quadratic field

短语

[计] 二次域

词形变化

quadratic fields 复数 quadratic fields

释义与例句

n.
  1. 1.

    A number field that is an extension field of degree two over the rational numbers.

    1985, Erich Kaltofen, Heinrich Rolletschek, Arithmetic in Quadratic Fields with Unique Factorization, Bob F. Caviness (editor), EUROCAL '85: European Conference on Computer Algebra, Proceedings, Volume 2, Springer, LNCS 204, page 279, In a quadratic field mathbf Q(√), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known.

    2007, H. M. Stark, The Gauss Class-Number Problems, William Duke, Yuri Tschinkel (editors), Analytic Number Theory: A Tribute to Gauss and Dirichlet, American Mathematical Society, Clay Mathematics Institute, page 247, Since Dedekind's time, these conjectures have been phrased in the language of quadratic fields. […] Throughout this paper, k= Q (√d) will be a quadratic field of discriminant d and h(k) or sometimes h(d) will be the class-number of k.