On the multi-threaded computation of integral polynomial greatest common divisors
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
An analysis of dag-consistent distributed shared-memory algorithms
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Modern computer algebra
Parallel Multiplication in GF(2^k) usingPolynomial Residue Arithmetic
Designs, Codes and Cryptography
On computer-assisted classification of coupled integrable equations
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Parallel Computation of Modular Multivariate Polynominal Resultants on a Shared Memory Machine
CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing
The truncated fourier transform and applications
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Architecture-aware classical Taylor shift by 1
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Parallel Montgomery Multiplication in GF (2^k) Using Trinomial Residue Arithmetic
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Implementation techniques for fast polynomial arithmetic in a high-level programming environment
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Automatic inversion generates divide-and-conquer parallel programs
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Multiprocessed parallelism support in ALDOR on SMPs and multicores
Proceedings of the 2007 international workshop on Parallel symbolic computation
Component-level parallelization of triangular decompositions
Proceedings of the 2007 international workshop on Parallel symbolic computation
Proceedings of the 2007 international workshop on Parallel symbolic computation
On the Virtues of Generic Programming for Symbolic Computation
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Efficient implementation of polynomial arithmetic in a multiple-level programming environment
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Component-level parallelization of triangular decompositions
Proceedings of the 2007 international workshop on Parallel symbolic computation
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Parallel sparse polynomial division using heaps
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
FFT-based dense polynomial arithmetic on multi-cores
HPCS'09 Proceedings of the 23rd international conference on High Performance Computing Systems and Applications
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We discuss the parallelization of arithmetic operations on polynomials modulo a triangular set. We focus on parallel normal form computations since this is a core subroutine in many high-level algorithms, such as triangular decompositions of polynomial systems. When computing modulo a triangular set, multivariate polynomials are regarded recursively as univariate ones, which leads to several implementation challenges when one targets highly efficient code. We rely on an algorithm proposed in [17] which addresses some of these issues. We propose a two-level parallel scheme. First, we make use of parallel multidimensional Fast Fourier Transform in order to perform multivariate polynomial multiplication. Secondly, we extract parallelism from the structure of the sequential normal form algorithm of [17]. We have realized a multithreaded implementation. We report on different strategies for the management of tasks and threads.