\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}}{8}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Wedderburn decomposition}}{8}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }WedderburnDecomposition}}{8}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }WedderburnDecompositionInfo}}{9}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Simple quotients}}{13}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }SimpleAlgebraByCharacter}}{13}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }SimpleAlgebraByCharacterInfo}}{13}{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)}}{14}{subsection.2.2.4}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Strong Shoda pairs}}{16}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Computing strong Shoda pairs}}{16}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }StrongShodaPairs}}{16}{subsection.3.1.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Properties related with Shoda pairs}}{17}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }IsStrongShodaPair}}{17}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }IsShodaPair}}{17}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }IsStronglyMonomial}}{18}{subsection.3.2.3}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Idempotents}}{19}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Computing idempotents from character table}}{19}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsByCharacterTable}}{19}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Testing lists of idempotents for completeness}}{19}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }IsCompleteSetOfOrthogonalIdempotents}}{19}{subsection.4.2.1}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }Idempotents from Shoda pairs}}{20}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsByStrongSP}}{20}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }PrimitiveCentralIdempotentsBySP}}{21}{subsection.4.3.2}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Crossed products}}{23}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Construction of crossed products}}{23}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color {Chapter }CrossedProduct}}{23}{subsection.5.1.1}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Crossed product elements and their properties}}{30}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }ElementOfCrossedProduct}}{30}{subsection.5.2.1}
\contentsline {chapter}{\numberline {6}\leavevmode {\color {Chapter }Useful properties and functions}}{31}{chapter.6}
\contentsline {section}{\numberline {6.1}\leavevmode {\color {Chapter }Semisimple group algebras of finite groups}}{31}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color {Chapter }IsSemisimpleZeroCharacteristicGroupAlgebra}}{31}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color {Chapter }IsSemisimpleRationalGroupAlgebra}}{31}{subsection.6.1.2}
\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color {Chapter }IsSemisimpleANFGroupAlgebra}}{32}{subsection.6.1.3}
\contentsline {subsection}{\numberline {6.1.4}\leavevmode {\color {Chapter }IsSemisimpleFiniteGroupAlgebra}}{32}{subsection.6.1.4}
\contentsline {section}{\numberline {6.2}\leavevmode {\color {Chapter }Operations with group rings elements}}{32}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}\leavevmode {\color {Chapter }Centralizer}}{32}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}\leavevmode {\color {Chapter }OnPoints}}{33}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}\leavevmode {\color {Chapter }AverageSum}}{34}{subsection.6.2.3}
\contentsline {section}{\numberline {6.3}\leavevmode {\color {Chapter }Cyclotomic classes}}{34}{section.6.3}
\contentsline {subsection}{\numberline {6.3.1}\leavevmode {\color {Chapter }CyclotomicClasses}}{34}{subsection.6.3.1}
\contentsline {subsection}{\numberline {6.3.2}\leavevmode {\color {Chapter }IsCyclotomicClass}}{35}{subsection.6.3.2}
\contentsline {section}{\numberline {6.4}\leavevmode {\color {Chapter }Other commands}}{35}{section.6.4}
\contentsline {subsection}{\numberline {6.4.1}\leavevmode {\color {Chapter }InfoWedderga}}{35}{subsection.6.4.1}
\contentsline {subsection}{\numberline {6.4.2}\leavevmode {\color {Chapter }WEDDERGABuildManual}}{35}{subsection.6.4.2}
\contentsline {subsection}{\numberline {6.4.3}\leavevmode {\color {Chapter }WEDDERGABuildManualHTML}}{36}{subsection.6.4.3}
\contentsline {chapter}{\numberline {7}\leavevmode {\color {Chapter }The basic theory behind \textsf {Wedderga}}}{37}{chapter.7}
\contentsline {section}{\numberline {7.1}\leavevmode {\color {Chapter }Group rings and group algebras}}{37}{section.7.1}
\contentsline {section}{\numberline {7.2}\leavevmode {\color {Chapter }Semisimple group algebras}}{37}{section.7.2}
\contentsline {section}{\numberline {7.3}\leavevmode {\color {Chapter }Wedderburn decomposition}}{37}{section.7.3}
\contentsline {section}{\numberline {7.4}\leavevmode {\color {Chapter }Characters and primitive central idempotents}}{38}{section.7.4}
\contentsline {section}{\numberline {7.5}\leavevmode {\color {Chapter }Central simple algebras and Brauer equivalence}}{39}{section.7.5}
\contentsline {section}{\numberline {7.6}\leavevmode {\color {Chapter }Crossed Products}}{39}{section.7.6}
\contentsline {section}{\numberline {7.7}\leavevmode {\color {Chapter }Cyclic Crossed Products}}{40}{section.7.7}
\contentsline {section}{\numberline {7.8}\leavevmode {\color {Chapter }Abelian Crossed Products}}{41}{section.7.8}
\contentsline {section}{\numberline {7.9}\leavevmode {\color {Chapter }Classical crossed products}}{41}{section.7.9}
\contentsline {section}{\numberline {7.10}\leavevmode {\color {Chapter }Cyclic Algebras}}{41}{section.7.10}
\contentsline {section}{\numberline {7.11}\leavevmode {\color {Chapter }Cyclotomic algebras}}{42}{section.7.11}
\contentsline {section}{\numberline {7.12}\leavevmode {\color {Chapter }Numerical description of cyclotomic algebras}}{42}{section.7.12}
\contentsline {section}{\numberline {7.13}\leavevmode {\color {Chapter }Idempotents given by subgroups}}{43}{section.7.13}
\contentsline {section}{\numberline {7.14}\leavevmode {\color {Chapter }Shoda pairs}}{43}{section.7.14}
\contentsline {section}{\numberline {7.15}\leavevmode {\color {Chapter }Strong Shoda pairs}}{43}{section.7.15}
\contentsline {section}{\numberline {7.16}\leavevmode {\color {Chapter }Strongly monomial characters and strongly monomial groups}}{44}{section.7.16}
\contentsline {section}{\numberline {7.17}\leavevmode {\color {Chapter }Cyclotomic Classes and Strong Shoda Pairs}}{45}{section.7.17}
