Sharply Doubly Transitive Groups
Dickson Nearfields
DicksonPairs(p, hlo, hhi, vlo, vhi ) : RngIntElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt) -> SeqEnum
DicksonPairs(p, h1, v1) : RngIntElt, RngIntElt, RngIntElt) -> SeqEnum
DicksonTriples(p, hb, vb) : RngIntElt, RngIntElt, RngIntElt) -> SeqEnum
Example FldNear_dicksonpairs (H22E1)
NumberOfVariants(q, v) : RngIntElt, RngIntElt -> RngIntElt
NumberOfVariants(N) : NfdDck -> RngIntElt
VariantRepresentatives(q, v) : RngIntElt, RngIntElt -> SeqEnum
Example FldNear_variants (H22E2)
DicksonNearfield(q, v : parameters) : RngIntElt, RngIntElt -> NfdDck
Example FldNear_dickson (H22E3)
Zassenhaus Nearfields
ZassenhausNearfield(n) : RngIntElt -> NfdZss
Example FldNear_zassenhaus (H22E4)
Nearfield Arithmetic
Inverse(a) : NfdElt -> NfdElt
Parent and Category
N ! x : Nfd, FldFinElt -> NfdElt
ElementToSequence(x) : NfdElt) -> SeqEnum
Predicates on Nearfield Elements
Example FldNear_simplearith (H22E5)
Example FldNear_leftdist (H22E6)
Operations on Nearfields
Cardinality(N) : Nfd -> RngIntElt
Random(N) : Nfd -> NfdElt
Identity(N) : Nfd -> NfdElt
Zero(N) : Nfd -> NfdElt
PrimeField(N) : Nfd -> FldFin
Kernel(N) : Nfd -> FldFin
The Group of Units
UnitGroup(N) : Nfd -> GrpMat, Map
Example FldNear_unitgrp (H22E7)
Order(x) : NfdElt -> RngIntElt
AffineGroup(N) : Nfd -> GrpMat
ExtendedUnitGroup(D) : NfdDck -> GrpMat
Automorphisms
IsIsomorphic(N1, N2) : NfdDck, NfdDck -> BoolElt, Map
AutomorphismGroup(N) : NfdDck -> GrpPerm, Map
Nearfield Planes
ProjectivePlane( N : parameters) : Nfd -> PlaneProj, PlanePtSet, PlaneLnSet
Example FldNear_projplane (H22E8)
Hughes Planes
HughesPlane(N : parameters) : Nfd -> PlaneProj, PlanePtSet, PlaneLnSet
Example FldNear_hughes (H22E9)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012