Quadratic Fields

• Discriminant, signature, conductor
• Maximal order, integral basis
• Division of integral elements of $\mbox{\bf Q}(\sqrt{d})$, for d = -1, -2, -3, -7, -11, 2, 3, 5, 13.
• Factorization of integral elements of $\mbox{\bf Q}(\sqrt{d})$, for d = -1, -2, -3, -7, -11.
• Class number (Shanks' algorithm)
• Ideal class group (Buchmann's method)
• Unit group, fundamental unit, regulator
• Decomposition of primes
• Factorization of an ideal
• Solution of norm equations (Cornaccia's algorithm for imaginary fields and Cremona's conics for real quadratic fields)
• Facilities for binary quadratic forms (see Modular Forms)