Introduction

Introduction

APU stands for Algebraic Programming Utilities and that is precisely what it provides - a collection of special-purpose C++ utilities which can be used for implementing algorithms involving polynomial equations and inequalities . APU can be used in two ways : as a stand-alone developmental platform which can be used to develop C++ application code or in conjunction with a computer algebra package like Maple to solve specific problems without necessarily developing application code.

The kinds of problems that APU can be used for are :

• Basic algebraic algorithms. Though APU provides a collection of basic routines like Sylvester resultants, it is by no means a comprehensive collection of routines. The user however can use the elementary operations on polynomials to write application code for specific algebraic algorithms.
• Algorithms for real algebraic geometry. APU provides a collection of routines which can used to solve systems of equations using resultant-based techniques. It provides routines for counting the real roots of a univariate polynomial and for determining the sign sequences of a collection of polynomials at its roots.
• Stand-alone applications. APU can be used to develop C++ stand-alone applications which take advantage of the implementation of straight-line programs in APU. Two examples for this which have been implemented are : implicit point location in semi-algebraic sets and geometric theorem proving.

• Writing Programs in APU
• Getting Started and Requirements
• Overview of Data Structures and Operators
• Important Things to Remember
• Example code