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)
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)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm
Communications of the ACM
Solutions of systems of polynomial equations by elimination
Communications of the ACM
ACM '73 Proceedings of the ACM annual conference
The exact solution of systems of linear equations with polynomial coefficients
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
Algorithm 628: An algorithm for constructing canonical bases of polynomial ideals
ACM Transactions on Mathematical Software (TOMS)
Analytical Optimization Using Computer Algebraic Manipulation
ACM Transactions on Mathematical Software (TOMS)
Analytically Solving Integral Equations by Using Computer Algebra
ACM Transactions on Mathematical Software (TOMS)
Solving systems of algebraic equations
ACM SIGSAM Bulletin
On solving systems of algebraic equations via ideal bases and elimination theory
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
ACM SIGSAM Bulletin
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Methods for finding numerical solutions of nonlinear algebraic systems of equations have been given considerable attention since the birth of the field of numerical analysis. The fact that these methods find many applications to problems in physics, engineering, economics, and mathematical theory of optimization cannot be overstressed. However, a significant number of these problems contain indeterminants or parameters, which should only be given numerical values at the very end of the computational processes. Sometimes numerical results simply cannot provide enough insight for the analysis of the problem. Furthermore, symbolic solutions via elimination theory provide not only all solutions to a given system of equations but also a classification of solutions into solution surfaces or parametrized solutions. Thus, the symbolic method can provide an infinite number of solutions where this feat is clearly impossible for the numerical methods.