The ALPAK System for Nonnumerical Algebra on a Digital Computer - III: Systems of Linear Equations and a Class of Side Relations

Abstract

This is the third and last in a series of papers describing the ALPAK system for nonnumerical algebra on a digital computer. The first paper1 is concerned with polynomials in several variables and truncated power series with polynomial coefficients. The second paper2 is concerned with rational functions in several variables and truncated power series with rational-function coefficients. The present paper discusses systems of linear equations with rational-function coefficients and a certain class of side relations. 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 six sections. The first two assume that the reader has no knowledge of computers or computer programming and the last four assume that the reader is familiar with basic computer programming and Refs. 1 and 2. Section I is a general description of ALPAK and this paper; Section II discusses the different forms in which a linear system can occur, including canonical form; Section III describes the ALPAK linear system operations for converting these forms; Section IV discusses side relations; Section V describes list naming operations; and Section VI discusses possible future developments and improvements.