User:VIxen/Code: Difference between revisions

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@@ Line 71: / Line 71: @@
 int printIsodiffTriads(){
 /* Find triads in ETs that satisfy the frequency relation bottom + top == 2 * middle.
-The root of x^{top} - 2 * x^{mid} + 1 is found by the Newton-Raphson method
+The root of x^{top} - 2 * x^{mid} + 1 is found by the Newton-Raphson method. */
-after dividing the polynomial by x-1. */
      const int MINDEG = 12;
@@ Line 96: / Line 95: @@
          /* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */
-             do{ /* Step of Newton-Raphson. TODO: avoid summing lots of powers,
+             do{ /* Step of Newton-Raphson */
-                   differentiate (x^k-1)/(x-1) like a fraction instead. */
+                 pwr = pow(x, mid);
-                 pwr = x;
+                 val = 1. - 2. * pwr;
-                 val = -x - 1.;
+                 der = -2. * mid * pwr / x;
-                 der = -1.;
+                pwr *= pow(x, top - mid);
-                for (p = 2; p < mid; p++){
+                val += pwr;
-                    pwr *= x;
+                der += top * pwr / x;
-                    val -= pwr;
-                    der -= pwr * p;
-                }
-                for (; p < top; p++){
-                    pwr *= x;
-                    val += pwr;
-                    der += pwr * p;
-                }
                  x -= val / der;
              } while (val > 1e-5);