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
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international 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
On the complexities of multipoint evaluation and interpolation
Theoretical Computer Science
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
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 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
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An in-place truncated fourier transform and applications to polynomial multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Almost linear time operations with triangular sets
ACM Communications in Computer Algebra
On the complexity of computing with zero-dimensional triangular sets
Journal of Symbolic Computation
Inversion modulo zero-dimensional regular chains
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Algorithms for the universal decomposition algebra
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On the complexity of solving bivariate systems: the case of non-singular solutions
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Modular Composition Modulo Triangular Sets and Applications
Computational Complexity
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.