TY - GEN A1 - Melenk, Herbert T1 - The Complexity Barrier in REDUCE - a Case Study. N2 - The power of the symbolic math system {\small REDUCE} for solving large and difficult problems in science and engineering is demonstrated by a set of model problems. These include algebraic equation solving, formal variable elimination, formal power series, symbolic treatment of differential equations and applications from theoretical physics. T3 - ZIB-Report - TR-94-06 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5119 ER - TY - GEN A1 - Melenk, Herbert T1 - Algebraic Solution of Nonlinear Equation Systems in REDUCE. N2 - The strategy for solving nonlinear equation systems automatically in the computer algebra system REDUCE is described. Kernel of the solver is a factoring Buchberger algorithm. Pre -- and postprocessors enable the use of the Gröbner techniques in a black box manner. In addition to polynomials equations with surds, trigonometric functions and separable transcendental functions are covered. T3 - ZIB-Report - TR-93-02 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4944 ER - TY - GEN A1 - Caprasse, H. A1 - Demaret, J. A1 - Gatermann, Karin A1 - Melenk, Herbert T1 - Power-Law Type Solutions of Fourth-Order Gravity N2 - We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension $ d = 3 $ , the Einsteinian Kasner metric is still the most general power-law type solution, for $ d > 3 $ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the $ d $-dimensional space into a ( $ d - 3 $)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when $ d = 9 $). T3 - ZIB-Report - SC-90-18 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-466 ER - TY - GEN A1 - Chevalier, C. A1 - Melenk, Herbert A1 - Warnatz, J. T1 - Automatic Generation of Reaction Mechanisms for Description of Oxidation of Higher Hydrocarbons. N2 - Oxidation mechanisms even for rather simple hydrocarbons like heptane consist due to the occurrence of many isomeric structures of thousands of reactions of hundreds of species. The automatic generation of these reaction mechanisms using artificial intelligence means is described. Results are presented for n-heptane-air mixtures, where a hand-written reaction mechanism tested against experimental data is available. T3 - ZIB-Report - SC-90-08 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-361 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - Implementation of Portable Standard LISP for the SPARC Processor. N2 - The SPARC processor is a RISC (Reduced Instruction Set Computer) microcomputer, built into the SUN4 workstations. Since RISC processors are very well-suited for LISP processing, the implementation of a dialect of LISP (Portable Standard LISP, PSL) boded well for a great speed-up in comparison with other types of microcomputers. A first approach was done at The RAND Corporation in Santa Monica, which was derived from classical processor types like MC68000 or VAX. At the Konrad- Zuse-Zentrum für Informationstechnik Berlin (ZIB) that initial implementation was redesigned in order to adapt PSL to the specific features of the SPARC processor. The present implementation, in some parts, is very close to Cray PSL version also done in ZIB. Some timing informations are given in the appendix. T3 - ZIB-Report - TR-89-06 Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4625 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3. N2 - This document describes operating procedures for running REDUCE specific to the CRAY 1 and CRAY X-MP computers running the Operating System UNICOS. The document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L. R. Seward, The Rand Corporation, Santa Monica, (CP85). T3 - ZIB-Report - TR-88-02 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4539 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3. N2 - This guide describes the CRAY/UNICOS REDUCE distribution tape and the procedures for installing, testing and maintaining REDUCE on a CRAY 1 or CRAY X-MP running UNICOS. This document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L.R. Seward, The Rand Corporation, Santa Monica, publication CP84. T3 - ZIB-Report - TR-88-03 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4541 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - Parallel Polynomial Operations in the Buchberger Algorithm. N2 - The Buchberger algorithm is a basic tool for the solution of systems of polynomial equations in an environment of computer algebra applications. A model for overlapped processing of different steps of the algorithm is presented, which uses the data structure of the polynomials (distributive representation) for synchronization. The model can be applied for multi processors with fast access to shared data. It is tested with Cray X-MP multi processors based on a parallel version of Portable Standard Lisp (PSL 3.4). T3 - ZIB-Report - SC-88-04 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-125 ER - TY - GEN A1 - Melenk, Herbert A1 - Möller, H. Michael A1 - Neun, Winfried T1 - Symbolic Solution of Large Stationary Chemical Kinetics Problems. N2 - The paper presents a new application of computer algebra to the treatment of steady states of reaction systems. The method is based on the Buchberger algorithm. This algorithm was modified such that it can exploit the special structure of the equations derived from reaction systems, so even large systems can be handled. In contrast to numerical approximation techniques, the algebraic solution gives a complete and definite overview of the solution space and it is even applicable when parameter values are unknown or undetermined. The algorithm, its adaptation to the problem class and its application to selected examples are presented. T3 - ZIB-Report - SC-88-07 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-157 ER - TY - GEN A1 - Neun, Winfried A1 - Melenk, Herbert T1 - Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor. N2 - Portable Standard LISP (PSL, Version 3.4) and REDUCE 3 were implemented for CRAY1 and Cray X- MP computers at the Konrad-Zuse-Zentrum Berlin in 1986. As an special aspect of the implementation of PSL, an interface to the vector hardware of CRAY processors was defined. With that interface and mostly driven by the needs of REDUCE applications (e.g. extensive calculations of Gröbner bases), the arbitrary precision integer arithmetic of PSL was rebuild using full power of the vector hardware. A modular arithmetic using vector hardware was also constructed. T3 - ZIB-Report - SC-88-01 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93 ER -