- Introduction
- Reflexive Forms
- Inner Products
- Isotropic and Singular Vectors and Subspaces
- The Standard Forms
- StandardAlternatingForm(n,R) : RngIntElt, Rng -> AlgMatElt
- Example FldForms_alternatingform (H30E8)
- StandardPseudoAlternatingForm(n,K) : RngIntElt, Fld -> AlgMatElt
- StandardHermitianForm(n,K) : RngIntElt, Fld -> AlgMatElt, Map
- StandardQuadraticForm(n, K : parameters) : RngIntElt, Fld -> AlgMatElt
- Example FldForms_minusform (H30E9)
- Example FldForms_revisedminus (H30E10)
- StandardSymmetricForm(n, K) : RngIntElt, Fld -> AlgMatElt
- Constructing Polar Spaces
- IsPolarSpace(V) : ModTupFld -> BoolElt
- PolarSpaceType(V) : ModTupFld -> MonStgElt
- Example FldForms_polarspace (H30E11)
- Symplectic Spaces
- Unitary Spaces
- Quadratic Spaces
- QuadraticSpace(Q) : AlgMatElt -> ModTupRng
- QuadraticSpace(f) : RngMPolElt -> ModTupRng
- SymmetricToQuadraticForm(J) : AlgMatElt -> AlgMatElt
- QuadraticFormMatrix(V) : ModTupRng -> ModAlgElt
- QuadraticNorm(v) : ModTupFldElt -> FldElt
- QuadraticFormPolynomial(V) : ModTupRng -> RngPolElt
- QuadraticFormPolynomial(Q) : AlgMatElt -> RngPolElt
- Example FldForms_polyquad (H30E13)
- OrthogonalSum(V, W) : ModTupFld, ModTupFld -> ModTupFld, Map, Map
- OrthogonalTensorProduct(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 (H30E14)
- Isometries and Similarities
- 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 (H30E15)
- Example FldForms_transform (H30E16)
- Example FldForms_transformalt (H30E17)
- CommonComplement(V, U, W) : ModTupFld, ModTupFld, ModTupFld -> ModTupFld
- ExtendIsometry(V, U, f) : ModTupFld, ModTupFld, Map -> Map
- IsometryGroup(V) : ModTupFld -> GrpMat
- Example FldForms_isometrygroup (H30E18)
- Example FldForms_conjisom (H30E19)
- Similarities
- IsSimilarity(U, V, f) : ModTupFld, ModTupFld, Map -> BoolElt, FldElt
- IsSimilarity(f) : Map -> BoolElt, FldElt
- IsSimilarity(V, g) : ModTupFld, Mtrx -> BoolElt, FldElt
- IsSimilar(V, W) : ModTupFld, ModTupFld -> BoolElt, Map
- Example FldForms_simherm (H30E20)
- SimilarityGroup(V) : ModTupFld -> GrpMat
- Gram-Schmidt Normalisation
- Classical Groups
- Lie Algebras and Bilinear Forms
- 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
- GeneralisedWallForm(V, f) : ModTupFld, Mtrx -> ModTupFld, Map
- Invariant Forms
- Bibliography
V2.28, 13 July 2023