Feedback control systems (3rd ed.)
Feedback control systems (3rd ed.)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A generic projection operator for partial cylindrical algebraic decomposition
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Complexity of the resolution of parametric systems of polynomial equations and inequations
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving parametric polynomial systems
Journal of Symbolic Computation
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A new Maple package for solving parametric systems of polynomial equations and inequalities is described. The main idea for solving such a system is as follows. The parameter space Rd is divided into two parts: the discriminant variety W and its complement RdnW. The discriminant variety is a generalization of the well-known discriminant of a univariate polynomial and contains all those parameter values leading to non-generic solutions of the system. The complement RdnW can be expressed as a finite union of open cells such that the number of real solutions of the input system is constant on each cell. In this way, all parameter values leading to generic solutions of the system can be described systematically. The underlying techniques used are Gröbner bases, polynomial real root finding, and cylindrical algebraic decomposition. This package offers a friendly interface for scientists and engineers to solve parametric problems, as illustrated by an example from control theory.