Usage of modular techniques for efficient computation of ideal operations

Authors:
Kazuhiro Yokoyama
Affiliations:
Department of Mathematics, Rikkyo University, Toshima-ku, Tokyo, Japan
Venue:
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Year:
2012

Citing 13
Cited 1

A p-adic approach to the computation ofGröbner bases

Journal of Symbolic Computation
A modular method for Gro¨bner-basis construction over Q and solving system of algebraic equations

Journal of Information Processing
On lucky ideals for Gro¨bner basis computations

Journal of Symbolic Computation
On lucky primes

Journal of Symbolic Computation
Modern computer algebra

Modern computer algebra
A modular method to compute the rational univariate representation of zero-dimensional ideals

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Gröbner Trace Algorithms

ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Modular algorithms for computing Gröbner bases

Journal of Symbolic Computation
Sharp estimates for triangular sets

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
Multi-modular algorithm for computing the splitting field of a polynomial

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Parallelization of Modular Algorithms

Journal of Symbolic Computation
Bit-size estimates for triangular sets in positive dimension

Journal of Complexity

Gröbner bases of symmetric ideals

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Modular techniques are widely applied to various algebraic computations. (See [5] for basic modular techniques applied to polynomial computations.) In this talk, we discuss how modular techniques are efficiently applied to computation of various ideal operations such as Gröbner base computation and ideal decompositions. Here, by modular techniques we mean techniques using certain projections for improving the efficiency of the total computation, and by modular computations, we mean corresponding computations applied to projected images.