Results 321 to 330 of about 1,412,537 (346)

Algebraic Number Fields

2016
Arithmetical algorithms considered in Chap. 5 are based on the arithmetical operations with matrices of the number systems. If the entries of these matrices are not integers or rationals, we need arithmetical algorithms which work with them. Such algorithms exist for algebraic numbers.
openaire   +2 more sources

Polynomial Computability of Fields of Algebraic Numbers

Доклады академии наук, 2018
© 2018, Pleiades Publishing, Ltd. We prove that the field of complex algebraic numbers and the ordered field of real algebraic numbers have isomorphic presentations computable in polynomial time. For these presentations, new algorithms are found for evaluation of polynomials and solving equations of one unknown.
V. L. Selivanov, V. L. Selivanov, P. E. Alaev, P. E. Alaev   +3 more
openaire   +3 more sources

Diophantine approximation of linear forms over an algebraic number field

, 1973
This paper gives an algorithm for generating all the solutions in integers x 0 , x 1 …, x n of the inequality where 1, α 1 , …,α n are numbers, linearly independent over the rationals, in a real algebraic number field of degree n + 1 ≥ 3 and c is any ...
T. Cusick
semanticscholar   +1 more source

Algebraic Numbers and Number Fields

1998
A number α is called an algebraic number if it satisfies an equation of degree m of the form $${\alpha ^m} + {a_1}{\alpha ^{m - 1}} + {a_2}{\alpha ^{m - 2}} + \cdots + {a_m} = 0$$ where a 1, a 2,..., a m are rational numbers.
openaire   +2 more sources

On power basis of a class of algebraic number fields

, 2016
Let K = ℚ(θ) be an algebraic number field with θ in the ring AK of algebraic integers of K and F(x) be the minimal polynomial of θ over the field ℚ of rational numbers.
Bablesh Jhorar, S. K. Khanduja
semanticscholar   +1 more source

A course in computational algebraic number theory

Graduate texts in mathematics, 1993
H. Cohen
semanticscholar   +1 more source

On the maximal unramified p-extension of an algebraic number field.

, 1993
Kay Wingberg
semanticscholar   +1 more source

Arithmetic in an Algebraic Number Field

2010
6.1. Let F be a field. A map \(\,\nu : F\to {\bold{R}}\cup\{\infty\}\) is called an order function of F if it satisfies the following conditions:
openaire   +2 more sources

On the number of solutions of linear equations in units of an algebraic number field

, 1979
K. Györy
semanticscholar   +1 more source

On a certain type of characters of the idèle-class group of an algebraic number-field

, 1979
A. Weil
semanticscholar   +1 more source