Introduction

      Definitions and Background

      Categories

 
Creation of Reductive Groups
      ReductiveGroup(G0, Comp) : GrpLie, Grp -> GrpRed
      ReductiveGroup(group_data) : List -> GrpRed
      SymplecticGroup(V) : SpcPlr -> GrpRed
      OrthogonalGroup(V) : SpcPlr -> GrpRed
      SpecialOrthogonalGroup(V) : SpcPlr -> GrpRed
      UnitaryGroup(V) : SpcPlr -> GrpRed

 
Properties of Reductive Groups
      ConnectedComponent(G) : GrpRed -> GrpRed
      ComponentGroup(G) : GrpRed -> GrpRed
      SplittingField(G) : GrpRed -> Fld
      FieldOfDefinition(G) : GrpRed -> Fld
      CartanName(G) : GrpRed -> MonStgElt
      InnerForm(G, i) : GrpRed, RngIntElt -> SpcPlr
      InnerForms(G) : GrpRed -> [ SpcPlr ]
      Dimension(G) : GrpRed -> RngIntElt
      Rank(G) : GrpRed -> RngIntElt

      Predicates
            IsConnected(G) : GrpRed -> BoolElt
            IsOrthogonal(G) : GrpRed -> BoolElt
            IsSpecialOrthogonal(G) : GrpRed -> BoolElt
            IsSymplectic(G) : GrpRed -> BoolElt
            IsUnitary(G) : GrpRed -> BoolElt
            IsCompact(G) : GrpRed -> BoolElt

 
Operations on Reductive Groups
      GetSplitPrimeWithSquare(G) : GrpRed -> RngIntElt

      Base change
            ChangeRing(G, S) : GrpRed, Rng -> GrpRed

 
Elements of Reductive Groups
      Parent(g) : GrpRedElt -> GrpRed

      Arithmetic of Elements
            x * y : GrpRedElt, GrpRedElt -> GrpRedElt
            x ^ n : GrpRedElt, RngIntElt -> GrpRedElt

      Other Operations with Elements
            ElementToSequence(x) : GrpRedElt -> SeqEnum

 
Bibliography

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