On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
Simple multivariate polynomial multiplication
Journal of Symbolic Computation
A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Modern computer algebra
Introduction to Algorithms
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
Architecture-aware classical Taylor shift by 1
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Multivariate power series multiplication
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
High-performance implementations of the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Efficient implementation of polynomial arithmetic in a multiple-level programming environment
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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
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
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Fast arithmetics in artin-schreier towers over finite fields
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computations modulo regular chains
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Balanced dense polynomial multiplication on multi-cores
ACM Communications in Computer Algebra
The modpn library: Bringing fast polynomial arithmetic into Maple
Journal of Symbolic Computation
Homotopy techniques for multiplication modulo triangular sets
Journal of 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
Algorithms for computing triangular decomposition of polynomial systems
Journal of Symbolic Computation
Fast arithmetics in Artin-Schreier towers over finite fields
Journal of Symbolic Computation
Hi-index | 0.00 |
We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean division, we obtain theoretical and practical improvements over a direct recursive approach; for a family of special cases, we reach quasi-linear complexity. The main outcome we have in mind is the acceleration of higher-level algorithms, by interfacing our low-level implementation with languages such as AXIOM or Maple We show the potential for huge speed-ups, by comparing two AXIOM implementations of van Hoeij and Monagan's modular GCD algorithm.