\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Introduction}}{5}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }General aims of \textsf {Wedderga} package}}{5}{section.1.1}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Main functions of \textsf {Wedderga} package}}{5}{section.1.2}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Installation and system requirements}}{6}{section.1.3}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Wedderburn decomposition}}{7}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Wedderburn decomposition}}{7}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }WedderburnDecomposition}}{7}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }WedderburnDecompositionInfo}}{8}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Simple quotients}}{12}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }SimpleAlgebraByCharacter}}{12}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }SimpleAlgebraByCharacterInfo}}{12}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }SimpleAlgebraByStrongSP (for rational group algebra)}}{13}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}\leavevmode {\color {Chapter }SimpleAlgebraByStrongSPInfo (for rational group algebra)}}{13}{subsection.2.2.4}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Strong Shoda pairs}}{15}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Computing strong Shoda pairs}}{15}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }StrongShodaPairs}}{15}{subsection.3.1.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Properties related with Shoda pairs}}{16}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }IsStrongShodaPair}}{16}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }IsShodaPair}}{16}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }IsStronglyMonomial}}{17}{subsection.3.2.3}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Idempotents}}{18}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Computing idempotents from character table}}{18}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsByCharacterTable}}{18}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Testing lists of idempotents for completeness}}{18}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }IsCompleteSetOfOrthogonalIdempotents}}{18}{subsection.4.2.1}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }Idempotents from Shoda pairs}}{19}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsByStrongSP}}{19}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsBySP}}{20}{subsection.4.3.2}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Crossed products}}{22}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Construction of crossed products}}{22}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color {Chapter }CrossedProduct}}{22}{subsection.5.1.1}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Crossed product elements and their properties}}{29}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }ElementOfCrossedProduct}}{29}{subsection.5.2.1}
\contentsline {chapter}{\numberline {6}\leavevmode {\color {Chapter }Useful properties and functions}}{30}{chapter.6}
\contentsline {section}{\numberline {6.1}\leavevmode {\color {Chapter }Semisimple group algebras of finite groups}}{30}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color {Chapter }IsSemisimpleZeroCharacteristicGroupAlgebra}}{30}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color {Chapter }IsSemisimpleRationalGroupAlgebra}}{30}{subsection.6.1.2}
\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color {Chapter }IsSemisimpleANFGroupAlgebra}}{31}{subsection.6.1.3}
\contentsline {subsection}{\numberline {6.1.4}\leavevmode {\color {Chapter }IsSemisimpleFiniteGroupAlgebra}}{31}{subsection.6.1.4}
\contentsline {section}{\numberline {6.2}\leavevmode {\color {Chapter }Operations over group rings elements}}{31}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}\leavevmode {\color {Chapter }Centralizer}}{31}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}\leavevmode {\color {Chapter }OnPoints}}{32}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}\leavevmode {\color {Chapter }AverageSum}}{33}{subsection.6.2.3}
\contentsline {section}{\numberline {6.3}\leavevmode {\color {Chapter }Cyclotomic classes}}{33}{section.6.3}
\contentsline {subsection}{\numberline {6.3.1}\leavevmode {\color {Chapter }CyclotomicClasses}}{33}{subsection.6.3.1}
\contentsline {subsection}{\numberline {6.3.2}\leavevmode {\color {Chapter }IsCyclotomicClass}}{34}{subsection.6.3.2}
\contentsline {section}{\numberline {6.4}\leavevmode {\color {Chapter }Other commands}}{34}{section.6.4}
\contentsline {subsection}{\numberline {6.4.1}\leavevmode {\color {Chapter }InfoWedderga}}{34}{subsection.6.4.1}
\contentsline {subsection}{\numberline {6.4.2}\leavevmode {\color {Chapter }WEDDERGABuildManual}}{34}{subsection.6.4.2}
\contentsline {subsection}{\numberline {6.4.3}\leavevmode {\color {Chapter }WEDDERGABuildManualHTML}}{35}{subsection.6.4.3}
\contentsline {chapter}{\numberline {7}\leavevmode {\color {Chapter }The basic theory behind \textsf {Wedderga}}}{36}{chapter.7}
\contentsline {section}{\numberline {7.1}\leavevmode {\color {Chapter }Group rings and group algebras}}{36}{section.7.1}
\contentsline {section}{\numberline {7.2}\leavevmode {\color {Chapter }Semisimple group algebras}}{36}{section.7.2}
\contentsline {section}{\numberline {7.3}\leavevmode {\color {Chapter }Wedderburn decomposition}}{36}{section.7.3}
\contentsline {section}{\numberline {7.4}\leavevmode {\color {Chapter }Characters and primitive central idempotents}}{37}{section.7.4}
\contentsline {section}{\numberline {7.5}\leavevmode {\color {Chapter }Central simple algebras and Brauer equivalence}}{38}{section.7.5}
\contentsline {section}{\numberline {7.6}\leavevmode {\color {Chapter }Crossed Products}}{38}{section.7.6}
\contentsline {section}{\numberline {7.7}\leavevmode {\color {Chapter }Cyclic Crossed Products}}{39}{section.7.7}
\contentsline {section}{\numberline {7.8}\leavevmode {\color {Chapter }Abelian Crossed Products}}{40}{section.7.8}
\contentsline {section}{\numberline {7.9}\leavevmode {\color {Chapter }Classical crossed products}}{40}{section.7.9}
\contentsline {section}{\numberline {7.10}\leavevmode {\color {Chapter }Cyclic Algebras}}{40}{section.7.10}
\contentsline {section}{\numberline {7.11}\leavevmode {\color {Chapter }Cyclotomic algebras}}{41}{section.7.11}
\contentsline {section}{\numberline {7.12}\leavevmode {\color {Chapter }Numerical description of cyclotomic algebras}}{41}{section.7.12}
\contentsline {section}{\numberline {7.13}\leavevmode {\color {Chapter }Idempotents given by subgroups}}{42}{section.7.13}
\contentsline {section}{\numberline {7.14}\leavevmode {\color {Chapter }Shoda pairs}}{42}{section.7.14}
\contentsline {section}{\numberline {7.15}\leavevmode {\color {Chapter }Strong Shoda pairs}}{42}{section.7.15}
\contentsline {section}{\numberline {7.16}\leavevmode {\color {Chapter }Strongly monomial characters and strongly monomial groups}}{43}{section.7.16}
\contentsline {section}{\numberline {7.17}\leavevmode {\color {Chapter }Cyclotomic Classes and Strong Shoda Pairs}}{44}{section.7.17}
