On the computation of quadratic $2$-class groups

Wieb Bosma; Peter Stevenhagen

On the computation of quadratic

2

-class groups

Wieb Bosma ; Peter Stevenhagen

Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 283-313.

corrigé par Erratum “On the computation of quadratic

2

-class groups”

Résumé
Abstract

Nous décrivons un algorithme dû à Gauss, Shanks et Lagarias qui étant donné un entier $D \equiv 0, 1$ mod $4$ non carré et la factorisation de $D$ , détermine la structure du $2$ -sous-groupe de Sylow du groupe des classes de l’ordre quadratique de déterminant $D$ ; la complexité de cet algorithme est en temps polynomial probabiliste en $log |D|$ .

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 $log |D|$ .

MR Zbl

Classification : Primary 11Y40, 11R11, Secondary 11E16, 11E20
Mots-clés : quadratic 2-class groups, binary and ternary quadratic forms

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     title = {On the computation of quadratic $2$-class groups},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {283--313},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
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     mrnumber = {1438471},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_283_0/}
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Wieb Bosma; Peter Stevenhagen. On the computation of quadratic $2$-class groups. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 283-313. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_283_0/

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