Automorphism Group and Isometry Testing
AutomorphismGroup(L) : Lat -> GrpMat
AutomorphismGroup(L, F) : Lat, [ AlgMatElt ] -> GrpMat
AutomorphismGroup(F) : [ AlgMatElt ] -> GrpMat
Example GLat_AutoAction (H31E1)
Example GLat_AutoStabilizers (H31E2)
Example GLat_AutoL19 (H31E3)
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, F1, M, F()2) : Lat, [ AlgMatElt ], Lat, [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsometric(F1, F()2) : [ AlgMatElt ], [ AlgMatElt ] -> BoolElt, AlgMatElt
Example GLat_Isom (H31E4)
Automorphism Group and Isometry Testing over Fq[t]
DominantDiagonalForm(X) : Mtrx[RngUPol] -> Mtrx, Mtrx, GrpMat, FldFin
Example GLat_DDF-fqt (H31E5)
AutomorphismGroup(G) : Mtrx[RngUPol] -> GrpMat, FldFin
IsIsometric(G1, G2) : Mtrx[RngUPol], Mtrx[RngUPol] -> BoolElt, Mtrx, FldFin
ShortestVectors(G) : Mtrx[RngUPol] -> SeqEnum
ShortVectors(G, B) : Mtrx[RngUPol], RngIntElt -> SeqEnum
Creation of G-Lattices
Lattice(G) : GrpMat -> Lat
LatticeWithBasis(G, B) : GrpMat, ModMatRngElt -> Lat
LatticeWithBasis(G, B, M) : GrpMat, ModMatRngElt, AlgMatElt -> Lat
LatticeWithGram(G, F) : GrpMat, AlgMatElt -> Lat
Operations on G-Lattices
IsGLattice(L) : Lat -> GrpMat
Group(L) : Lat -> GrpMat
NumberOfActionGenerators(L) : Lat -> RngIntElt
ActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
NaturalGroup(L) : Lat -> GrpMat
NaturalActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
Invariant Forms
InvariantForms(L) : Lat -> [ AlgMatElt ]
InvariantForms(L, n) : Lat, RngIntElt -> [ AlgMatElt ]
SymmetricForms(L) : Lat -> [ AlgMatElt ]
SymmetricForms(L, n) : Lat, RngIntElt -> [ AlgMatElt ]
AntisymmetricForms(L) : Lat -> [ AlgMatElt ]
AntisymmetricForms(L, n) : Lat, RngIntElt -> [ AlgMatElt ]
NumberOfInvariantForms(L) : Lat -> RngIntElt, RngIntElt
NumberOfSymmetricForms(L) : Lat -> RngIntElt
NumberOfAntisymmetricForms(L) : Lat -> RngIntElt
PositiveDefiniteForm(L) : Lat -> AlgMatElt
Endomorphisms
EndomorphismRing(L) : Lat -> AlgMat
Endomorphisms(L, n) : Lat, RngIntElt -> [ AlgMatElt ]
DimensionOfEndomorphismRing(L) : Lat -> RngIntElt
CentreOfEndomorphismRing(L) : Lat -> AlgMat
CentralEndomorphisms(L, n) : Lat, RngIntElt -> [ AlgMatElt ]
DimensionOfCentreOfEndomorphismRing(L) : Lat -> RngIntElt
G-invariant Sublattices
Sublattices(G, Q) : GrpMat, [ RngIntElt ] -> [ Lat ], BoolElt
Sublattices(G, p) : GrpMat, RngIntElt -> [ Lat ], BoolElt
Sublattices(G) : GrpMat -> [ Lat ], BoolElt
SublatticeClasses(G) : GrpMat -> [ Lat ]
Example GLat_Sublattices (H31E6)
Example GLat_Sublattices2 (H31E7)
Creating the lattice of sublattices
SublatticeLattice(G, Q) : GrpMat, [ RngIntElt ] -> LatLat, BoolElt
SublatticeLattice(G, p) : GrpMat, RngIntElt -> LatLat, BoolElt
SublatticeLattice(G) : GrpMat, RngIntElt -> LatLat, BoolElt
Example GLat_SublatticeLatticeCreate (H31E8)
Operations on the Lattice of Sublattices
# V : LatLat -> RngIntElt
V ! i: LatLat, RngIntElt -> LatLatElt
V ! M: LatLat, Lat -> LatLatElt
NumberOfLevels( V ) : LatLat -> RngIntElt
Level(V, i) : LatLat, RngIntElt -> [ LatLatElt ]
Levels(v) : LatLat -> [ [LatLatElt] ]
Primes(V) : LatLat -> [ RngIntElt ]
Constituents(V) : LatLat -> SeqEnum
IntegerRing() ! e : RngInt, LatLatElt -> RngIntElt
e + f : LatLatElt, LatLatElt -> LatLatElt
e meet f : LatLatElt, LatLatElt -> LatLatElt
e eq f : LatLatElt, LatLatElt -> BoolElt
MaximalSublattices(e) : LatLatElt -> [ LatLatElt ], [ RngIntElt ]
MinimalSuperlattices(e) : LatLatElt -> [ LatLatElt ] , [ RngIntElt ]
Lattice(e) : SubModLatElt -> Lat
BasisMatrix(e) : SubModLatElt -> Mtrx
Example GLat_SublatticeLattice (H31E9)
Example GLat_SublatticeLattice2 (H31E10)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012