### Finding the reduced form equivalent to a positive definite binary quadratic form

Given a positive definite binary quadratic form ax^{2}+bxy+cy^{2}, we use an algorithm of Gauss to determine an equivalent reduced form (A,B,C) and the corresponding unimodular transformation matrix.

Note: d=b^{2} - 4ac < 0, a > 0, c > 0.

(A,B,C) satisfies B^{2} - 4AC = d, -A < B ≤ A < C or 0 ≤ B ≤ A = C.

The number of steps taken in the reduction is returned.
(See L.E. Dickson, *Introduction to the theory of numbers*, page 69.)

*Last modified 7th June 2011*

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