Using Strassen's algorithm to accelerate the solution of linear systems
The Journal of Supercomputing
AXIOM: the scientific computation system
AXIOM: the scientific computation system
Algorithms for computer algebra
Algorithms for computer algebra
A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Modern computer algebra
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Practical fast polynomial multiplication
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
The truncated fourier transform and applications
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The Middle Product Algorithm I
Applicable Algebra in Engineering, Communication and Computing
Architecture-aware classical Taylor shift by 1
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Half-GCD and fast rational recovery
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Triangular decompositions of polynomial systems: from theory to practice
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Multithreaded parallel implementation of arithmetic operations modulo a triangular set
Proceedings of the 2007 international workshop on Parallel symbolic computation
Change of order for regular chains in positive dimension
Theoretical Computer Science
On the Virtues of Generic Programming for Symbolic Computation
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
The modpn library: bringing fast polynomial arithmetic into MAPLE
ACM Communications in Computer Algebra
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic Computation
Spiral-generated modular FFT algorithms
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
The modpn library: Bringing fast polynomial arithmetic into Maple
Journal of Symbolic Computation
Efficient implementation of polynomial arithmetic in a multiple-level programming environment
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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Though there is increased activity in the implementation of asymptotically fast polynomial arithmetic, little is reported on the details of such effort. In this paper, we discuss how we achieve high performance in implementing some well-studied fast algorithms for polynomial arithmetic in two high-level programming environments, AXIOM and Aldor.Two approaches are investigated. With Aldor we rely only on high-level generic code, whereas with AXIOM we endeavor to mix high-level, middle-level and low-level specialized code. We show that our implementations are satisfactory compared with other known computer algebra systems or libraries such as Magma v2.11-2 and NTL v5.4.