An Approach for Solving Systems of Parametric Polynomial Equations
Deepak Kapur · 1995
An approach for solving nonlinear polynomial equations involving parameters is proposed. A distinction is made between parameters and variables. The objective is to generate from a system of parametric equations, solved forms from which solutions for specific values of parameters can be obtained without much additional computations. It should be possible to analyze the parametrized solved forms so that it can be determined for different parameter values whether there are infinitely many solutions, finitely many solutions, or no solutions at all. The approach is illustrated for two different symbolic methods for solving parametric equations -- Grobner basis computations and characteristic set computations. These methods are illustrated on a number of examples. 1.2 Introduction Many complex phenomena can be modeled using nonlinear polynomial equations. Examples include imaging transformations in computer vision, computing geometric invariants, geometric and solid modeling, constraint-b...