On the computation of Hermite-Humbert constants for real quadratic number fields

Michael E. Pohst; Marcus Wagner

Displaying similar documents to “On the computation of Hermite-Humbert constants for real quadratic number fields”

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François Sigrist (2000)

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Voronoï ’s algorithm is a method for obtaining the complete list of perfect $n$ -dimensional quadratic forms. Its generalization to $G$ -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of $G$ -perfect forms ( $G$ is a finite subgroup of $G L (n, ℤ))$ . We study the standard, $φ (m)$ -dimensional irreducible representation of the cyclic group $C_{m}$ of order $m$ , and give the, often new, densest $G$ -forms. Perfect cyclotomic forms are completely classified...

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This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.

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We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer $D \equiv 0, 1$ mod $4$ and the factorization of $D$ , computes the structure of the $2$ -Sylow subgroup of the class group of the quadratic order of discriminant $D$ in random polynomial time in $log |D|$ .

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