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Magma
Computer • algebra
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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
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V2.29, 21 October 2025