Eurocal ’87: European Conference on Computer Algebra Leipzig, GDR, June 2–5, 1987 Proceedings

R. N. Fedorova, V. P. Gerdt, N. N. Govorun, V. P. Shirikov (auth.), James H. Davenport (eds.)3540515178, 9783540515173, 0387515178

This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations – one thread of the conference was devoted to polynomial algorithms – or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry – a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations.

---

Table of contents :
Computer algebra in physical research of jinr….Pages 1-10
Complexity of quantifier elimination in the theory of ordinary differential equations….Pages 11-25
Groups and polynomials….Pages 26-33
Symbolic computation in relativity theory….Pages 34-43
A zero structure theorem for polynomial-equations-solving and its applications….Pages 44-44
Some algorithms of rational function algebra….Pages 45-47
The computer algebra system simath….Pages 48-49
Converting SAC-2 code to lisp….Pages 50-51
Computer algebra system for continued fractions manipulation….Pages 52-53
Computing a lattice basis from a system of generating vectors….Pages 54-63
Expression optimization using high-level knowledge….Pages 64-70
Catfact: Computer algebraic tools for applications of catastrophe theory….Pages 71-80
Computer algebra application for investigating integrability of nonlinear evolution systems….Pages 81-92
Computer classification of integrable seventh order MKdV — Like equations….Pages 93-94
Symbolic computation and the finite element method….Pages 95-96
Application of lie group and computer algebra to nonliner mechanics….Pages 97-106
Hierarchical symbolic computations in the analysis of large-scale dynamical systems….Pages 107-115
Schoonschip for computing of gravitino interaction cross sections in N=2 supergravity….Pages 116-117
Creation of efficient symbolic-numeric interface….Pages 118-119
Automatic generation of FORTRAN-Coded Jacobians and Hessians….Pages 120-131
Laplace transformations in reduce 3….Pages 132-133
Reduce 3. 2 on iAPX86/286 — based personal computers….Pages 134-135
Some extensions and applications of reduce system….Pages 136-137
Infinite structures in scratchpad II….Pages 138-148
Application of a structured LISP system to computer algebra….Pages 149-160
Number-theoretic transforms of prescribed length….Pages 161-162
A hybrid algebraic-numeric system ANS and its preliminary implementation….Pages 163-171
The calculation of QCD triangular Feynman graphs in the external gluonic field using reduce-2 system….Pages 172-173
Computer algebra application for determining local symmetries of differential equations….Pages 174-175
Trace calculations for gauge theories on a personal computer….Pages 176-177
Evaluation of plasma fluid equations collision integrals using reduce….Pages 178-178
Computerized system of analytic transformations for analysing of differential equations….Pages 179-185
Integral equation with hidden eigenparameter solver: Reduce + fortran in tandem….Pages 186-191
Combinatorial aspects of simplification of algebraic expressions….Pages 192-201
Dynamic program improvement….Pages 202-203
Computer algebra and numerical convergence….Pages 204-205
Computer algebra and computation of puiseux expansions of algebraic functions….Pages 206-207
Boundary value problems for the laplacian in the Euclidean space solved by symbolic computation….Pages 208-215
The methods for symbolic evaluation of determinants and their realization in the planner-analytic system….Pages 216-222
Transformation of computation formulae in systems of recurrence relations….Pages 223-224
“Dimreg” the package for calculations in the dimensional regularization with 4-dimensional γ 5 -matrix in quantum field theory….Pages 225-232
CTS — Algebraic debugging system for reduce programs….Pages 233-243
Applications of computer algebra in solid modelling….Pages 244-245
Implementation of a geometry theorem proving package in SCRATCHPAD II….Pages 246-257
Collision of convex objects….Pages 258-259
Solving algebraic equations via Buchberger’s algorithm….Pages 260-269
Primary ideal decomposition….Pages 270-281
Solving systems of algebraic equations by using gröbner bases….Pages 282-292
Properties of Gröbner bases under specializations….Pages 293-297
The computation of polynomial greatest common divisors over an algebraic number field….Pages 298-299
An extension of buchberger’s algorithm to compute all reduced gröbner bases of a polynomial ideal….Pages 300-310
Singularities of moduli spaces….Pages 311-312
Radical simplification using algebraic extension fields….Pages 313-314
Hermite normal forms for integer matrices….Pages 315-316
Mr. Smith goes to Las Vegas: Randomized parallel computation of the Smith Normal form of polynomial matrices….Pages 317-322
Fonctions symétriques et changements de bases….Pages 323-332
Complexity of standard bases in projective dimension zero….Pages 333-335
Gröbner bases for polynomial ideals over commutative regular rings….Pages 336-347
Some algebraic algorithms based on head term elimination over polynomial rings….Pages 348-354
Algorithmic determination of the jacobson radical of monomial algebras….Pages 355-364
A recursive algorithm for the computation of the hilbert polynomial….Pages 365-375
An affine point of view on minima finding in integer lattices of lower dimensions….Pages 376-378
A combinatorial and logical approach to linear-time computability (extended abstract)….Pages 379-380
Complexity of computation of embedded resolution of algebraic curves….Pages 381-390
Polynomial factorisation: an exploration of Lenstra’s algorithm….Pages 391-402
A matrix-approach for proving inequalities….Pages 403-411
Using automatic program synthesizer as a problem solver: Some interesting experiments….Pages 412-423
Strong splitting rules in automated theorem proving….Pages 424-425
Towards a refined classification of geometric search and computation problems….Pages 426-437
Matrix Padé fractions….Pages 438-449
Computation of generalized Padé approximants….Pages 450-451
A critical pair criterion for completion modulo a congruence….Pages 452-453
Shortest paths of a disc inside a polygonal region….Pages 454-455
Rabin’s width of a complete proof and the width of a semialgebraic set….Pages 456-462
Practical aspects of symbolic integration over Q ( x )….Pages 463-464
Integration: Solving the Risch differential equation….Pages 465-467
Computation and simplification in lie fields….Pages 468-478
A package for the analytic investigation and exact solution of differential equations….Pages 479-490
An algorithm for the integration of elementary functions….Pages 491-497