### Calculating the class number h(d) for real quadratic fields Q(√d)

h(d) is listed for all squarefree d in the range m ≤ d ≤ n, where n < 10^{6}.

Here D is the field discriminant.

We locate all reduced irrationals of the form (b+√D)/(2|c|), where c is negative and 4c divides D-b^{2}. We use the PQa continued fraction algorithm of Lagrange to break the set into disjoint cycles, retaining one number from each cycle. Each reduced number then gives rise to a reduced form (a,b,c) of discriminant D, where a=(b^{2}-D)/(4c).

We are able to also determine if the Pell equation x^{2}-Dy^{2}=-4 has a solution, by using the fact that the equation is soluble iff at least one of the above cycles is odd.
We write the output as h(d)- or h(d)+, according as the negative Pell equation is, or is not, soluble.

(See note and Henri Cohen p. 260, *A course in computational number theory*, First Edition.)

*Last modified 18th July 2011*

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