Lecture series
A hands-on, type-it-yourself introduction to GAP - the system for computational group theory.
A self-paced, hands-on introduction to GAP (Groups, Algorithms, Programming) - the computer algebra system for computational group theory. The approach is deliberate: you type every command yourself in your own GAP session, predict what each will return before you evaluate it, and build up from the language to real group computations one concept at a time.
The lessons move through three arcs - getting started (surviving your first session), the language (lists, loops, functional operations, records, and functions), and groups, concretely (permutations, permutation groups, orbits and stabilizers, subgroups, and products). Each lesson is self-contained and assumes only the vocabulary - not the exercises - of the ones before it.
Environment assumed: GAP 4.16 (any recent 4.x is fine for this part); no extra packages are needed.
Launch gap, evaluate an expression, read the prompt, ; versus ;;, := versus =, recover from the brk> break loop, last, ?help, and quit.
1-based indexing, brackets, Add and Append, slicing, and the mutability trap - a list is a reference, not a value.
The [1..n] range, for … in … do … od, while loops, and ranges as compact lists.
List as map, Filtered, ForAll and ForAny, Number, Set, Sum, and arrow functions x -> expr.
rec( … ), fields, RecNames, IsBound, and when a record beats a list for structured data.
The full function … local … end form, return semantics, and Read-ing a .g file you wrote in your own editor.
Cycle notation, composition order (left-to-right), an element's Order and inverse, and LargestMovedPoint.
Group and generators, Size versus Order, SymmetricGroup and AlternatingGroup, IsAbelian, IsPerfect, and Center.
Orbit, Orbits, and Stabilizer, and the orbit–stabilizer theorem as an arithmetic check.
Subgroup and IsSubgroup, Centralizer, ConjugacyClassesSubgroups, and Representative.
DirectProduct and Embedding, Image and Kernel, FactorGroup, and GroupHomomorphismByImages.