Matrix Groups over Q and Z

• Overview
• Invariant Forms
  • PositiveDefiniteForm(G): GrpMat → Mtrx
  • InvariantForms(G): GrpMat → [ AlgMatElt ]
  • SymmetricForms(G): GrpMat → [ AlgMatElt ]
  • AntisymmetricForms(G): GrpMat → [ AlgMatElt ]
  • InvariantForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]
  • SymmetricForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]
  • AntisymmetricForms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]
  • NumberOfInvariantForms(G): GrpMat → RngIntElt, RngIntElt
  • NumberOfSymmetricForms(G): GrpMat → RngIntElt
  • NumberOfAntisymmetricForms(G): GrpMat → RngIntElt
• Endomorphisms
  • EndomorphismRing(G): GrpMat → AlgMat
  • EndomorphismAlgebra(G): GrpMat → AlgMat
  • CentreOfEndomorphismRing(G): GrpMat → AlgMat
  • CentreOfEndomorphismAlgebra(G): GrpMat → AlgMat
  • DimensionOfEndomorphismRing(G): GrpMat → RngIntElt
  • DimensionOfCentreOfEndomorphismRing(G): GrpMat → RngIntElt
  • Endomorphisms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]
  • CentralEndomorphisms(G, n): GrpMat, RngIntElt → [ AlgMatElt ]
• New Groups From Others
  • BravaisGroup(G): GrpMat[RngInt] → GrpMat
  • IntegralGroup(G): GrpMat → GrpMat, AlgMatElt
  • IntegralGroup(G): [Mtrx] → [Mtrx], AlgMatElt
• Perfect Forms and Normalizers
  • PerfectForms(G): GrpMat[RngInt] → SeqEnum
  • NormalizerGLZ(G): GrpMat[RngInt] → GrpMat[RngInt]
  • CentralizerGLZ(G): GrpMat[RngInt] → GrpMat[RngInt]
• Conjugacy
  • ZClasses(G): GrpMat → SeqEnum, SeqEnum
  • IsGLZConjugate(G, H): GrpMat[RngInt], GrpMat[RngInt] → BoolElt, GrpMatElt
  • IsBravaisEquivalent(G, H): GrpMat[RngInt], GrpMat[RngInt] → BoolElt, GrpMatElt
  • IsGLQConjugate(G, H): GrpMat, GrpMat → BoolElt, GrpMatElt
• Conjugacy Tests for Matrices
  • IsGLZConjugate(A, B): AlgMatElt, AlgMatElt → BoolElt, GrpMatElt
  • IsGLZConjugate(A, B): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt
  • IsSLZConjugate(A, B): AlgMatElt, AlgMatElt → BoolElt, GrpMatElt
  • IsSLZConjugate(A, B): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt
  • CentralizerGLZ(A): AlgMatElt → GrpMat
  • CentralizerGLZ(A): GrpMatElt → GrpMat
  • AreGLConjugate(A, B : parameters): AlgMatElt, AlgMatElt → BoolElt, AlgMatElt
  • AreGLConjugate(A, B : parameters): GrpMatElt, GrpMatElt → BoolElt, GrpMatElt
  • GLCentraliser(A : parameters): AlgMatElt → GrpMat
  • GLCentraliser(A : parameters): GrpMatElt → GrpMat
• Examples
  • Example: Z Classes
  • Example: conjugacy
  • Example: Conjugacy Matrices
  • Example: GLnZClasses EHOB