\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Preface}}{5}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{The \textsf {GAP} System}}{5}{section.1.1}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{A First Session with \textsf {GAP}}}{8}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{Starting and Leaving \textsf {GAP}}}{8}{section.2.1}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Loading Source Code from a File}}{9}{section.2.2}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{The Read Evaluate Print Loop}}{9}{section.2.3}%
\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{Constants and Operators}}{11}{section.2.4}%
\contentsline {section}{\numberline {2.5}\textcolor {Chapter }{Variables versus Objects}}{13}{section.2.5}%
\contentsline {section}{\numberline {2.6}\textcolor {Chapter }{Objects vs. Elements}}{15}{section.2.6}%
\contentsline {section}{\numberline {2.7}\textcolor {Chapter }{About Functions}}{15}{section.2.7}%
\contentsline {section}{\numberline {2.8}\textcolor {Chapter }{Help}}{16}{section.2.8}%
\contentsline {section}{\numberline {2.9}\textcolor {Chapter }{Further Information introducing the System}}{17}{section.2.9}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Lists and Records}}{19}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Plain Lists}}{19}{section.3.1}%
\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{Identical Lists}}{22}{section.3.2}%
\contentsline {section}{\numberline {3.3}\textcolor {Chapter }{Immutability}}{23}{section.3.3}%
\contentsline {section}{\numberline {3.4}\textcolor {Chapter }{Sets}}{24}{section.3.4}%
\contentsline {section}{\numberline {3.5}\textcolor {Chapter }{Ranges}}{25}{section.3.5}%
\contentsline {section}{\numberline {3.6}\textcolor {Chapter }{For and While Loops}}{26}{section.3.6}%
\contentsline {section}{\numberline {3.7}\textcolor {Chapter }{List Operations}}{28}{section.3.7}%
\contentsline {section}{\numberline {3.8}\textcolor {Chapter }{Vectors and Matrices}}{29}{section.3.8}%
\contentsline {section}{\numberline {3.9}\textcolor {Chapter }{Plain Records}}{31}{section.3.9}%
\contentsline {section}{\numberline {3.10}\textcolor {Chapter }{Further Information about Lists}}{32}{section.3.10}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Functions}}{33}{chapter.4}%
\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Writing Functions}}{33}{section.4.1}%
\contentsline {section}{\numberline {4.2}\textcolor {Chapter }{If Statements}}{34}{section.4.2}%
\contentsline {section}{\numberline {4.3}\textcolor {Chapter }{Local Variables}}{35}{section.4.3}%
\contentsline {section}{\numberline {4.4}\textcolor {Chapter }{Recursion}}{36}{section.4.4}%
\contentsline {section}{\numberline {4.5}\textcolor {Chapter }{Further Information about Functions}}{37}{section.4.5}%
\contentsline {chapter}{\numberline {5}\textcolor {Chapter }{Groups and Homomorphisms}}{38}{chapter.5}%
\contentsline {section}{\numberline {5.1}\textcolor {Chapter }{Permutation groups}}{38}{section.5.1}%
\contentsline {section}{\numberline {5.2}\textcolor {Chapter }{Actions of Groups}}{41}{section.5.2}%
\contentsline {section}{\numberline {5.3}\textcolor {Chapter }{Subgroups as Stabilizers}}{45}{section.5.3}%
\contentsline {section}{\numberline {5.4}\textcolor {Chapter }{Group Homomorphisms by Images}}{50}{section.5.4}%
\contentsline {section}{\numberline {5.5}\textcolor {Chapter }{Nice Monomorphisms}}{53}{section.5.5}%
\contentsline {section}{\numberline {5.6}\textcolor {Chapter }{Further Information about Groups and Homomorphisms}}{55}{section.5.6}%
\contentsline {chapter}{\numberline {6}\textcolor {Chapter }{Vector Spaces and Algebras}}{56}{chapter.6}%
\contentsline {section}{\numberline {6.1}\textcolor {Chapter }{Vector Spaces}}{56}{section.6.1}%
\contentsline {section}{\numberline {6.2}\textcolor {Chapter }{Algebras}}{59}{section.6.2}%
\contentsline {section}{\numberline {6.3}\textcolor {Chapter }{Further Information about Vector Spaces and Algebras}}{65}{section.6.3}%
\contentsline {chapter}{\numberline {7}\textcolor {Chapter }{Domains}}{66}{chapter.7}%
\contentsline {section}{\numberline {7.1}\textcolor {Chapter }{Domains as Sets}}{66}{section.7.1}%
\contentsline {section}{\numberline {7.2}\textcolor {Chapter }{Algebraic Structure}}{67}{section.7.2}%
\contentsline {section}{\numberline {7.3}\textcolor {Chapter }{Notions of Generation}}{67}{section.7.3}%
\contentsline {section}{\numberline {7.4}\textcolor {Chapter }{Domain Constructors}}{68}{section.7.4}%
\contentsline {section}{\numberline {7.5}\textcolor {Chapter }{Forming Closures of Domains}}{68}{section.7.5}%
\contentsline {section}{\numberline {7.6}\textcolor {Chapter }{Changing the Structure}}{68}{section.7.6}%
\contentsline {section}{\numberline {7.7}\textcolor {Chapter }{Subdomains}}{69}{section.7.7}%
\contentsline {section}{\numberline {7.8}\textcolor {Chapter }{Further Information about Domains}}{70}{section.7.8}%
\contentsline {chapter}{\numberline {8}\textcolor {Chapter }{Operations and Methods}}{71}{chapter.8}%
\contentsline {section}{\numberline {8.1}\textcolor {Chapter }{Attributes}}{71}{section.8.1}%
\contentsline {section}{\numberline {8.2}\textcolor {Chapter }{Properties and Filters}}{72}{section.8.2}%
\contentsline {section}{\numberline {8.3}\textcolor {Chapter }{Immediate and True Methods}}{74}{section.8.3}%
\contentsline {section}{\numberline {8.4}\textcolor {Chapter }{Operations and Method Selection}}{74}{section.8.4}%
\contentsline {chapter}{References}{77}{chapter*.3}%
\contentsline {chapter}{Index}{78}{section*.4}%
