Constructions and Conversions

SymmetricMatrix(f) : RngMPolElt -> Mtrx

Given a multivariate polynomial f that is homogeneous of degree 2, this returns a symmetric matrix representing the same quadratic form.

GramMatrix(L) : Lat -> Mtrx

The symmetric matrix giving the quadratic form on the lattice L.

QuadraticForm(L) : Lat -> RngMPolElt

The quadratic form associated to the lattice L, as a multivariate polynomial.

QuadraticForm(M) : Mtrx -> RngMPolElt

The quadratic form for a symmetric matrix M, as a multivariate polynomial.

QuadraticFormWithInvariants(n, d, F, N) : RngIntElt, RngElt, RngIntElt , RngIntElt -> AlgMatElt

QuadraticFormWithInvariants(n, d, F, N) : RngIntElt, FldAlgElt, RngOrdIdl , [ RngIntElt ] -> AlgMatElt

Quadratic form of dimension n and determinant d that has Hasse invariants -1 at the primes in F. The number of negative entries of the i-th real signature is given by N_i.