# Symbolic Computation: A Formula is Worth 10000 Numbers

• J. H. Davenport
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

## Abstract

Hamming [29] remarked that “The purpose of computing is insight, not numbers”, and the aim of all computation must be to help the user obtain insight into his problem. Insight is rarely achieved by large quantities of numbers alone, and one very common way of increasing the insight obtained is to use graphics — “A picture is worth ten thousand numbers”. In this paper we present another means of gaining insight — the use of symbolic manipulation (also known as Computer Algebra) — “a formula is worth 10000 numbers”. There are three ways in which symbolic manipulation can help solve problems:
1. a)

It may provide a complete answer;

2. b)

It may provide a symbolic approximate answer;

3. c)

It may assist in the provision of a numeric answer.

This distinction is somewhat vague, since a symbolic approximate answer is an exact answer to an approximation problem (unlike the case in numerical analysis), and the assistance in providing numerical answers comes from the previous two areas. We will look at these three areas, give some examples of major uses of each, and discuss, where possible, applications particularly related to control theory. Where there seems a technique of wide applicaibility for which we do not know a reference in control theory however, we have not hesitated to quote details from elsewhere.

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