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\\ --------------- GP code --------------------------------------- \\ \\ Time-stamp: <Fri, Mar 26, 1999 - 14:13:17 - villegas@linux47> \\ \\ Description: Compute class number of imaginary quadratic field \\ analytically \\ \\ File: classno.gp \\ \\ Original Author: Fernando Rodriguez-Villegas \\ villegas@math.utexas.edu \\ University of Texas at Austin \\ \\ Created: Fri Mar 26 1999 \\----------------------------------------------------------------- \\ Class number h(-d), -d fundamental. \\ Adjust constant cc for accuracy, default at least 9 decimal places. cl(d,cc) = { local(q0,sd,t,c, s = 0, q = 1); if (!isfundamental(-d), error("Discriminant not fundamental")); if (!cc, cc = 5); sd = sqrt(d); q0 = exp(-2*Pi/sd); c = -4*Pi/sd; for (n=1, ceil(sd*cc), q *= q0; t = 1/(1-q); s += kronecker(-d,n) * q * t * (1 + c*t*n) ); if (d==3, s *= 3); if (d==4, s *= 2); -2*s }