Generating random factored Gaussian integers, easily

Generating 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...

Generating normal numbers over Gaussian integers

In this paper we consider normal numbers over Gaussian integers generated by polynomials. This corresponds to results by Nakai and Shiokawa in the case of real numbers. A generalization of normal numbers to Gaussian integers and their canonical number systems, which were characterized by Kátai and Szabó, is given. With help of this we construct normal numbers of the form 0. bf(z1)c bf(z2)c bf(z...

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...

Generating Gaussian Pseudo-Random Deviates

Generating 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....