The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm
Communications of the ACM
Letters to the editor: comment on a paper by Ku and Adler
Communications of the ACM
PM, a system for polynomial manipulation
Communications of the ACM
Solutions of systems of polynomial equations by elimination
Communications of the ACM
The SAC-1 system: An introduction and survey
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Integer arithmetic algorithms for polynomial real zero determination
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
The SAC-1 system: An introduction and survey
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Modular arithmetic and finite field theory: A tutorial
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
SIGCSE '73 Proceedings of the third SIGCSE technical symposium on Computer science education
A complete modular resultant algorithm targeted for realization on graphics hardware
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Parallel computation of bivariate polynomial resultants on graphics processing units
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Computing resultants on Graphics Processing Units: Towards GPU-accelerated computer algebra
Journal of Parallel and Distributed Computing
| Hi-index | 0.00 |
An efficient algorithm is presented for the exact calculation of resultants of multivariate polynomials with integer coefficients. The algorithm applies modular homomorphisms and the Chinese remainder theorem, evaluation homomorphisms and interpolation, in reducing the problem to resultant calculation for univariate polynomials over GF(p), whereupon a polynomial remainder sequence algorithm is used. The computing time of the algorithm is analyzed theoretically as a function of the degrees and coefficient sizes of its inputs . As a very special case , it is shown that when all degrees are equal and the coefficient size is fixed, its computing time is approximately proportional to &lgr;2r+l , where &lgr; is the common degree and r is the number of variables . Empirically observed computing times of the algorithm are tabulated for a large number of examples, and other algorithms are compared. Potential application of the algorithm to the solution of systems of polynomial equations is briefly discussed.