# 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 $N_i$.