quadratic field

Noun

quadratic field (plural quadratic fields)

1. (algebraic number theory) A number field that is an extension field of degree two over the rational numbers.
   • 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.1985, Erich Kaltofen, Heinrich Rolletschek, Arithmetic in Quadratic Fields with Unique Factorization, Bob F. Caviness (editor), EUROCAL '85: European Conference on Computer Algebra, Proceedings...
   • The foundations of the theory of binary quadratic forms, the forerunner of our modern theory of quadratic fields, were laid by Gauss in his famous Disquisitiones Arithmeticae.1990, Alan Baker, Transcendental Number Theory, Cambridge University Press, page 47