Return to classno.gp CVS log

Up to [local] / OpenXM_contrib / pari / examples

Annotation of OpenXM_contrib/pari/examples/classno.gp, Revision 1.1.1.1

1.1       maekawa     1: \\ ---------------  GP code  ---------------------------------------
                      2: \\
                      3: \\ Time-stamp: <Fri, Mar 26, 1999 - 14:13:17 - villegas@linux47>
                      4: \\
                      5: \\ Description: Compute class number of imaginary quadratic field
                      6: \\ analytically
                      7: \\
                      8: \\ File: classno.gp
                      9: \\
                     10: \\ Original Author: Fernando Rodriguez-Villegas
                     11: \\                  villegas@math.utexas.edu
                     12: \\                  University of Texas at Austin
                     13: \\
                     14: \\ Created:         Fri Mar 26 1999
                     15: \\-----------------------------------------------------------------
                     16:
                     17: \\ Class number h(-d), -d fundamental.
                     18: \\ Adjust constant cc for accuracy, default at least 9 decimal places.
                     19:
                     20: cl(d,cc) =
                     21: {
                     22:   local(q0,sd,t,c, s = 0, q = 1);
                     23:
                     24:   if (!isfundamental(-d), error("Discriminant not fundamental"));
                     25:   if (!cc, cc = 5);
                     26:   sd = sqrt(d);
                     27:   q0 = exp(-2*Pi/sd); c = -4*Pi/sd;
                     28:   for (n=1, ceil(sd*cc),
                     29:     q *= q0; t = 1/(1-q);
                     30:     s += kronecker(-d,n) * q * t * (1 + c*t*n)
                     31:   );
                     32:   if (d==3, s *= 3);
                     33:   if (d==4, s *= 2);
                     34:   -2*s
                     35: }