@misc{MelenkNeun, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4539}, number = {TR-88-02}, abstract = {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).}, language = {en} } @misc{MelenkNeun, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4541}, number = {TR-88-03}, abstract = {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.}, language = {en} } @misc{MelenkNeun, author = {Melenk, Herbert and Neun, Winfried}, title = {Parallel Polynomial Operations in the Buchberger Algorithm.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-125}, number = {SC-88-04}, abstract = {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).}, language = {en} } @misc{MelenkMoellerNeun, author = {Melenk, Herbert and M{\"o}ller, H. Michael and Neun, Winfried}, title = {Symbolic Solution of Large Stationary Chemical Kinetics Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-157}, number = {SC-88-07}, abstract = {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.}, language = {en} } @misc{NeunMelenk, author = {Neun, Winfried and Melenk, Herbert}, title = {Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93}, number = {SC-88-01}, abstract = {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 Gr{\"o}bner 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.}, language = {en} } @misc{MelenkMoellerNeun, author = {Melenk, Herbert and M{\"o}ller, H. Michael and Neun, Winfried}, title = {On Gr{\"o}bner Bases Computation on a Supercomputer Using REDUCE.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-107}, number = {SC-88-02}, abstract = {Gr{\"o}bner bases are the main tool for solving systems of algebraic equations and some other problems in connection with polynomial ideals using Computer Algebra Systems. The procedure for the computation of Gr{\"o}bner bases in REDUCE 3.3 has been modified in order to solve more complicated algebraic systems of equations by some general improvements and by some tools based on the specific resources of the CRAY X-MP. We present this modification and illustrate it by examples.}, language = {en} }