Showing papers in "Journal of Symbolic Computation in 1997"

TL;DR: MAGMA as mentioned in this paper is a new system for computational algebra, and the MAGMA language can be used to construct constructors for structures, maps, and sets, as well as sets themselves.

TL;DR: A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented and the code is tested on several well-known partial differential equations from soliton theory.

TL;DR: An algorithm which converts a given Grobner basis of a polynomial ideal I to a Grobners basis of I with respect to another term order is presented.

TL;DR: This method solves the main problem in Beke's factorization method, which is the use of splitting fields and/or Grobner basis.

TL;DR: It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r( t) possesses rational parametrizations.

TL;DR: An implementation of the algorithm has been successfully applied to lattices up to dimension 40 and allows, for example, obtaining of generators for the automorphism group of the Leech lattice in less than 30 min on a HP 9000/730 workstation.

TL;DR: An overview is given over various methods combining elements of field theory, order theory, and logic that do not require a Boolean normal form computation for simplifying intermediate and final results of automatic quantifier elimination by elimination sets.

TL;DR: This paper shows how to write all common stability problems as quantifier-elimination problems, and develops a set of computer-algebra tools that allows us to find analytic solutions to simple stability problems in a few seconds, and to solve some interesting problems in from a few minutes to a few hours.

TL;DR: This paper considers dynamical systems described by polynomial differential equations subjected to constraints on control and system variables and shows how to formulate questions in the above framework which can be answered by quantifier elimination.

TL;DR: This paper presents a complete theoretical analysis of the rationality and unirationality of generalized offsets and characterizations for deciding whether the generalized offset to a hypersurface is parametric or it has two parametric components.

TL;DR: This paper shows how certain robust multi-objective feedback design problems can be reduced to quantifier elimination (QE) problems and how robust stabilization and robust frequency domain performance specifications can be reduction to systems of polynomial inequalities with suitable logic quantifiers.

TL;DR: Implicitization using moving conics yields more compact representations for the implicit equation than standard resultant techniques, and these compressed expressions may lead to faster evaluation algorithms.

TL;DR: Computational procedures for the solution of the task of partitioning the zeros of a real or complex polynomial into clusters and of determining their location and multiplicity for polynomials with coefficients of limited accuracy are derived.

TL;DR: An algorithm that uses an integral basis for computing L (D) for a suitably chosenD and shows how to construct a rational point onC2, which means defined without algebraic extensions, ofC2.

TL;DR: The author's elimination method for parametric linear programming is extended to the non-convex case by allowing arbitrary and?orcombinations of parametriclinear inequalities as constraints as constraints, and a new strategy for finding smaller elimination sets and thus smaller elimination trees is presented.

TL;DR: An efficient algorithm for computing optimal parametrizations of plane algebraic curves over an algebraic extension of least degree over the field of definition is presented and a classical theorem of Hilbert and Hurwitz about birational transformations is generalized.

TL;DR: It is proved that this semi algorithm is an algorithm, i.e. that it always terminates, unless it is given a problem containing a counterexample to Schanuel?s conjecture.

TL;DR: The notion of exponential parts is introduced to give a description of factorization properties and to characterize the formal solutions of linear differential equations with formal power series coefficients.

TL;DR: This work investigates for which ideals inRx1,?,xn and admissible orders the formation of leading monomial ideals commutes with the homomorphism from K to K.

TL;DR: This work presents a procedure for proof by test set induction which is refutationally complete for a larger class of specifications than has been shown in previous work.

TL;DR: An approach to computing the Darboux polynomials required in the Prelle?Singer algorithm is presented which avoids algebraic extensions of the constant field, and a partial implementation in REDUCE is described in which the leading terms of the poynomials are obtained by a modified version of the method described by Christopher and Collins.

TL;DR: This work reports on a technique developed to enhance a class of constructive geometric constraint solvers with the capability of managing functional relationships between dimension variables that is shown to be correct.

TL;DR: A new algorithm with excellent performance is presented, investigating the complexity of such computations, indicating relationships with NP-complete problems, and describing new heuristics which perform well in practice.

TL;DR: Two methods of computing with complex algebraic numbers are presented, the first uses isolating rectangles to distinguish between the roots of the minimal polynomial, the second uses validated numeric approximations.

TL;DR: New algorithms computing the implicit equation of a parametric plane curve and several classes of parametric surfaces in the three dimensional euclidean space are presented.

TL;DR: It is shown how the MAPLE package diffgrob2 can be used to analyse overdetermined systems of PDE to find classical symmetries of differential equations of mathematical and physical interest.

TL;DR: An algorithm is described which computes the class group and the unit group of a general number field, and solves the principal ideal problem, and performs well in practice.

TL;DR: The solution to both problems is given here by a simple algorithm, requiring essentially just a gcd computation and a parametrization of a real line or circle.

TL;DR: A lower bound for the minimum distance between two zeros of a polynomial system is given in terms of the distance offto a variety of ill-posed problems.

TL;DR: Two polynomial time algorithms for determining a Grobner basis, relative to an arbitrary term order, of solutions of the congruence, and, in particular, for finding its minimal element are given.