Composition of two positive definite binary quadratic forms of the same discriminant
We start with two positive definite binary quadratic forms a1x2+b1xy+c1y2 and a2x2+b2xy+c2y2, where b12- 4a1c1=b22- 4a2c2.
We use an algorithm due to F. Arndt (Auflösung einer Aufgabe in der Composition der quadratischen Formen, J. Reine Angew. Math. 56, 64-71, 1859) to find the composite of the two forms.
This is a BCMATH version of Algorithm 5.4.7 from p. 241-242 of A Course in Computational Number Theory, 1993, by Henri Cohen.
The output form is reduced.
The program is a translation to BCMATH of the BC function compose1 in the BC file reduceneg.
Last modified 25th July 2011
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