AXIOM: the scientific computation system
AXIOM: the scientific computation system
Modern computer algebra
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Implementation techniques for fast polynomial arithmetic in a high-level programming environment
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
Open source computer algebra systems: Axiom
ACM Communications in Computer Algebra
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
Towards parallel general-size library generation for polynomial multiplication
ACM Communications in Computer Algebra
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The purpose of this study is to investigate implementation techniques for polynomial arithmetic in a multiple-level programming environment. Indeed, certain polynomial data types and algorithms can further take advantage of the features of lower level languages, such as their specialized data structures or direct access to machine arithmetic. Whereas, other polynomial operations, like Gröbner basis over an arbitrary field, are suitable for generic programming in a high-level language. We are interested in the integration of polynomial data type implementations realized at different language levels, such as Lisp, C and Assembly. In particular, we consider situations for which code from different levels can be combined together within the same application in order to achieve high-performance. We have developed implementation techniques in the multiple-level programming environment provided by the computer algebra system AXIOM. For a given algorithm realizing a polynomial operation, available at the user level, we combine the strengths of each language level and the features of a specific machine architecture. Our experimentations show that this allows us to improve performances of this operation in a significant manner.