Efficient Reduction of Quadratic Forms

The positive definite integer quadratic form, ax2 + bxy + cy2, is of some importance in number theory. For example such quadratic forms have been shown useful in factorization of large integers. For many applications it is important to be able to recognize when two quadratic forms are equivalent, so it is useful to be able to reduce these quadratic forms to a canonical representation.For applications in factorization, the quadratic forms used have large coefficients, which must be represented as multiple computer words. This paper shows how to efficiently reduce such multi precision quadratic forms.