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# 1 About the GAP Reference Manual

### Sections

1. Manual Conventions
2. Credit

This is one of four parts of the GAP documentation, the others being the GAP Tutorial, a beginner's introduction to GAP, Programming in GAP and Extending GAP, which provide information for those who want to write their own GAP extensions.

This manual, the GAP reference manual contains the official definitions of GAP functions. It should give all information to someone who wants to use GAP as it is. It is not intended to be read cover-to-cover.

This manual is divided into chapters. Each chapter is divided into sections and, within each section, important definitions are numbered. References are therefore triples.

Chapter The Help System describes the help system, which provides online access to the information of the manual. Chapter Running GAP gives technical advice for running GAP. Chapter The Programming Language introduces the GAP language, while the next chapters deal with the environment provided by GAP for the user. These are followed by the main bulk of chapters which is devoted to various mathematical structures that GAP can handle.

Pages are numbered consecutively in each of the four manuals.

## 1.1 Manual Conventions

The printed manual uses different text styles for several purposes. Note that the online help may use other symbols to express the meanings listed below.

`*text*`

Text printed in boldface is used to emphasize single words or phrases.

``text``

Text printed in italics is used for arguments in the descriptions of functions and for other place holders. It means that you should not actually enter this text into GAP but replace it by appropriate text depending on what you want to do. For example when we write that you should enter `?`section`` to see the section with the name section, section serves as a place holder, indicating that you can enter the name of the section that you want to see at this place.

`text`

Text printed in a monospaced (all characters have the same width) typewriter font is used for names of variables and functions and other text that you may actually enter into your computer and see on your screen. Such text may contain place holders printed in italics as described above. For example when the information for `IsPrime` says that the form of the call is `IsPrime(` n`)` this means that you should actually enter the strings ``IsPrime('' and ``)'', without the quotes, but replace the ``n`` with the number (or expression) that you want to test.

`Oper(` arg1`,` arg2`[,` opt`] ) F`

starts a subsection on the command `Oper` that takes two arguments arg1 and arg2 and an optional third argument opt. As in the above example, the letter `F` at the end of a line that starts with a little black triangle in the left margin indicates that the command is a simple function. Other possible letters at the end of such a line are `A`, `P`, `O`, `C`, `R`, and `V`; they indicate ``Attribute'', ``Property'', ``Operation'', ``Category'', ``Representation'' (see Chapter Types of Objects), or ``Variable'', respectively.

In the printed manual, mathematical formulas are typeset in italics (actually math italics), and subscripts and superscripts are actually lowered and raised.

Longer examples are usually paragraphs of their own. Everything on the lines with the prompts `gap>` and `>`, except the prompts themselves of course, is the input you have to type; everything else is GAP's response. In the printed manual, examples are printed in a monospaced typewriter font.

## 1.2 Credit

The manual tries to give credit to designers and implementors of major parts of GAP. For many parts of the GAP code it is impossible to give detailed credit, because over the time of its development many persons have contributed from first ideas, even in prerunners of GAP such as CAS or SOGOS, via first implementations, improvements, and even total reimplementations. The documentation of the code gives further details, but again, it suffers from the same problem. We have attempted to give attributions with the different chapters of the manual where this seemed to be possible, but we apologise for all (unavoidable) shortcomings of this attempt.

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GAP 4 manual
September 2006