# quadratic form over the integers with odd coefficients

Hi,

I'm a newcomer in Sage, and even after thorough examination of the manual I cannot understand the constructor QuadraticFrom :

```
sage: Q = QuadraticForm(ZZ, 2, [1,2,3])
sage: Q
Quadratic form in 2 variables over Integer Ring with coefficients:
[ 1 2 ]
[ * 3 ]
```

But

```
sage: Q.polynomial()
2*x0^2 + 4*x0*x1 + 6*x1^2
```

So how do I construct a quadratic form with odd coefficients in its polynomial expression ? The polynomial x0^2 + 4*x0*x1 + 3*x1^2 defines a genuine quadratic form over the integers. Is it made on purpose for some reasons related to classification of lattices ?

Thank you.

If you are interested in binary quadratic forms this may be of interest for you: http://oeis.org/wiki/User:Peter_Lusch...