Subexponential class group and unit group computation in large degree number fields

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/S1461157014000345

Jean-François Biasse, C. Fieker

引用次数: 56

Abstract

We describe how to compute the ideal class group and the unit group of an order in a number field in subexponential time. Our method relies on the generalized Riemann hypothesis and other usual heuristics concerning the smoothness of ideals. It applies to arbitrary classes of number fields, including those for which the degree goes to infinity.

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大次数域的次指数类群和单位群计算

讨论了如何在次指数时间内计算数域上一阶的理想类群和单位群。我们的方法依赖于广义黎曼假设和其他关于理想平滑性的常用启发式。它适用于任意类型的数域，包括那些趋近于无穷度的数域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.