Binary quadratic form: Difference between revisions

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Lagrange proved that for every value ''D'', there are only finitely many classes of binary quadratic forms with discriminant ''D''. Their number is the '''{{vanchor|class number}}'''<!--boldface per WP:R#PLA--> of discriminant ''D''. He described an algorithm, called '''reduction''', for constructing a canonical representative in each class, the '''reduced form''', whose coefficients are the smallest in a suitable sense.

Gauss gave a superior reduction algorithm in ''[[Disquisitiones Arithmeticae]]'', which has ever since has been the reduction algorithm most commonly given in textbooks. In 1981, Zagier published an alternative reduction algorithm which has found several uses as an alternative to Gauss's.<ref>{{harvnb|Zagier|1981||loc=}}</ref>

== Composition ==