See quadratic field on Wiktionary
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"text": "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,\nIn 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."
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"ref": "1990, Alan Baker, Transcendental Number Theory, Cambridge University Press, page 47:",
"text": "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.",
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"ref": "2000, Henri Cohen, A Course in Computational Algebraic Number Theory, Springer, page 223:",
"text": "In this chapter, we consider the simplest of all number fields that are different from #x5C;Q, i.e. quadratic fields. Since n#x3D;2#x3D;r#x5F;1#x2B;2r#x5F;2, the signature (r#x5F;1,r#x5F;2) of a quadratic field K is either (2,0), in which case we will speak of real quadratic fields, or (0,1), in which case we will speak of imaginary (or complex) quadratic fields. By Proposition 4.8.11 we know that imaginary quadratic fields are those of negative discriminant, and that real quadratic fields are those with positive discriminant.",
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"text": "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,\nSince 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."
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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