Inner Products
Example FldForms_generalform (H29E1)
DotProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
DotProductMatrix(W) : SeqEnum[ModTupFldElt] -> AlgMatElt
GramMatrix(V) : ModTupRng -> AlgMatElt
InnerProductMatrix(V) : ModTupRng -> AlgMatElt
Example FldForms_grammatrix (H29E2)
Example FldForms_innerprod (H29E3)
Orthogonality
OrthogonalComplement(V, X : parameters) : ModTupFld, ModTupFld -> ModTupFld
Radical(V : parameters) : ModTupFld -> ModTupFld
IsNondegenerate(V) : ModTupFld -> BoolElt
SingularRadical(V) : ModTupFld -> ModTupFld
IsNonsingular(V) : ModTupFld -> BoolElt
Isotropic and Singular Vectors and Subspaces
HasIsotropicVector(V) : ModTupFld -> BoolElt, ModTupFldElt
HasSingularVector(V) : ModTupFld -> BoolElt, ModTupFldElt
HyperbolicPair(V, u) : ModTupFld, ModTupFldElt -> ModTupFldElt
Example FldForms_pseudoalt (H29E4)
HyperbolicSplitting(V) : ModTupFld -> SeqEnum, SeqEnum
Example FldForms_hypsplit (H29E5)
Example FldForms_extradical (H29E6)
IsTotallyIsotropic(V) : ModTupFld) -> BoolElt
IsTotallySingular(V) : ModTupFld) -> BoolElt
WittDecomposition(V) : ModTupFld -> SeqEnum[ModTupFld]
WittIndex(V) : ModTupFld -> RngIntElt
MaximalTotallyIsotropicSubspace(V) : ModTupFld -> ModTupFld
MaximalTotallySingularSubspace(V) : ModTupFld -> ModTupFld
The Standard Forms
StandardAlternatingForm(n,R) : RngIntElt, Rng -> AlgMatElt
Example FldForms_alternatingform (H29E7)
StandardPseudoAlternatingForm(n,K) : RngIntElt, Fld -> AlgMatElt
StandardHermitianForm(n,K) : RngIntElt, Fld -> AlgMatElt, Map
StandardQuadraticForm(n, K : parameters) : RngIntElt, Fld -> AlgMatElt
Example FldForms_minusform (H29E8)
Example FldForms_revisedminus (H29E9)
StandardSymmetricForm(n, K) : RngIntElt, Fld -> AlgMatElt
Constructing Polar Spaces
IsPolarSpace(V) : ModTupFld -> BoolElt
PolarSpaceType(V) : ModTupFld -> MonStgElt
Example FldForms_polarspace (H29E10)
Symplectic Spaces
SymplecticSpace(J) : AlgMatElt -> ModTupRng
IsSymplecticSpace(W) : ModTupFld -> BoolElt
IsPseudoSymplecticSpace(W) : ModTupFld -> BoolElt
Unitary Spaces
UnitarySpace(J, sigma) : AlgMatElt, Map -> ModTupFld
IsUnitarySpace(W) : ModTupFld -> BoolElt
Example FldForms_unitaryform (H29E11)
ConjugateTranspose(M, sigma) : Mtrx, Map -> Mtrx
Quadratic Spaces
QuadraticSpace(Q) : AlgMatElt -> ModTupFld
QuadraticSpace(f) : RngMPolElt -> ModTupFld
SymmetricToQuadraticForm(J) : AlgMatElt -> AlgMatElt
QuadraticFormMatrix(V) : ModTupRng -> ModAlgElt
QuadraticNorm(v) : ModTupFldElt -> FldElt
QuadraticFormPolynomial(V) : ModTupRng -> RngPolElt
Example FldForms_polyquad (H29E12)
OrthogonalSum(V, W) : ModTupFld, ModTupFld) -> ModTupFld
TotallySingularComplement(V, U, W) : ModTupFld, ModTupFld, ModTupFld) -> ModTupFld
Discriminant(V) : ModTupFld -> RngIntElt
ArfInvariant(V) : ModTupFld -> RngIntElt
DicksonInvariant(V, f) : ModTupFld, Mtrx -> RngIntElt
SpinorNorm(V, f) : ModTupFld, Mtrx -> RngIntElt
HyperbolicBasis(U, B, W) : ModTupFld, SeqEnum, ModTupFld -> SeqEnum
OrthogonalReflection(a) : ModTupFldElt -> AlgMatElt
RootSequence(V, f) : ModTupFld, Mtrx -> SeqEnum
ReflectionFactors(V, f) : ModTupFld, Mtrx) -> SeqEnum
SiegelTransformation(u, v) : ModTupFldElt, ModTupFldElt -> AlgMatElt
Example FldForms_siegel (H29E13)
Isometries
IsIsometry(U, V, f) : ModTupFld, ModTupFld, Map -> BoolElt
IsIsometry(f) : Map -> BoolElt
IsIsometry(V, g) : ModTupFld, Mtrx -> BoolElt
IsIsometric(V, W) : ModTupFld, ModTupFld -> BoolElt, Map
Example FldForms_isometric (H29E14)
Example FldForms_transform (H29E15)
Example FldForms_transformalt (H29E16)
CommonComplement(V, U, W) : ModTupFld, ModTupFld, ModTupFld) -> ModTupFld
ExtendIsometry(V, U, f) : ModTupFld, ModTupFld, Map -> Map
IsometryGroup(V) : ModTupFld) -> GrpMat
Example FldForms_isometrygroup (H29E17)
Example FldForms_conjisom (H29E18)
Similarities
IsSimilarity(U, V, f) : ModTupFld, ModTupFld, Map -> BoolElt
IsSimilarity(f) : Map -> BoolElt
IsSimilarity(V, g) : ModTupFld, Mtrx -> BoolElt
SimilarityGroup(V) : ModTupFld) -> GrpMat
Wall Forms
WallForm(V, f) : ModTupFld, Mtrx -> ModTupFld, Map
WallIsometry(V, I, mu) : ModTupFld, ModTupFld, Map -> Mtrx
WallDecomposition(V, f) : ModTupFld, Mtrx -> Mtrx, Mtrx
SemiOrthogonalBasis(V) : ModTupFld) -> SeqEnum
Invariant Forms
InvariantBilinearForms(G) : GrpMat -> SeqEnum[AlgMatElt], SeqEnum[AlgMatElt]
Example FldForms_reducible (H29E19)
Example FldForms_nonabs (H29E20)
InvariantQuadraticForms(G) : GrpMat -> SeqEnum[AlgMatElt]
Example FldForms_invquadform (H29E21)
SemilinearDual(M, mu) : ModGrp,Map -> ModGrp
InvariantSesquilinearForms(G) : GrpMat -> SeqEnum[AlgMatElt]
Example FldForms_sesquiforms (H29E22)
Example FldForms_hermandalt (H29E23)
InvariantFormBases(G) : GrpMat -> SeqEnum[AlgMatElt], SeqEnum[AlgMatElt], SeqEnum[AlgMatElt], SeqEnum[AlgMatElt]
Semi-invariant Forms
TwistedDual(M, lambda) : ModGrp, Map -> ModGrp
SemiInvariantBilinearForms(G) : GrpMat -> SeqEnum
SemiInvariantQuadraticForms(G) : GrpMat -> SeqEnum
TwistedSemilinearDual(M, lambda, mu) : ModGrp, Map, Map -> ModGrp
SemiInvariantSesquilinearForms(G) : GrpMat -> SeqEnum
Example FldForms_semiinv (H29E24)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012