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GAP - Reference Manual

Release 4.8.6, 12-Nov-2016

The GAP Group
Email: support@gap-system.org
Homepage: http://www.gap-system.org

Copyright

Copyright © (1987-2016) for the core part of the GAP system by the GAP Group.

Most parts of this distribution, including the core part of the GAP system are distributed under the terms of the GNU General Public License, see http://www.gnu.org/licenses/gpl.html or the file GPL in the etc directory of the GAP installation.

More detailed information about copyright and licenses of parts of this distribution can be found in Section 1.4 of this manual.

GAP is developed over a long time and has many authors and contributors. More detailed information can be found in Section 1.2 of this manual.

Contents

1 Preface
2 The Help System
3 Running GAP
4 The Programming Language
5 Functions
6 Main Loop and Break Loop
7 Debugging and Profiling Facilities
8 Options Stack
9 Files and Filenames
10 Streams
11 Processes
12 Objects and Elements
13 Types of Objects
14 Integers
15 Number Theory
16 Combinatorics
17 Rational Numbers
18 Cyclotomic Numbers
19 Floats
20 Booleans
21 Lists
22 Boolean Lists
23 Row Vectors
24 Matrices
25 Integral matrices and lattices
26 Vector and matrix objects
27 Strings and Characters
28 Dictionaries and General Hash Tables
29 Records
30 Collections
31 Domains and their Elements
32 Mappings
33 Relations
34 Orderings
35 Magmas
36 Words
37 Associative Words
38 Rewriting Systems
39 Groups
40 Group Homomorphisms
41 Group Actions
42 Permutations
43 Permutation Groups
44 Matrix Groups
45 Polycyclic Groups
46 Pc Groups
47 Finitely Presented Groups
48 Presentations and Tietze Transformations
49 Group Products
50 Group Libraries
51 Semigroups and Monoids
52 Finitely Presented Semigroups and Monoids
53 Transformations
54 Partial permutations
55 Additive Magmas
56 Rings
57 Modules
58 Fields and Division Rings
59 Finite Fields
60 Abelian Number Fields
61 Vector Spaces
62 Algebras
63 Finitely Presented Algebras
64 Lie Algebras
65 Magma Rings
66 Polynomials and Rational Functions
67 Algebraic extensions of fields
68 p-adic Numbers (preliminary)
69 The MeatAxe
70 Tables of Marks
71 Character Tables
72 Class Functions
73 Maps Concerning Character Tables
74 Unknowns
75 Monomiality Questions
76 Using GAP Packages
77 Replaced and Removed Command Names
78 Method Selection
79 Creating New Objects
80 Examples of Extending the System
81 An Example – Residue Class Rings
82 An Example – Designing Arithmetic Operations
83 Library Files
84 Interface to the GAP Help System
85 Function-Operation-Attribute Triples
86 Weak Pointers
87 More about Stabilizer Chains
References
Index

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