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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Gauss's ternary form reduction and the $ 2$-Sylow subgroup


Author: Daniel Shanks
Journal: Math. Comp. 25 (1971), 837-853
MSC: Primary 12A99
Corrigendum: Math. Comp. 32 (1978), 1328-1329.
Corrigendum: Math. Comp. 32 (1978), 1328-1329.
MathSciNet review: 0297737
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Abstract: An algorithm is developed for determining the 2-Sylow subgroup of the class group of a quadratic field provided the complete factorization of the discriminant d is known. It uses Gauss's ternary form reduction with some new improvements and is applicable even if d is so large that the class number $ h(d)$ is inaccessible. Examples are given for various d that illustrate a number of special problems.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0297737-4
PII: S 0025-5718(1971)0297737-4
Keywords: Quadratic field, class group, 2-Sylow subgroup, genera, principal genus, ambiguous forms, reduction of ternary quadratic forms, cycle graph
Article copyright: © Copyright 1971 American Mathematical Society