Introduction to the Maple Power Tool Intpakx

Abstract

The Maple Power Tool intpakX [24] de nes 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, 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 zeroes (Interval Newton Me- thod) with the possibility to find all zeroes 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. The source code (about 2000 lines of Maple{code) of the extension intpakX is freely available [23].