An algorithm for computing genera of ternary and quaternary quadratic forms

It is well known that due to the simple shape of the reduction conditions in these dimensions [Mil, Ca] it is in principle no problem to compute representatives of all classes of such quadratic forms whose discriminant is below a given bound. This has been done by hand in the ternary case for halfdiscriminant up to 1000 by Brandt and Intrau [BI], for quaternaries see [Ge, To]. It is, however, sometimes desirable to be able to quickly determine representatives of all classes in some fixed genus of quadratic forms of possibly high discriminant without having to generate along the way all forms of smaller discriminant.

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