On the computation of quadratic 2-class groups
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”

Nous décrivons un algorithme dû à Gauss, Shanks et Lagarias qui étant donné un entier D≡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 logD.

We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D≡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 logD.

Classification : Primary 11Y40, 11R11, Secondary 11E16, 11E20
Mots-clés : quadratic 2-class groups, binary and ternary quadratic forms 
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Bosma, Wieb; Stevenhagen, Peter. On the computation of quadratic $2$-class groups. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 283-313. http://www.numdam.org/item/JTNB_1996__8_2_283_0/

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