TABLE OF CONTENTS In this chapter we extend the concept of a mathematical algorithm to include function and procedure definitions, decision structures, and iteration structures. In Section 4.1 we discuss the general concept of a mathematical algorithm and examine some properties of mathematical operators that are used in an algorithm. In Section 4.2 we describe the basic programming structures that are used in MPL and give examples of procedures that use these structures. Finally, in the case study in Section 4.3 we describe a more involved algorithm that finds the solution of some first order ordinary differential equations.
Broadly speaking, a mathematical algorithm is a step by step process for solving a mathematical problem that is suitable for computer implementation. Although this definition includes much of what is found in mathematics texts, it is too broad to be useful in practice. We are primarily interested in those algorithms that can be expressed in terms of a computer program using the operators and programming structures available in CAS languages.
Computer scientists are quite explicit about the properties a process must have to be called an algorithm. Ideally, a mathematical algorithm should have the following properties.
Each step in the algorithm is precisely defined.
Each step in the algorithm is effective which means it is sufficiently basic so that it can be performed with finite computational resources (time and memory).
For example, the operation of multiplying two rational numbers is effective while the operation of multiplying two...
