Reduced Quadratic Form Calculator

Original: f(x,y) = x^2 + xy + y^2
Reduced: g(x,y) = f(1x + 0y, 0x + 1y) = 1x^2 + 1xy + 1y^2

Definition: A quadratic form f(x,y) = ax^2 + bxy + cy^2 with non-square determinant is reduced if -|a| < b <= |a| < |c| or 0 < b < |a| = |c|.