rqf.m

Reduce a binary quadratic form, given as a row vector of length 3.

This function reduces a binary quadratic form, given as a row vector of length 3. An imaginary (positive definite) binary quadratic form

F(X,Y) = a X^2 + b X Y + c Y^2,

represented as [a b c], is reduced if |b| <= a <= c and b is nonnegative if a=|b| or a=c. A real binary quadratic
form of the same form is reduced
if abs(sqrt(D)-2*abs(c))<b<sqrt(D),
where D = b^2 - 4*a*c is the discriminant.

The output of this function is two
cells, the first the reduced
form and the second the linear
transformation from the original
form to the reduced form, represented
as a 2*2 matrix.