Computing multihomogeneous resultants using straight-line programs

Authors:
Gabriela Jeronimo;Juan Sabia
Affiliations:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina;Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Venue:
Journal of Symbolic Computation
Year:
2007

Citing 11
Cited 7

Parallel arithmetic computations: a survey

Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
On the Newton Polytope of the Resultant

Journal of Algebraic Combinatorics: An International Journal
A product-decomposition bound for Bezout numbers

SIAM Journal on Numerical Analysis
Matrices in elimination theory

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
A subdivision-based algorithm for the sparse resultant

Journal of the ACM (JACM)
Deformation techniques for efficient polynomial equation solving

Journal of Complexity
An Efficient Algorithm for the Sparse Mixed Resultant

AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Sparse Resultant under Vanishing Coefficients

Journal of Algebraic Combinatorics: An International Journal
Multihomogeneous resultant formulae by means of complexes

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
The Computational Complexity of the Chow Form

Foundations of Computational Mathematics
Algebraic Complexity Theory

Algebraic Complexity Theory

Multihomogeneous resultant formulae for systems with scaled support

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
A parametric representation of totally mixed Nash equilibria

Computers & Mathematics with Applications
The multivariate resultant is NP-hard in any characteristic

MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): Algorithms and complexity

Journal of Symbolic Computation
Multihomogeneous resultant formulae for systems with scaled support

Journal of Symbolic Computation
On the complexity of the multivariate resultant

Journal of Complexity
Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new algorithm for the computation of resultants associated with multihomogeneous (and, in particular, homogeneous) polynomial equation systems using straight-line programs. Its complexity is polynomial in the number of coefficients of the input system and the degree of the resultant computed.