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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.
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 $).
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).
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.
Portable Standard LISP (PSL) is a portable implementation of the programming language LISP constructed at the University of Utah. The version 3.4 of PSL was implemented for CRAY X-MP computers by Konrad Zuse-Zentrum Berlin; this implementation is based to an important part on the earlier implementation of PSL 3.2 at Salt Lake City, Los Alamos and Mendota Heights.
This guide describes the CRAY/COS REDUCE distribution tape and the procedures for installing, testing and maintaining REDUCE on a CRAY 1 or CRAY X-MP running COS. 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.
This document describes operating procedures for running REDUCE specific to the CRAY 1 and CRAY X-MP computers running the CRAY Operating System (COS). 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).
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.
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.
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).
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.
Automatic Generation of Reaction Mechanisms for Description of Oxidation of Higher Hydrocarbons.
(1990)
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.
Portable Standard LISP (PSL) is a portable implementation of the programming language LISP constructed at the University of Utah. The version 3.4 of PSL was implemented for CRAY X-MP computers by Konrad-Zuse-Zentrum Berlin; this implementation is based to an important part on the earlier implementation of PSL 3.2 at the University of Utah, Los Alamos National Laboratories and CRAY Research Inc. at Mendota Heights. During the work on implementing PSL the language LISP was investigated for areas which can be supported by vector hardware. One area was found in the COMMON LISP sequence functions and some typical application areas of LISP programming can be improved by vector processing too. A model for the implementation of vector instructions in LISP was developed. For arithmetic an experimental vectorizing extent of the PSL compiler was constructed. With this means full vector hardware capacity can become available for LISP applications.
Portable Standard LISP (PSL), a dialect of LISP developed at the University of Utah, has been implemented and optimized for the CRAY 1 and CRAY X-MP supercomputers. This version uses a new implementation technique that permits a step-by-step development of the PSL kernel. The initial CRAY version was acceptable, although the execution speed of the PSL was not as fast as had been anticipated. CRAY-specific optimizations were undertaken that in some cases provided a ten-fold speed improvement, resulting in a fast LISP implementation.
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.
Gröbner 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 Gröbner 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.