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Reduction of Positive Definite Forms

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Binary Quadratic Forms

Part of the book series: Algorithms and Computation in Mathematics ((AACIM,volume 20))

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Abstract

In this chapter we solve the problems of deciding equivalence and finding the minimum of forms of negative discriminant. First we show, that it suffices to solve those problems for positive definite forms. Then we solve the problems for positive definite forms using reduction theory.

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Buchmann, J., Vollmer, U. (2007). Reduction of Positive Definite Forms. In: Binary Quadratic Forms. Algorithms and Computation in Mathematics, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46368-9_6

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