Generating random factored ideals in number fields
نویسندگان
چکیده
منابع مشابه
Generating Random Factored Ideals in Number Fields
We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can produce a random ideal in the ring of algebraic integers uniformly at random among ideals with norm up to N , in polynomial time. We also present a variant of...
متن کاملGenerating random factored Gaussian integers, easily
We present a (random) polynomial-time algorithm to generate a randomGaussian integer with the uniform distribution among those with norm at most N , along with its prime factorization. The method generalizes to finding a random ideal in the ring of integers of a quadratic number field together with its prime ideal factorization. We also discuss the analogous problem for higher degree number fie...
متن کاملHilbert-Speiser number fields and Stickelberger ideals
Let p be a prime number. We say that a number field F satisfies the condition (H ′ pn) when any abelian extension N/F of exponent dividing p has a normal integral basis with respect to the ring of p-integers. We also say that F satisfies (H ′ p∞) when it satisfies (H ′ pn) for all n ≥ 1. It is known that the rationals Q satisfy (H ′ p∞) for all prime numbers p. In this paper, we give a simple c...
متن کاملGenerating Cosmological Gaussian Random Fields
We present a generic algorithm for generating Gaussian random initial conditions for cosmological simulations on periodic rectangular lattices. We show that imposing periodic boundary conditions on the real-space correlator and choosing initial conditions by convolving a white noise random field results in a significantly smaller error than the traditional procedure of using the power spectrum....
متن کاملApplications of Prime Factorization of Ideals in Number Fields
For a number fieldK, that is, a finite extension of Q, and a prime number p, a fundamental theorem of algebraic number theory implies that the ideal (p) ⊆ OK factors uniquely into prime ideals as (p) = p1 1 · · · p eg g . In this paper we explore different interpretations of this using the factorization of polynomials in finite and p-adic fields and Galois theory. In particular, we present some...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2017
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3283