Resultant Procedure and the Mechanization of the Graeffe Process
Journal of the ACM (JACM)
Algebra of Polynomials in Several Variables for a Digital Computer
Journal of the ACM (JACM)
PM, a system for polynomial manipulation
Communications of the ACM
FORMAC an experimental formula manipulation Compiler
ACM '64 Proceedings of the 1964 19th ACM national conference
Syntax and Display of Mathematical Expressions
Syntax and Display of Mathematical Expressions
Hash-Coding Functions of a Complex Variable
Hash-Coding Functions of a Complex Variable
LISP 1.5 Programmer's Manual
Journal of Symbolic Computation
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm
Communications of the ACM
Survey of formula manipulation
Communications of the ACM
Kinematics in Robotics by the Morphogenetic Neuron
Computer Aided Systems Theory - EUROCAST 2001-Revised Papers
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algebraic simplification a guide for the perplexed
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On algorithms for solving systems of polynomial equations
ACM SIGSAM Bulletin
Problem #11: generation of Runge-Kutta equations
ACM SIGSAM Bulletin
Paper: Characterization of equilibrium sets for bilinear systems with feedback control
Automatica (Journal of IFAC)
Hi-index | 48.25 |
The elimination procedure as described by Williams has been coded in LISP and FORMAC and used in solving systems of polynomial equations. It is found that the method is very effective in the case of small systems, where it yields all solutions without the need for initial estimates. The method, by itself, appears inappropriate, however, in the solution of large systems of equations due to the explosive growth in the intermediate equations and the hazards which arise when the coefficients are truncated. A comparison is made with difficulties found in other problems in non-numerical mathematics such as symbolic integration and simplification.