner bases, we must select parameter from variables before computation. By extending them, we introduce full comprehensive Gröbner bases as comprehensive Gröbner bases such that we can choose parameters to be instantiated from variables freely after computation. In this paper, we give an algorithm to compute full comprehensive Gröbner bases. [ABSTRACT FROM AUTHOR]

We present an extension of constraint logic programming, where the admissible constraints are arbitrary first-order formulas over various domains: real numbers with ordering, linear constraints over p-adic numbers, complex numbers, linear constraints over the integers with ordering and congruences (parametric Presburger Arithmetic), quantified propositional calculus (parametric qsat), term algebras. Our arithmetic is always exact. For are there are no restrictions on the polynomial degree of admissible constraints. Constraint solving is realized by effective quantifier elimination. We have implemented our methods in our system clp(rl). A number of computation examples with clp(rl) are given in order to illustrate the conceptual generalizations provided by our approach and to demonstrate its feasibility. [ABSTRACT FROM AUTHOR]

In this paper we present a procedure that allows us to distinguish all branches of a space curve near the singular point and to compute parametric form of them with any accuracy. The same procedure works for finding the branches of a space curve such that some (or all) coordinates tend to infinity. [ABSTRACT FROM AUTHOR]

Factorization of differential equations has been intensively studied (see, for instance, [1], [2]). Less results are known for difference equations. In this publication we are not giving a general approach to the theory of factorization but rather present some observations and derive formulae for further use in reference books and for symbolic computations. Several specific examples which arise from the theory of classsical orthogonal polynomials are studied. They have, to our mind, significance for practical applications in physics. The paper is based to some extent on the ideas developed in other publications of the authors [3], [5], [6] but the angle of view on the problem is different. In the first section differential equations are dealt with. In the second section, our studies are concentrated on difference equations. In both cases knowing the equation for orthogonal polynomials we derive equations for their products. These latter equations are of higher order than the starting ones, and polynomial solutions can be sought as solutions of multiparametric spectral problem [4]. [ABSTRACT FROM AUTHOR]

We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in parametric form that is easy to use. Then by combining the explicit solution with a minimization scheme, we develop a unified method to match the parameters and integration constants needed by the explicit solutions and given boundary conditions. The method presented in the paper can be adapted to a variety of boundary conditions. We detail our method on two commonly used boundary conditions. [ABSTRACT FROM AUTHOR]

Computer algebra system is applied for studying the elastic torsional nonlinear waves in a rod using the second order approximation. It is shown that the nonlinear correction to the classic linear solution is a combination of a stationary longitudinal wave, a progressive longitudinal wave, and a progressive transverse wave. The solution describing a stationary longitudinal wave is a quadratic polynomial of cylindrical functions. The expressions for a progressive longitudinal wave and a progressive transverse wave inevitably include quadratures from polynomials of the cylindrical functions. [ABSTRACT FROM AUTHOR]

The present study demonstrates a very helpful role of computer algebra systems (CAS) for deriving and testing new numerical methods. We use CAS to construct and test a new numerical method for solving boundary - value problems for the 2D Navier — Stokes equations governing steady incompressible viscous flows. We firstly describe the core of the method and the algorithm of its construction, then we describe the implementation in CAS for deriving formulas of the method and for testing them, and finally we give some numerical results and concluding remarks. [ABSTRACT FROM AUTHOR]

The LEDA number type real is extended by the diamond operator, which allows to compute exactly with real algebraic numbers given as roots of polynomials. The coefficients of these polynomials can be arbitrary real algebraic numbers. The implementation is presented and experiments with two other existing implementations of real algebraic numbers (CORE, EXACUS) are done. [ABSTRACT FROM AUTHOR]

Computer Algebra Systems (CASs) are convenient high-level programming languages that provide the programmer not only with symbolic capabilities and exact arithmetic, but also with different structures handling and plotting capabilities. We have used the CAS Maple as development tool for designing Meta-Petro, a system for training undergraduates in metamorphic rocks recognition and classification using photomicrographies. This expert system includes a collection of photomicrographies of thin sections of samples that are randomly presented to the user. The user can ask the system for details about: the different rocks, his guess of the solution and the right solution. Moreover, this information can be shown on the decision tree the system uses. As far as we know, in this field only "catalogs" with fixed photomicrographies have been developed so far. Keywords: Metamorphic Petrology, Computer Algebra Systems, Expert Systems. [ABSTRACT FROM AUTHOR]

We present a memory management subsystem for the computer algebra library SACLIB that removes the potential for memory leaks or double deletes in applications using the system. The system encapsulates the management of arrays that are allocated on the heap or on the system stack. The system makes arrays responsible for their own memory management, and enables the compiler to prevent other parts of SACLIB from managing array memory. To prove that our memory module and all applications using it are leak free and double delete free we introduce a new iterator concept and implement a model of that concept using generic programming techniques such as template meta-programming. Our innovations reduce the amount of code responsible for array memory management from 10,000 lines of code to 2,000 lines of code. Using hardware performance counters we show optimizing compilers are capable of avoiding any runtime overhead. [ABSTRACT FROM AUTHOR]

We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. In the former paper, we studied some improvements on Kaltofen and May's method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study the similar improvements on the method using the criterion due to Gao and Rodrigues for sparse polynomials satisfying Newton polytope conditions, by which we are able to find more accurate separation bounds, for such bivariate polynomials. We also discuss a concept of separation bound continuations for both dense and sparse polynomialsThis research is partly helped by Grants-in-Aid of MEXT, JAPAN, #16700016.. [ABSTRACT FROM AUTHOR]

A fast verification algorithm of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a small additional cost. Finally, this paper includes some numerical examples to show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Two algorithmic techniques for specifying the existence of a k × k submatrix with elements 0,±1 in a skew and symmetric conference matrix of order n are described. This specification is achieved using an appropriate computer algebra system. Key Words and Phrases: Gaussian elimination, growth, complete pivoting, weighing matrices, symbolic computation. AMS Subject Classification: 65F05, 65G05, 20B20. [ABSTRACT FROM AUTHOR]

In this paper we present a method that uses solutions of linear systems to construct all possible orthogonal arrays OA(n,q,2,2+), when 3 ≤ q ≤ 6. A note on its complexity is also presented. [ABSTRACT FROM AUTHOR]

An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Gröbner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological concepts and constructions. We illustrate the approach by application to some two-state cellular automata. In the two-state case the Gröbner basis method is also applicable, and we compare both approaches. [ABSTRACT FROM AUTHOR]

Some results of analysis of Kirchhoff equations, which describe the motion of a rigid body in the ideal incompressible fluid, are presented. With respect to these equations, a problem is stated to obtain steady-state motions, invariant manifolds of steady-state motions (IMSMs), and to investigate their properties in the aspect of stability and stabilization of motion. Our methods of investigation are based on classical results obtained by Lyapunov [1]. The computer algebra systems (CAS) "Mathematica", "Maple", and a software [2] are used as the tools. Lyapunov's sufficient stability conditions are derived for some steady-state motions obtained. A problem of optimal stabilization with respect to the first approximation equations is solved for some cases of unstable motion. This paper represents a continuation of our research, the results of which have been reported during CASC'2004 in St. Petersburg [3]. [ABSTRACT FROM AUTHOR]

A new computational approach is proposed for the solution of the time-dependent Schrödinger equation (TDSE), in which a symbolic algorithm named GATEO and a numerical scheme based on the finite-element method (FEM) are effectively composed. The GATEO generates the multi-layer operator-difference scheme for TDSE and evaluates the effective Hamiltonian from the original time-dependent Hamiltonian by means of the Magnus expansion and the Pade-approximation. In order to solve the TDSE with the effective Hamiltonian thus obtained, the FEM is applied to a discretization of spatial domain which brings the difference scheme in operator form to the one in algebraic form. The efficiency and accuracy of GATEO and the numerical scheme associated with FEM is confirmed in the second-, fourth-, and sixth-order time-step computations for certain integrable atomic models with external fields. [ABSTRACT FROM AUTHOR]

Using the computer algebra methods, different authors have proved the existence of new classes of the homografic solutions, in the Lagrange-Wintner sense [1], in the Newtonian many-body problem [2-6]. E.A. Grebenicov has also shown that any homographic solution of the n-body problem generates a new dynamical model, namely, "the restricted Newtonian (n + 1)-body problem". These problems are similar to the famous "restricted three-body problem" which was proposed for the first time by K. Jacobi [7]. Then the theorems of the existence of stationary solutions (the equilibrium positions) for some fixed values of the parameter n were proved [8-10], and the problem of studying the stability of these solutions in the Lyapunov sense was formulated. The study of this problem can be done only on the basis of the KAM-theory [11-13] and only for the dynamical systems with two degrees of freedom it can be realized. We have shown that all the planar restricted n-body problems belong to this class for any n. The situation is essentially complicated for the critical (resonance) cases, when the eigenvalues of the linearized system of differential equations in the neighborhood of the stationary solution are rationally commensurable. In these critical cases the stability problem for hamiltonian dynamics may be studied only on the basis of Markeev and Sokolsky theorems [14,15]. These theorems contain mathematical estimations of the influence of so-called "non-annihilable resonance terms" in the Poincaré-Birkho. normalizing transformations, which must be taken into account in the theorems on the stability of stationary solutions of hamiltonian equations in critical cases [16]. [ABSTRACT FROM AUTHOR]

In this paper we generalize a method to analyze inhomogeneous polynomial systems containing parameters. In particular, the Hilbert function is used as a tool to check that the specialization of a "generic" Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called Hilbert stratification of the associated variety. We classify the possible specializations according to the value of the Hilbert function of the specialized system. Some computation examples with the PoSSoLib are reported. Keywords and phrases: Gröbner bases, Hilbert function, Specialization. AMS Subject Classification: 68W30, 13P10, 13F20, 13D40. [ABSTRACT FROM AUTHOR]

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary-valued images, each of them defined as 2D arrays of pixels. Our answer is based on an algebraic-topological coding, called AT-model, for a nD (n=2,3) digital binary-valued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT-models for all the 2D digital images in a time sequence, it is possible to get an AT-model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence. If the frames are represented in a quadtree format, a similar positive result can be derived. [ABSTRACT FROM AUTHOR]

It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the graph's diameter and average distance on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural tool. We obtain some properties of the ideals we are concerned. In particular, we prove that the corresponding MDD is also an L-shape in the affine r-dimensional space. We implement in PostScript language a graphic representation of MDDs for circulant digrahs with two or three jumps. Given the irredundant irreducible decomposition of the associated monomial ideal, we provide formulae to compute the diameter and the average distance. Finally, we present a new and attractive family (parametrized with the diameter d>2) of circulant digraphs of degree three associated to an irreducible monomial ideal. [ABSTRACT FROM AUTHOR]

We define a new type of Gröbner bases called Janet-like, since their properties are similar to those for Janet bases. In particular, Janet-like bases also admit an explicit formula for the Hilbert function of polynomial ideals. Cardinality of a Janet-like basis never exceeds that of a Janet basis, but in many cases it is substantially less. Especially, Janet-like bases are much more compact than their Janet counterparts when reduced Gröbner bases have "sparce" leading monomials sets, e.g., for toric ideals. We present an algorithm for constructing Janet-like bases that is a slight modification of our Janet division algorithm. The former algorithm, by the reason of checking not more but often less number of nonmultiplicative prolongations, is more efficient than the latter one. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new type of monomial division called Janet-like, since its properties are similar to those of Janet division. We show that the former division improves the latter one. This means that a Janet divisor is always a Janet-like divisor but the converse is generally not true. Though Janet-like division is not involutive, it preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity. Due to superiority of Janet-like division over Janet division, the algorithm for constructing Gröbner bases based on the new division is more efficient than its Janet division counterpart. [ABSTRACT FROM AUTHOR]

Let f1,..., fp be polynomials in C[x1,..., xn] and let D = Dn be the n-th Weyl algebra. The annihilating ideal of in D[s]=D[s1,...,sp] is a necessary step for the computation of the Bernstein-Sato ideals of f1,..., fp. We point out experimental differences among the efficiency of the available methods to obtain this annihilating ideal and provide some upper bounds for the complexity of its computation. [ABSTRACT FROM AUTHOR]

We propose exact, complete and efficient methods for 2 problems: First, the real solving of systems of two bivariate rational polynomials of arbitrary degree. This means isolating all common real solutions in rational rectangles and calculating the respective multiplicities. Second, the computation of the sign of bivariate polynomials evaluated at two algebraic numbers of arbitrary degree. Our main motivation comes from nonlinear computational geometry and computer-aided design, where bivariate polynomials lie at the inner loop of many algorithms. The methods employed are based on Sturm-Habicht sequences, univariate resultants and rational univariate representation. We have implemented them very carefully, using advanced object-oriented programming techniques, so as to achieve high practical performance. The algorithms are integrated in the public-domain C++ software library synaps, and their efficiency is illustrated by 9 experiments against existing implementations. Our code is faster in most cases; sometimes it is even faster than numerical approaches. [ABSTRACT FROM AUTHOR]

The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite) bit-streams. In other words, coefficients can be approximated to any desired accuracy, but are not known exactly. We show that a variant of the Descartes algorithm can cope with bit-stream coefficients. To isolate the real roots of a square-free real polynomial with root separation ρ, coefficients and , it needs coefficient approximations to O(n(log(1/ρ) + τ)) bits after the binary point and has an expected cost of O(n4 (log(1/ρ) + τ)2) bit operations. [ABSTRACT FROM AUTHOR]

The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substituted by a univariate polynomial in a distinct variable. It is shown that a Dixon projection operator (a multiple of the resultant) of the composed system can be expressed as a power of the resultant of the outer polynomial system multiplied by powers of the leading coefficients of the univariate polynomials substituted for variables in the outer system. The derivation of the resultant formula for the composed system unifies all the known related results in the literature. A new resultant formula is derived for systems where it is known that the Cayley-Dixon construction does not contain any extraneous factors. The approach demonstrates that the resultant of a composed system can be effectively calculated by considering only the resultant of the outer system. [ABSTRACT FROM AUTHOR]

In the present paper we discuss single-electron states in a quantum dot by solving the Schrödinger equation taking into account spatial constraints, in which the confinement is modeled by a spherical potential wall (particle-in-a-sphere model). After the separation of variables we obtain second order ordinary differential equations, so that automatic methods for finding a closed-form solution are needed. We present a symbolic algorithm implemented in Maple based on the method of indeterminate coefficients, which reduces the obtained equations to the well-known differential equations. The latter can be solved in terms of hypergeometric or Bessel functions. The usage of indeterminate coefficients allows one to obtain the solution of the problem equations in terms of control parameters, which can then be choosen according to the purposes of a nanotechological process. [ABSTRACT FROM AUTHOR]

We propose a new algorithm for the generation of orthogonal grids on regions bounded by arbitrary number of polynomial inequalities. Instead of calculation of the grid nodes positions for a particular region, we perform all calculations for general polynomials given with indeterminate coefficients. The first advantage of this approach is that the calculations can be performed only once and then used to generate grids on arbitrary regions and of arbitrary mesh size with constant computational costs. The second advantage of our algorithm is the avoidance of singularities, which occur while using the existing algebraic grid generation methods and lead to the intersection of grid lines. All symbolic calculation can be performed with general purpose Computer Algebra Systems, and expressions obtained in this way can be translated in Java/C++ code. [ABSTRACT FROM AUTHOR]

The stability of cylindrical precession of the dynamically symmetric satellite in the Newtonian gravitational field is studied. We consider the case when a center of mass of the satellite moves in an elliptic orbit, while the satellite rotates uniformly about the axis of its dynamical symmetry that is perpendicular to the orbit plane. In the case of the resonance 3:2 (Mercury type resonance) we have found the domains of instability of cylindrical precession of the satellite in the Liapunov sense and domains of its linear stability in the parameter space. Using the infinite determinant method we have calculated analytically the boundaries of the domains of instability as power series in the eccentricity of the orbit. All the calculations have been done with the computer algebra system Mathematica. [ABSTRACT FROM AUTHOR]

We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations. [ABSTRACT FROM AUTHOR]

We consider a special case of the Euler-Poisson system describing the motion of a rigid body with a fixed point. It is the autonomous ODE system of sixth order with one parameter. Among the stationary points of the system we select two one-parameter families with resonance (0,0,λ,-λ,2λ,-2λ) of eigenvalues of the matrix of the linear part. For the stationary points, we compute the resonant normal form of the system using a program based on the MATHEMATICA package. Our results show that in cases of the existence of an additional first integral of the system its normal form is degenerate. So we assume that the integrability of a system can be checked through its normal form. [ABSTRACT FROM AUTHOR]

Some algorithmic properties are obtained related with the computation of the elementary divisors and a set of canonical generators of a finite abelian group, this properties are based on Gröbner bases techniques used as a theoretical framework. As an application a new algorithm for computing the structure of the abelian group is presented. [ABSTRACT FROM AUTHOR]

We present an OBDD-based Computer Algebra system for relational algebra, called RelView. After a short introduction to the OBDD-implementation of relations and the system, we exhibit its application by presenting two typical examples. [ABSTRACT FROM AUTHOR]

The symbolic-numeric program SELFA for solving the the 2D boundary-value problem in self-consistent basis method is presented. The corresponding algorithm of this program using a conventional pseudocode is described too. As example, the energy spectrum and wave functions of E-type for generalized Henon-Heiles Hamiltonian were obtained. [ABSTRACT FROM AUTHOR]

We describe an algorithm for computing the zero-th and the first Betti numbers of the union of n simply connected compact semi-algebraic sets in , where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n3). We also describe an implementation of this algorithm in the particular case of arrangements of ellipsoids in and describe some of our results. [ABSTRACT FROM AUTHOR]

We present an approach to construct all the regular solutions of systems of linear ordinary differential equations using the desingularization algorithm of Abramov & Bronstein (2001) as an auxiliary tool. A similar approach to find all the solutions with entries in C(z) [log z] is presented as well, together with a new hybrid method for constructing the denominator of rational and logarithmic solutions. [ABSTRACT FROM AUTHOR]