Quadratic Forms#
- Introduction
- Constructions and Conversions
SymmetricMatrix(f): RngMPolElt → MtrxGramMatrix(L): Lat → MtrxQuadraticForm(L): Lat → RngMPolEltQuadraticForm(M): Mtrx → RngMPolEltQuadraticFormWithInvariants(n, d, F, N): RngIntElt, RngElt, { RngIntElt }, RngIntElt → AlgMatEltQuadraticFormWithInvariants(n, d, F, N): RngIntElt, FldAlgElt, { RngOrdIdl }, [ RngIntElt ] → AlgMatElt
- Local Invariants
pSignature(f,p): RngMPolElt, RngIntElt → RngIntEltpSignature(M,p): Mtrx, RngIntElt → RngIntEltpSignature(L,p): Lat, RngIntElt → RngIntEltOddity(f): RngMPolElt → RngIntEltOddity(L): Lat → RngIntEltOddity(M): Mtrx → RngIntEltpExcess(f, p): RngMPolElt, RngIntElt → RngIntEltpExcess(M, p): Mtrx, RngIntElt → RngIntEltpExcess(L, p): Lat, RngIntElt → RngIntEltWittInvariant(f, p): RngMPolElt, RngIntElt → RngIntEltWittInvariant(M, p): AlgMatElt, RngIntElt → RngIntEltWittInvariant(L, p): Lat, RngIntElt → RngIntEltWittInvariant(L, P): Lat, RngInt → RngIntEltWittInvariant(L, P): LatNF, RngOrdIdl → RngIntEltHasseInvariant(f, p): RngMPolElt, RngIntElt → RngIntEltHasseInvariant(M, p): AlgMatElt, RngIntElt → RngIntEltHasseMinkowskiInvariant(f, p): RngMPolElt, RngIntElt → RngIntEltHasseMinkowskiInvariant(M, p): AlgMatElt, RngIntElt → RngIntEltHasseInvariant(L, p): Lat, RngIntElt → RngIntEltHasseMinkowskiInvariant(L, p): Lat, RngIntElt → RngIntEltHasseInvariant(L, P): Lat, RngInt → RngIntEltHasseInvariant(L, P): LatNF, RngOrdIdl → RngIntEltHasseMinkowskiInvariant(L, P): Lat, RngInt → RngIntEltWittInvariants(f): RngMPolElt → SeqEnumWittInvariants(M): AlgMatElt → SeqEnumWittInvariants(L): Lat → SeqEnumHasseInvariants(f): RngMPolElt → SeqEnumHasseInvariants(M): AlgMatElt → SeqEnumHasseInvariants(L): Lat → SeqEnumHasseMinkowskiInvariants(f): RngMPolElt → SeqEnumHasseMinkowskiInvariants(M): AlgMatElt → SeqEnumHasseMinkowskiInvariants(L): Lat → SeqEnumQuadraticFormInvariants(f): RngMPolElt → FldElt, SetEnum, SeqEnum[RngIntElt]QuadraticFormInvariants(M): AlgMatElt → FldElt, SetEnum, SeqEnum[RngIntElt]QuadraticFormInvariants(L): LatNF → FldElt, SetEnum, SeqEnum[RngIntElt]
- Isotropic Subspaces
- Equivalence
IsRationallyEquivalent(X, Y): AlgMatElt, AlgMatElt → BoolElt, AlgMatEltIsRationallyEquivalent(f, g): RngMPolElt, RngMPolElt → BoolElt, AlgMatEltIsRationallySimilar(X, Y): AlgMatElt, AlgMatElt → BoolElt, AlgMatElt, RngIntEltIsRationallySimilar(f, g): RngMPolElt, RngMPolElt → BoolElt, AlgMatElt, RngIntElt