The ALPAK System for Nonnumerical Algebra on a Digital Computer - II: Rational Functions of Several Variables and Truncated Power Series with Rational-Function Coefficients

This is the second in a series of papers describing the ALPAK system for nonnumerical algebra on a digital computer. The first paper, Ref. 1, is concerned with polynomials in several variables and truncated power series with polynomial coefficients. This paper is concerned with rational functions of several variables and truncated power series with rationalfunction coefficients. A third paper, Ref. 3, will discuss systems of linear equations with rational-function coefficients. The ALPAK system has been programmed within the BE-SYS-4 monitor system on the IBM 7090 computer, but the language and concepts are machine-independent. Several practical applications are described in Ref. 1. This paper is divided into five sections. The first deals with basic concepts, the second defines canonical forms, and the third describes ALPAK's greatest common divisor algorithm. These three sections do not presuppose any knowledge of computers or computer programming. Section IV describes the use and, the implementation of the algebraic operations relating to rational functions of several variables and truncated power series with rational-function coefficients. The reader of this section is assumed to be familiar with the basic concepts of computer programming and with Ref. 1. Finally, Section V dismisses very briefly some of our plans and hopes for the future. TABI.E OF CONTENTS Page I . SUMMARY O F T H E A V A I L A B L E R A T I O N A L F U N C T I O N O P E R A T I O N S 1.1 Introduction 786 78(5 785 786 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , MARCH 19G4 1.2 Input-Output 1.3 An Example of the ALPAK Language I I .