Extending maple capabilities for solving and displaying inequalities

Abstract

Solving inequalities is a very important topic in computational algebra. This paper presents a new Maple package, IneqGraphics, for displaying the two-dimensional solution sets of several inequalities of real variables. The package also deals with inequalities involving complex variables by displaying the corresponding solutions on the complex plane. The package provides graphical solutions to many inequalities (such as those involving polynomial, rational, logarithmic, exponential and trigonometric functions) that cannot be solved by using the standard Maple commands, which are basically reduced to linear inequalities. In addition, our outputs are consistent with Maple's notation and results in the sense that the package provides a similar output for those cases that can also be solved with Maple. To show the performance of the package, several illustrative and interesting examples are described. © Springer-Verlag Berlin Heidelberg 2006.