static void Faulhaber(int p) { Console.Write("{0} : ", p); Frac q = new Frac(1, p + 1); int sign = -1; for (int j = 0; j <= p; j++) { sign *= -1; Frac coeff = q * new Frac(sign, 1) * new Frac(Binomial(p + 1, j), 1) * Bernoulli(j); if (Frac.ZERO == coeff) { continue; } if (j == 0) { if (Frac.ONE != coeff) { if (-Frac.ONE == coeff) { Console.Write("-"); } else { Console.Write(coeff); } } } else { if (Frac.ONE == coeff) { Console.Write(" + "); } else if (-Frac.ONE == coeff) { Console.Write(" - "); } else if (Frac.ZERO < coeff) { Console.Write(" + {0}", coeff); } else { Console.Write(" - {0}", -coeff); } } int pwr = p + 1 - j; if (pwr > 1) { Console.Write("n^{0}", pwr); } else { Console.Write("n"); } } Console.WriteLine(); }
static Frac Bernoulli(int n) { if (n < 0) { throw new ArgumentException("n may not be negative or zero"); } Frac[] a = new Frac[n + 1]; for (int m = 0; m <= n; m++) { a[m] = new Frac(1, m + 1); for (int j = m; j >= 1; j--) { a[j - 1] = (a[j - 1] - a[j]) * new Frac(j, 1); } } // returns 'first' Bernoulli number if (n != 1) { return(a[0]); } return(-a[0]); }