The Maple Power Tool intpakX

Walter Kr\"amer

University of Wuppertal
42119 Wuppertal, Germany

The package intpakX defines Maple types for real intervals and complex disc intervals. On the level of basic operations, intpakX includes the four basic arithmetic operators, including extended interval division as an extra function. Furthermore there are power, square, square root, logarithm and exponential functions, a set of standard functions and union and intersection. Reimplementations of the Maple construction, conversion and unapplication functions are available. Additionally, there is a range of operators for complex disc arithmetic.

As applications, verified computation of zeros (Interval Newton Method) with the possibility to find all zeros of a function on a specified interval, and range enclosure for real-valued functions of one or two variables are implemented, the latter using either interval evaluation or evaluation via the mean value form and adaptive subdivision of intervals. The user can choose between a non-graphical and a graphical version of the above algorithms displaying the resulting intervals of each iteration step.