Abstract
In this chapter, we consider the simplest of all number fields that are different from ℚ, i.e. quadratic fields. Since n = 2 = r 1 + 2r 2, the signature (r 1, r 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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© 1993 Springer-Verlag Berlin Heidelberg
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Cohen, H. (1993). Algorithms for Quadratic Fields. In: A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02945-9_5
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DOI: https://doi.org/10.1007/978-3-662-02945-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08142-2
Online ISBN: 978-3-662-02945-9
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