Methods and applications of error-free computation
Methods and applications of error-free computation
Multiprecision integer division examples using arbitrary radix
ACM Transactions on Mathematical Software (TOMS)
Bounded parallelism in computer algebra
Bounded parallelism in computer algebra
Theory of linear and integer programming
Theory of linear and integer programming
Structure and interpretation of computer programs
Structure and interpretation of computer programs
Gaussian elimination on hypercubes
Proceedings of the international workshop on Parallel algorithms & architectures
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Exact Solution of Systems of Linear Equations with Polynomial Coefficients
Journal of the ACM (JACM)
Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations
ACM Transactions on Mathematical Software (TOMS)
Gaussian Elimination on Message Passing Architecture
Proceedings of the 1st International Conference on Supercomputing
A critical-pair/completion algorithm for finitely generated ideals in rings
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
PAC: first experiments on a 128 transputers méganode
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Parallel lattice basis reduction
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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PAC is a computer algebra system, based on MIMD type parallelism. It uses parallelism as a tool for processing problems wich are too complex for a sequential treatment. Basic fundamentals of the system are firstly discussed. Then, different problems are studied, particularly the implementation of infinite-precision arithmetic, the solution of linear systems and of Diophantine equations, the parallelization of Buchberger's algorithm for Gröbner bases.A prototype of PAC is implemented on the Floating Point System hypercube Tesseract 20 (16 nodes), and different timing results obtained on this machine are given.