This is the manual for the &SEMIGROUPS; package for ⪆ version &VERSION;.
&SEMIGROUPS; &VERSION; is a distant descendant of the
<URL Text = "Monoid package for GAP 3"> http://schmidt.nuigalway.ie/monoid/index.html</URL> by Goetz Pfeiffer,
Steve A. Linton, Edmund F. Robertson, and Nik Ruskuc.<P/>
From Version 3.0.0, &SEMIGROUPS; includes a copy of the &LIBSEMIGROUPS; C++
library which contains implementations of the Froidure-Pin, Todd-Coxeter,
and Knuth-Bendix algorithms (among others) that &SEMIGROUPS; utilises.
</Section>
This manual is organised as follows:
<List>
<Mark>Part I: elements</Mark>
<Item>
the different types of elements that are introduced in &SEMIGROUPS;
are described in Chapters <Ref Chap = "Bipartitions and blocks"/>,
<Ref Chap = "Partitioned binary relations (PBRs)"/>, and
<Ref Chap = "Matrices over semirings"/>. These include
<Ref Func="Bipartition"/>, <Ref Oper="PBR"/>, and
<Ref Oper="Matrix" Label="for a filter and a matrix"/>, which
supplement those already defined in the &GAP; library, such as
<Ref Oper="Transformation" Label="for an image list" BookName="ref"/> or
<Ref Oper="PartialPerm" Label="for a domain and image" BookName="ref"/>.
</Item>
<Mark>Part II: semigroups and monoids defined by generating sets</Mark>
<Item>
functions and operations for creating semigroups and monoids defined by
generating sets (of the type described in Part I) are described
in Chapter <Ref Chap
= "Semigroups and monoids defined by generating sets"/>.
</Item>
<Mark>Part III: standard examples and constructions</Mark>
<Item>
standard examples of semigroups, such as <Ref Oper = "FullBooleanMatMonoid"/> or <Ref Oper = "UniformBlockBijectionMonoid"/>, are described in
Chapter <Ref Chap = "Standard examples"/>, and standard constructions,
such as <Ref Func = "DirectProduct"/> are given in Chapter <Ref Chap
= "Standard constructions"/>.
</Item>
<Mark>Part IV: the structure of a semigroup or monoid</Mark>
<Item>
the functionality for determining various structural properties of a
given semigroup or monoid are described in Chapters <Ref Chap = "Ideals"/>, <Ref Chap = "Green's relations"/>, <Ref Chap = "Attributes and operations for semigroups"/>, and <Ref Chap = "Properties of semigroups"/>.
</Item>
<Mark>Part V: congruences, quotients, and homomorphisms</Mark>
<Item>
methods for creating and manipulating congruences and homomorphisms are
described by Chapters <Ref Chap = "Congruences"/> and <Ref Chap = "Semigroup homomorphisms"/>.
</Item>
<Mark>Part VI: finitely presented semigroups and monoids</Mark>
<Item>
methods for finitely presented semigroups and monoids, in particular,
for Tietze transformations can be found in Chapters <Ref Chap = "Finitely presented semigroups and Tietze transformations"/>.
</Item>
<Mark>Part VII: utilities and helper functions</Mark>
<Item>
functions for reading and writing semigroups and their elements, and
for visualising semigroups, and some of their elements, can be found in
Chapters <Ref Chap = "Visualising semigroups and elements"/> and
<Ref Chap = "IO"/>.
</Item>
</List>
</Section>
</Chapter>
¤ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
¤
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
