Solving Parametric Polynomial Equations and Inequalities by Symbolic Algorithms
نویسنده
چکیده
The talk gives a survey on some symbolic algorithmic methods for solving systems of algebraic equations with special emphasis on parametric systems. Besides complex solutions I consider also real solutions of systems including inequalities. The techniques described include the Euclidean algorithm, Grr obner bases, characteristic sets, univariate and multivariate Sturm-Sylvester theorems, comprehensive Grr obner bases and elimination methods for parametric optimization problems. Some examples illustrate the use of symbolic algorithms for the solution of parametric systems.
منابع مشابه
Numerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method
In this paper, we present some efficient numerical algorithm for solving system of fuzzy polynomial equations based on Newton's method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.
متن کاملGlobal optimization of mixed-integer polynomial programming problems: A new method based on Grobner Bases theory
Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...
متن کاملProgram Verification by Using DISCOVERER
Recent advances in program verification indicate that various verification problems can be reduced to semi-algebraic system (SAS for short) solving. An SAS consists of polynomial equations and polynomial inequalities. Algorithms for quantifier elimination of real closed fields are the general method for those problems. But the general method usually have low efficiency for specific problems. To...
متن کاملThe Posso Library for Polynomial System Solving
The PoSSo library is a sophisticated library of tools for solving systems of polynomial equations. Each tool is supplied as a framework, rather than as a traditional program library or as a self-contained package, providing a unusual level of exibility. Each framework consists of a collection of C++ classes, which allows the customisation of each tool. Customisation can happen either at compile...
متن کاملNumeric vs. symbolic homotopy algorithms in polynomial system solving: a case study
We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semilinear second order parabolic partial differential equations. We prove that this family is well–conditioned from the numeric point of view, and ill–conditioned from the symbolic point of view. We exhibit a polynomial–time numeric algorithm solving any m...
متن کامل