Binary quadratic form: Difference between revisions

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== Main questions ==

A classical question in the theory of integral quadratic forms is the '''representation problem''': describe the set of numbers represented by a given a quadratic form ''q''. If the number of representations is finite then a further question is to give a closed formula for this number. The notion of ''equivalence'' of quadratic forms and the related ''reduction theory'' are the principal tools in addressing these questions.

Two integral forms are called '''equivalent''' if there exists an invertible integral linear change of variables that transforms the first form into the second. This defines an [[equivalence relation]] on the set of integral quadratic forms, whose elements are called '''classes''' of quadratic forms. Equivalent forms necessarily have the same [[discriminant of a quadratic form|discriminant]]