Computer Algebra and Parallelism: Second International Workshop Ithaca, USA, May 9–11, 1990 Proceedings

✍ Scribed by Wolfgang Küchlin (auth.), Richard E. Zippel (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1992
• Tongue: English
• Leaves: 120
• Series: Lecture Notes in Computer Science 584
• Edition: 1
• Category: Library

✦ Synopsis

This book contains papers presented at a workshop on the use of parallel techniques in symbolic and algebraic computation held at Cornell University in May 1990. The eight papers in the book fall into three groups. The first three papers discuss particular programming substrates for parallel symbolic computation, especially for distributed memory machines. The next three papers discuss novel ways of computing with elements of finite fields and with algebraic numbers. The finite field technique is especially interesting since it uses the Connection Machine, a SIMD machine, to achievesurprising amounts of parallelism. One of the parallel computing substrates is also used to implement a real root isolation technique. One of the crucial algorithms in modern algebraic computation is computing the standard, or Gr|bner, basis of an ideal. The final two papers discuss two different approaches to speeding their computation. One uses vector processing on the Cray and achieves significant speed-ups. The other uses a distributed memory multiprocessor and effectively explores the trade-offs involved with different interconnect topologies of the multiprocessors.

✦ Table of Contents

The S-threads environment for parallel symbolic computation....Pages 1-18
Algebraic computing on a local net....Pages 19-31
An environment for parallel algebraic computation....Pages 33-50
Finite field arithmetic using the connection machine....Pages 51-61
Embarrassingly parallel algorithms for algebraic number arithmetic — and some less trivial issues....Pages 63-70
Parallel real root isolation using the coefficient sign variation method....Pages 71-87
Very large Gröbner basis calculations....Pages 89-99
Boolean Gröbner bases and their MIMD implementation....Pages 101-114

✦ Subjects

Symbolic and Algebraic Manipulation; System Performance and Evaluation; Algorithms; Numerical Analysis; Algorithm Analysis and Problem Complexity; Algebra