Summary and Schedule
GAP is a system for discrete computational algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects, for example the Small Groups Library which contains, among others, all 423 164 062 groups of order at most 2000 except 1024.
This lesson gives an introduction to GAP. It is centred around a common task of searching in the Small Groups Library for interesting examples and counterexamples, and a particular research problem in which we will be interested is to find examples of non-trivial groups such that the average order of their elements is an integer.
The lesson will lead the learner along the path from working in the GAP command line and exploring algebraic objects interactively to saving the GAP code into files, creating functions and regression tests, and further to performing comprehensive search and extending the system by adding new attributes.
On this path, the learner will become familiar with:
basic constructions of the GAP programming language,
ways to find necessary information in the GAP system, and
good design practices to organise GAP code into complex programs.
Prerequisites
The lesson is oriented on learners possessing the minimal theoretical background (at least at the level of an undergraduate group theory course) and willing to learn how concepts from abstract algebra may be explored using computational tools. No previous experience of working with GAP is required.
Learners only need to understand the concepts of files and directories (including home and working directories) and know how to start GAP.
Getting ready
- In your home directory, create a new directory called
avgord
. - Start GAP:
- on Linux and macOS, open the terminal and call
path-to-your-gap-installation/gap-4.X.Y/gap
(edit the path as necessary); - on Windows, start GAP using the Start menu or a desktop shortcut created after GAP installation.
- Set your current directory to
avgord
:
- on Linux and macOS, call
ChangeDirectoryCurrent("/Users/username/avgord");
(edit the path as necessary; remember to type the full path to your home directory instead of~
). - on Windows, call
ChangeDirectoryCurrent("C:/Users/username/avgord");
(edit the path as necessary; remember to use/
instead of\
);
- Verify that your current directory is set up properly: call
DirectoryCurrent();
and check that the path in the output points to theavgord
directory.
Setup Instructions | Download files required for the lesson | |
Duration: 00h 00m | 1. First session with GAP | Working with the GAP command line |
Duration: 00h 40m | 2. Some more GAP objects | Further examples of objects and operations with them |
Duration: 01h 00m | 3. Functions in GAP | Functions as a way of code re-use |
Duration: 01h 55m | 4. Using regression tests | Test-driven development |
Duration: 02h 45m | 5. Small groups search |
Modular programming: putting functions together How to check some conjecture for all groups of a given order |
Duration: 03h 40m | 6. Attributes and Methods | How to record information in GAP objects |
Duration: 04h 30m | Finish |
The actual schedule may vary slightly depending on the topics and exercises chosen by the instructor.
Windows
From the GAP Downloads
page, download the .exe
installer and double click on
the file to run it. When you are asked for the installation path, note
that it should not contain spaces. For example, you may install GAP
4.X.Y in C:\gap-4.X.Y
(default), D:\gap-4.X.Y
or C:\Math\GAP\gap-4.X.Y
, but you must not install it in a
directory such as C:\Program Files\gap-4.X.Y
or
C:\Users\alice\My Documents\gap-4.X.Y
.
macOS
On macOS, you need to install GAP from source as explained at the GAP Downloads page.
Download one of the archives provided there, unpack it and run
./configure && make
in the unpacked directory. Then
change to the pkg
subdirectory and call
../bin/BuildPackages.sh
to run the script which will build
most of the packages that require compilation (provided sufficiently
many libraries, headers and tools are available).
Alternatively, you may also install GAP using Homebrew. After installing Homebrew, follow the instructions for the GAP Homebrew tap.
Linux
On Linux, you need to install GAP from source as explained at the GAP Downloads page.
Download one of the archives provided there, unpack it and run
./configure && make
in the unpacked directory. Then
change to the pkg
subdirectory and call
../bin/BuildPackages.sh
to run the script which will build
most of the packages that require compilation (provided sufficiently
many libraries, headers and tools are available).