On the complexity of solving bivariate systems: the case of non-singular solutions

Authors:
Romain Lebreton;Esmaeil Mehrabi;Eric Schost
Affiliations:
Universite de Montpellier II, Montpellier, France;Western University, London, ON, Canada;Western University, London, ON, Canada
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

Citing 25
Cited 0

Ideal Bases and Primary Decomposition: Case of Two Variables

Journal of Symbolic Computation
From algebraic sets to monomial linear bases by means of combinatorial algorithms

Proceedings of the 4th conference on Formal power series and algebraic combinatorics
A new polynomial factorization algorithm and its implementation

Journal of Symbolic Computation
Asymptotically fast computation of subresultants

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fast rectangular matrix multiplication and applications

Journal of Complexity
Modern computer algebra

Modern computer algebra
On the theories of triangular sets

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Fast Algorithms for Manipulating Formal Power Series

Journal of the ACM (JACM)
Using Galois ideals for computing relative resolvents

Journal of Symbolic Computation - Algorithmic methods in Galois Theory
A Gröbner free alternative for polynomial system solving

Journal of Complexity
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
Change of order for bivariate triangular sets

Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Change of order for regular chains in positive dimension

Theoretical Computer Science
Topology of real algebraic space curves

Journal of Symbolic Computation
Solving structured linear systems with large displacement rank

Theoretical Computer Science
On the asymptotic and practical complexity of solving bivariate systems over the reals

Journal of Symbolic Computation
Fast arithmetic for triangular sets: From theory to practice

Journal of Symbolic Computation
Computations modulo regular chains

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
On solving systems of bivariate polynomials

ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Real solving of bivariate polynomial systems

CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Multiplying matrices faster than coppersmith-winograd

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fast Polynomial Factorization and Modular Composition

SIAM Journal on Computing
On the complexity of computing with zero-dimensional triangular sets

Journal of Symbolic Computation
On the complexity of solving a bivariate polynomial system

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give an algorithm for solving bivariate polynomial systems over either k(T)[X,Y] or Q[X,Y] using a combination of lifting and modular composition techniques.