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Improvements in the computation of ideal class groups of imaginary quadratic number fields

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  • We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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