منابع مشابه
Stable Computation of the Complex Roots of Unity Stable Computation of the Complex Roots of Unity
In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at rst. In particular, the formulas given in a standard programmer's reference book Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable, giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both b...
متن کاملTHE q–CHARACTERS AT ROOTS OF UNITY
We consider various specializations of the untwisted quantum affine algebras at roots of unity. We define and study the q–characters of their finite-dimensional representations.
متن کاملNews about Roots of Unity
This text was originally intended for non-mathematicians; during its preparation B. Mazur and A. Wiles announced the solution of the ’Main Conjecture’ in the theory of cyclotomic fields. It seemed appropriate to us to try to give an explanation of what this sensational discovery is all about.
متن کاملRoots of unity in orders
We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite...
متن کاملCohen–lenstra Heuristic and Roots of Unity
We report on computational results indicating that the well-known Cohen–Lenstra–Martinet heuristic for class groups of number fields may fail in many situations. In particular, the underlying assumption that the frequency of groups is governed essentially by the reciprocal of the order of their automorphism groups, does not seem to be valid in those cases. The phenomenon is related to the prese...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0302748-9