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      GAP - Reference Manual

      Release 4.11.0, 29-Feb-2020

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

      Copyright

      Copyright ? (1987-2020) 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 Version 2, see https://www.gnu.org/licenses/old-licenses/gpl-2.0.html or the LICENSE file in the root 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 has been 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 and Developing 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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