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Follow the documentation on Quadratic forms (which includes a number of examples). You can also access the documentation from within Sage by typing QuadraticForm?. You can view the source code by typing QuadraticForm??.

The documentation on Quadratic forms (which includes a number of examples). forms indeed documents this restriction.

You can also access the this documentation from within Sage by typing QuadraticForm?. You can view the source code by typing QuadraticForm??.

You can also access this documentation online. On the online documentation for quadratic forms in Sage, the "Next Topic" is Binary Quadratic Forms with Integer Coefficients, which does not have this restriction.

So if your quadratic forms are only in two variables, use BinaryQF.

[Edited 2014-12-12]2014-12-12, 2014-12-13.]

The documentation on Quadratic forms indeed documents this restriction.

You can access this documentation within Sage by typing QuadraticForm?. You can view the source code by typing QuadraticForm??.

You can also access this documentation online. On the online documentation for quadratic forms in Sage, the "Next Topic" is Binary Quadratic Forms with Integer Coefficients, which does not have this restriction.

So if your quadratic forms are only in two variables, use BinaryQF.. Here the quadratic form you gave as an example:

sage: Q = BinaryQF([1,4,3])
sage: Q
x^2 + 4*x*y + 3*y^2