aclib
- Ebuilds: 1, Testing: 1.3.3 Description:
The AClib package contains a library of almost crystallographic
groups and a some algorithms to compute with these groups. A group
is called almost crystallographic if it is finitely generated
nilpotent-by-finite and has no non-trivial finite normal subgroups.
Homepage:https://www.gap-system.org/Packages/aclib.html License: Artistic-2
alnuth
- Ebuilds: 1, Stable: 3.2.1, Testing: 3.2.1 Description:
The Alnuth package provides various methods to compute with number
fields which are given by a defining polynomial or by
generators. Some of the methods provided in this package are written
in GAP code. The other part of the methods is imported from the
computer algebra system PARI/GP.
License: GPL-2+
atlasrep
- Ebuilds: 1, Stable: 2.1.9, Testing: 2.1.9 Description:
AtlasRep provides an interface between GAP and databases such as the
Atlas of Group Representations, which comprises representations of
many almost simple groups and information about their maximal
subgroups, and is included in the GAP package.
License: GPL-3+
autodoc
- Ebuilds: 2, Stable: 2023.06.19, Testing: 2025.05.09 Description:
AutoDoc is a package for the GAP computer algebra system. It is
meant to simplify the creation of reference manuals for GAP
packages. It makes it possible to create documentation from source
code comments, without writing XML files. It is not a substitute for
GAPDoc, but rather builds on GAPDoc, by generating XML input for the
latter. As such, you can combine an existing GAPDoc manual with
AutoDoc.
License: GPL-2+
autpgrp
- Ebuilds: 1, Stable: 1.11, Testing: 1.11 Description:
The AutPGrp package introduces a new function to compute the
automorphism group of a finite p-group. The underlying algorithm is
a refinement of the methods described in O'Brien (1995). In
particular, this implementation is more efficient in both time and
space requirements and hence has a wider range of applications than
the ANUPQ method. It also usually out-performs all but the method
designed for finite abelian groups.
License: GPL-2+
browse
- Ebuilds: 1, Stable: 1.8.21-r2, Testing: 1.8.21-r2 Description:
The Browse package provides three levels of functionality:
1 A GAP interface to the C-library ncurses.
2 A generic function for interactive browsing through
two-dimensional arrays of data.
3 Several applications of the first two, e.g., a method for
browsing character tables, browsing through the content of some
data collections, or some games.
License: GPL-3+
congruence
- Ebuilds: 1, Testing: 1.2.7 Description:
The GAP package Congruence provides functions to construct several
types of canonical congruence subgroups in SL_2(Z), and also
intersections of a finite number of such subgroups. Furthermore, it
implements the algorithm for generating Farey symbols for congruence
subgroups and using them to produce a system of independent
generators for these subgroups.
License: GPL-2+
corelg
- Ebuilds: 1, Testing: 1.57 Description: GAP package to compute with real semisimple Lie algebras
License: GPL-2+
crime
- Ebuilds: 1, Testing: 1.6 Description:
This CRIME package computes cohomology rings for finite p-groups
using Jon Carlson's method, both as GAP objects, and also in terms
of generators and relators. It also computes induced homomorphisms
on cohomology and Massey products in the cohomology ring.
License: GPL-2+
crisp
- Ebuilds: 2, Stable: 1.4.6, Testing: 1.4.8 Description:
CRISP provides algorithms for computing subgroups of finite soluble
groups related to a group class C. In particular, it allows to
compute C-radicals and C-injectors for Fitting classes (and Fitting
sets) C, C-residuals for formations C, and C-projectors for Schunck
classes C. In order to carry out these computations, the group class
C must be represented by an algorithm which can decide membership in
the group class. Moreover, CRISP contains algorithms for the
computation of normal subgroups invariant under a prescribed set of
automorphisms and belonging to a given group class. This includes
an improved method to compute the set of all normal subgroups of a
finite soluble group, its characteristic subgroups, minimal normal
subgroups and the socle and p-socles for given primes p.
License: BSD-2
crypting
- Ebuilds: 1, Testing: 0.10.6 Description: GAP implementation of SHA256 and HMAC for the Jupyter kernel
License: BSD
cryst
- Ebuilds: 1, Testing: 4.1.29 Description:
This package, previously known as CrystGAP, provides a rich set of
methods for the computation with affine crystallographic groups, in
particular space groups. Affine crystallographic groups are fully
supported both in representations acting from the right or from the
left, the latter one being preferred by crystallographers. Functions
to determine representatives of all space group types of a given
dimension are also provided.
License: GPL-2+
crystcat
- Ebuilds: 1, Testing: 1.1.10 Description:
This package provides a catalog of crystallographic groups of
dimensions 2, 3, and 4 which covers most of the data contained in
the book Crystallographic groups of four-dimensional space by
H. Brown, R. Bülow, J. Neubüser, H. Wondratschek, and H. Zassenhaus
(John Wiley, New York, 1978).
License: GPL-2+
ctbllib
- Ebuilds: 1, Stable: 1.3.9, Testing: 1.3.9 Description: The GAP Character Table Library
License: GPL-3+
cvec
- Ebuilds: 1, Testing: 2.8.4 Description:
This package provides an implementation of compact vectors over
finite fields. Contrary to earlier implementations no table lookups
are used but only word-based processor arithmetic. This allows for
bigger finite fields and higher speed.
License: GPL-2+
datastructures
- Ebuilds: 1, Testing: 0.3.3 Description:
The datastructures package aims at providing standard
datastructures, consolidating existing code and improving on it, in
particular in view of HPC-GAP.
The datastructures package consists of two parts: interface
declarations and implementations. The goal of interface declarations
is to define standard interfaces for datastructures and decouple
them from the implementations. This enables easy exchangability of
implementations, for example for more efficient implementations, or
implementations more suited for parallelisation or sequential use.
The datastructures package declares interfaces for the following
datastructures:
* queues
* doubly linked lists
* heaps
* priority queues
* hash tables
* dictionaries
License: GPL-2+
design
- Ebuilds: 1, Testing: 1.8.2 Description: The Design Package for GAP
License: GPL-2+
digraphs
- Ebuilds: 1, Testing: 1.13.1 Description: Graphs, digraphs, and multidigraphs in GAP
License: GPL-3+
edim
- Ebuilds: 1, Testing: 1.3.8 Description:
This package provides a collection of functions for computing the
Smith normal form of integer matrices and some related utilities.
License: GPL-2+
factint
- Ebuilds: 1, Stable: 1.6.3, Testing: 1.6.3 Description:
This package provides routines for factoring integers, in
particular:
* Pollard's p-1
* Williams' p+1
* Elliptic Curves Method (ECM)
* Continued Fraction Algorithm (CFRAC)
* Multiple Polynomial Quadratic Sieve (MPQS)
It also provides access to Richard P. Brent's tables of factors of
integers of the form b^k +/- 1.
License: GPL-2+
fga
- Ebuilds: 1, Stable: 1.5.0, Testing: 1.5.0 Description:
The FGA package installs methods for computations with finitely
generated subgroups of free groups and provides a presentation for
their automorphism groups.
License: GPL-2+
gapdoc
- Ebuilds: 1, Stable: 1.6.7, Testing: 1.6.7 Description:
This package contains a definition of a structure for GAP (package)
documentation, based on XML. It also contains conversion programs
for producing text-, PDF- or HTML-versions of such documents, with
hyperlinks if possible.
License: GPL-2+
gbnp
- Ebuilds: 1, Testing: 1.1.0 Description:
The GBNP package provides algorithms for computing Grobner bases of
noncommutative polynomials with coefficients from a field
implemented in GAP and with respect to the "total degree first then
lexicographical" ordering. Further provided are some variations,
such as a weighted and truncated version and a tracing facility. The
word "algorithm" is to be interpreted loosely here: in general one
cannot expect such an algorithm to terminate, as it would imply
solvability of the word problem for finitely presented (semi)groups.
License: LGPL-2.1+
genss
- Ebuilds: 1, Testing: 1.6.9 Description:
The genss package implements the randomised Schreier-Sims algorithm
to compute a stabiliser chain and a base and strong generating set
for arbitrary finite groups.
License: GPL-3+
grape
- Ebuilds: 1, Testing: 4.9.2 Description:
GRAPE is a package for computing with graphs and groups, and is
primarily designed for constructing and analysing graphs related to
groups, finite geometries, and designs.
License: Apache-2.0 GPL-2+
guava
- Ebuilds: 1, Testing: 3.20 Description: GAP package for computing with error-correcting codes
License: || ( GPL-2 GPL-3 )
hap
- Ebuilds: 1, Testing: 1.70 Description:
HAP is a package for some calculations in elementary algebraic
topology and the cohomology of groups. The initial focus of the
library was on computations related to the cohomology of finite and
infinite groups, with particular emphasis on integral
coefficients. The focus has since broadened to include Steenrod
algebras of finite groups, Bredon homology, cohomology of simplicial
groups, and general computations in algebraic topology relating to
finite CW-complexes, covering spaces, knots, knotted surfaces, and
topics such as persitent homology arising in topological data
analysis.
License: GPL-2+
hapcryst
- Ebuilds: 1, Testing: 0.1.15 Description:
This is an extension to the HAP package by Graham Ellis. It
implements geometric methods for the calculation of resolutions of
Bieberbach groups.
License: GPL-2+
hecke
- Ebuilds: 1, Testing: 1.5.4 Description:
The Hecke package provides functions for calculating decomposition
matrices of Hecke algebras of the symmetric groups and q-Schur
algebras.
License: GPL-2+
images
- Ebuilds: 1, Testing: 1.3.3 Description: Find minimal and canonical images in permutation groups
License: MPL-2.0
io
- Ebuilds: 2, Stable: 4.9.1, Testing: 4.9.3 Description:
The IO package, as its name suggests, provides bindings for GAP to
the lower levels of Input/Output functionality in the C library.
License: GPL-3+
irredsol
- Ebuilds: 1, Stable: 1.4.4, Testing: 1.4.4 Description:
The GAP package IRREDSOL provides a library of all irreducible
soluble subgroups of GL(n,q), up to conjugacy, for q^n up to 2^24-1,
and a library of the primitive soluble groups of degree up to
2^24-1.
License: BSD-2
laguna
- Ebuilds: 1, Stable: 3.9.7, Testing: 3.9.7 Description:
The LAGUNA package replaces the LAG package and provides
functionality for calculation of the normalized unit group of the
modular group algebra of the finite p-group and for investigation of
Lie algebra associated with group algebras and other associative
algebras.
License: GPL-2+
liealgdb
- Ebuilds: 1, Testing: 2.2.1 Description:
LieAlgDB provides access to several classifications of Lie algebras.
In the mathematics literature many classifications of Lie algebras
of various types have been published. This package aims at making a
few classifications of small dimensional Lie algebras that have
appeared in recent years more accessible. For each classification
that is contained in the package, functions are provided that
construct Lie algebras from that classification inside GAP. This
allows the user to obtain easy access to the often rather
complicated data contained in a classification, and to directly
interface the Lie algebras to the functionality for Lie algebras
which is already contained in GAP.
License: GPL-2+
liepring
- Ebuilds: 1, Testing: 2.9.1 Description: Database and algorithms for Lie p-rings
License: GPL-2+
liering
- Ebuilds: 1, Testing: 2.4.2 Description:
The package LieRing contains functionality for working with finitely
presented Lie rings and the Lazard correspondence.
License: GPL-2+
loops
- Ebuilds: 1, Testing: 3.4.4 Description:
The LOOPS package provides researchers in nonassociative algebra
with a computational tool that integrates standard notions of loop
theory with libraries of loops and group-theoretical algorithms of
GAP. The package also expands GAP toward nonassociative structures.
License: GPL-2+
mapclass
- Ebuilds: 1, Testing: 1.4.6 Description: A GAP package to compute mapping-class group orbits
License: GPL-2+
nq
- Ebuilds: 1, Testing: 2.5.11 Description:
This package provides access to the ANU nilpotent quotient program
for computing nilpotent factor groups of finitely presented groups.
License: GPL-2+
orb
- Ebuilds: 1, Testing: 5.0.1 Description: GAP methods to enumerate orbits
License: GPL-3+
polenta
- Ebuilds: 2, Stable: 1.3.10, Testing: 1.3.11 Description:
The Polenta package provides methods to compute polycyclic
presentations of matrix groups (finite or infinite). As a
by-product, this package gives some functionality to compute certain
module series for modules of solvable groups. For example, if G is
a rational polycyclic matrix group, then we can compute the radical
series of the natural Q[G]-module Q^d.
License: GPL-2+
polycyclic
- Ebuilds: 2, Stable: 2.16, Testing: 2.17 Description:
This package provides various algorithms for computations with
polycyclic groups defined by polycyclic presentations. The features
of this package include,
* creating a polycyclic group from a polycyclic presentation
arithmetic in a polycyclic group
* computation with subgroups and factor groups of a polycyclic
group
* computation of standard subgroup series such as the derived
series, the lower central series
* computation of the first and second cohomology
* computation of group extensions
* computation of normalizers and centralizers
* solutions to the conjugacy problems for elements and subgroups
* computation of torsion and various finite subgroups
* computation of various subgroups of finite index
* computation of the Schur multiplicator, the non-abelian exterior
square and the non-abelian tenor square
License: GPL-2+
polymaking
- Ebuilds: 1, Testing: 0.8.7 Description:
This package provides a very basic interface to the polymake program
by Ewgenij Gawrilow, Michael Joswig et al.
License: GPL-2+
primgrp
- Ebuilds: 2, Stable: 3.4.4, Testing: 4.0.0 Description:
The PrimGrp package provides the library of primitive permutation
groups which includes, up to permutation isomorphism (i.e., up to
conjugacy in the corresponding symmetric group), all primitive
permutation groups of degree less than 4096.
License: GPL-2+
qpa
- Ebuilds: 1, Testing: 1.36 Description:
The QPA package provides data structures and algorithms for doing
computations with finite dimensional quotients of path algebras, and
finitely generated modules over such algebras. The current version
of the QPA package has data structures for quivers, quotients of
path algebras, and modules, homomorphisms and complexes of modules
over quotients of path algebras.
License: GPL-2+
quagroup
- Ebuilds: 1, Testing: 1.8.4 Description:
The package QuaGroup contains functionality for working with
quantized enveloping algebras of finite-dimensional semisimple Lie
algebras.
License: GPL-2+
radiroot
- Ebuilds: 1, Stable: 2.9, Testing: 2.9 Description:
The package can compute and display an expression by radicals for
the roots of a solvable, rational polynomial. Related to this, it is
possible to create the Galois group and the splitting field of a
rational polynomial.
License: GPL-2+
resclasses
- Ebuilds: 1, Stable: 4.7.3, Testing: 4.7.3 Description:
This package permits to compute with set-theoretic unions of residue
classes of Z and a few other rings. In particular it provides
methods for computing unions, intersections and differences of these
sets.
License: GPL-2+
semigroups
- Ebuilds: 2, Testing: 5.5.4 Description:
The Semigroups package is a GAP package for semigroups, and
monoids. There are particularly efficient methods for finitely
presented semigroups and monoids, and for semigroups and monoids
consisting of transformations, partial permutations, bipartitions,
partitioned binary relations, subsemigroups of regular Rees 0-matrix
semigroups, and matrices of various semirings including boolean
matrices, matrices over finite fields, and certain tropical
matrices. Semigroups contains efficient methods for creating
semigroups, monoids, and inverse semigroups and monoids, calculating
their Green's structure, ideals, size, elements, group of units,
small generating sets, testing membership, finding the inverses of a
regular element, factorizing elements over the generators, and so
on. It is possible to test if a semigroup satisfies a particular
property, such as if it is regular, simple, inverse, completely
regular, and a large number of further properties. There are methods
for finding presentations for a semigroup, the congruences of a
semigroup, the maximal subsemigroups of a finite semigroup, smaller
degree partial permutation representations, and the character tables
of inverse semigroups. There are functions for producing pictures of
the Green's structure of a semigroup, and for drawing graphical
representations of certain types of elements.
License: GPL-3+
singular
- Ebuilds: 1, Testing: 2025.08.26 Description: GAP interface to sci-mathematics/singular
License: GPL-2+
sla
- Ebuilds: 1, Testing: 1.6.2 Description: GAP package for simple Lie algebra computations
License: GPL-2+
smallgrp
- Ebuilds: 1, Stable: 1.5.4, Testing: 1.5.4 Description:
The SmallGrp package provides the library of groups of certain
"small" orders. The groups are sorted by their orders and they are
listed up to isomorphism; that is, for each of the available orders
a complete and irredundant list of isomorphism type representatives
of groups is given.
License: Artistic-2
sonata
- Ebuilds: 1, Testing: 2.9.6 Description:
SONATA stands for "systems of nearrings and their applications." It
provides methods for the construction and the analysis of finite
nearrings:
* Methods for constructing all endomorphisms and all
fixed-point-free automorphisms of a given group.
* Methods for constructing the following nearrings of functions on
a group G: the nearring of polynomial functions of G (in the sense
of Lausch-Nöbauer); the nearring of compatible functions of G;
distributively generated nearrings such as I(G), A(G), E(G);
centralizer nearrings.
* A library of all small nearrings (up to order 15) and all small
nearrings with identity (up to order 31).
* Functions to obtain solvable fixed-point-free automorphism
groups on abelian groups, nearfields, planar nearrings, as well
as designs from those.
* Various functions to study the structure (size, ideals,
N-groups, ...) of nearrings, to determine properties of nearring
elements, and to decide whether two nearrings are isomorphic.
* If the package XGAP is installed, the lattices of one- and
two-sided ideals of a nearring can be studied interactively using
a graphical representation
License: GPL-2+
sophus
- Ebuilds: 1, Stable: 1.27, Testing: 1.27 Description:
The Sophus package is written to compute with nilpotent Lie algebras
over finite prime fields. Using this package, you can compute the
cover, the list of immediate descendants, and the automorphism group
of such Lie algebras. You can also test if two such Lie algebras are
isomorphic.
The immediate descendant function of the package can be used to
classify small-dimensional nilpotent Lie algebras over a given
field. For instance, the package author obtained a classification of
nilpotent Lie algebras with dimension at most 9 over F_2.
License: GPL-2+
spinsym
- Ebuilds: 1, Stable: 1.5.2, Testing: 1.5.2 Description:
This package contains Brauer tables of Schur covers of symmetric and
alternating groups, and provides some related functionalities.
License: GPL-2+
tomlib
- Ebuilds: 1, Stable: 1.2.11, Testing: 1.2.11 Description:
The concept of a table of marks was introduced by W. Burnside in his
1955 book Theory of Groups of Finite Order. Therefore a table of
marks is sometimes called a Burnside matrix.
The table of marks of a finite group G is a matrix whose rows and
columns are labelled by the conjugacy classes of subgroups of G and
where for two subgroups H and K the (H, K)-entry is the number of
fixed points of K in the transitive action of G on the cosets of H
in G. So the table of marks characterizes the set of all permutation
representations of G. Moreover, the table of marks gives a compact
description of the subgroup lattice of G, since from the numbers of
fixed points the numbers of conjugates of a subgroup K contained in
a subgroup H can be derived.
For small groups the table of marks of G can be constructed directly
in GAP by first computing the entire subgroup lattice of G. However,
for larger groups this method is unfeasible. The GAP Table of Marks
library provides access to several hundred tables of marks and their
maximal subgroups.
License: GPL-2+
toric
- Ebuilds: 1, Testing: 1.9.6 Description: GAP package for computing with toric varieties
License: MIT
transgrp
- Ebuilds: 1, Stable: 3.6.5, Testing: 3.6.5 Description:
A library of transitive groups.
Groups of degree 15-30 are due to Alexander Hulpke Degree 32 is due
to John Cannon and Derek Holt Degree 34-48 is due to Derek Holt and
Gordon Royle. Groups of degree 32 (~30MB) and 48 (~30GB) need to be
downloaded separately.
License: GPL-3 Artistic-2
utils
- Ebuilds: 2, Stable: 0.87, Testing: 0.91 Description:
This package collects together utility functions from a selection of
GAP packages in order to make them more widely visible to other
package authors.
Other generally useful functions, which are not deemed suitable for
the main library, and also welcome. For example, recent additions
are functions to convert certain types of group to Magma format.
License: GPL-2+