The GAP (Groups, Algorithms and Programming) Workshop will be held in conjunction with the 7BIGTC in Potchefstroom. The workshop aims to give the participants an introduction to GAP and its applications in various branches of algebra, especially group theory. The Workshop seeks to promote the use of the GAP system. GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. This is a very resourceful tool for group theorists and some algebraists and should benefit local participants, including Graduate Academics and Postgraduate students. It 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. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. Users can study and easily modify or extend it for their special use.
What is covered in the workshop?
- Pre-attendance GAP workshop check:
- installation, starting, how to save your work and load files.
- GAP as a fancy calculator
- List operations
- Possible error messages and how to fix them
- Groups: properties, subgroups, normal subgroups, quotient groups, conjugacy class and lots more.
- Small group library
- Cayley's theorem and rewriting a group as a permutation group
- Finitely presented groups
- Other algebraic systems
- Defining functions in GAP
- Regression tests in GAP
- Using GAP to make and/or tackle conjectures
- Follow-up and subscription to GAP forum mailing list.
Some useful links
What to do before the workshop (PDF file)
GAP download link for windows (EXE file)
A sample GAP program (.g file)
Introduction to GAP for 7BIGTC 2023
Detailed programme
Day 1: August 8, 2023 (Tuesday)
- 14:00–14:15: Pre-attendance GAP workshop check:
- installation, starting, how to save your work and load files.
- 14:15–14:45: Introduction to GAP (Part I)
- GAP as a fancy calculator
- List operations
- Possible error messages and how to fix them
- 14:45–15:00: Exercise session I
Day 2: August 9, 2023 (Wednesday)
- 14:00–14:40: Introduction to GAP (Part II)
- Groups: properties, subgroups, normal subgroups, quotient groups, conjugacy class and lots more.
- Small group library
- Cayley's theorem and rewriting a group as a permutation group
- Finitely presented groups
- Other algebraic systems
- 14:40–15:00: Exercise session II
Day 3: August 10, 2023 (Thursday)
- 08:00–09:00: Introduction to GAP (Part III)
- Defining functions in GAP
- Regression tests in GAP
- Using GAP to make and/or tackle conjectures
- 09:00–09:25: Exercise session III
- 09:25–09:55: Project activities
- 09:55–10:00: Concluding remarks