### Composition of two indefinite binary quadratic forms of the same discriminant

We start with two indefinite binary quadratic forms a_{1}x^{2}+b_{1}xy+c_{1}y^{2} and a_{2}x^{2}+b_{2}xy+c_{2}y^{2}, where b_{1}^{2}- 4a_{1}c_{1}=b_{2}^{2}- 4a_{2}c_{2}.

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.

*Last modified 19th July 2011*

Return to main page