19 Jan
2007
19 Jan
'07
2:38 p.m.
(c186) subst(%,x,d184)
What does d184 do?
That's the Newton step to solve e^(ix)=-1 for x.
(interesting that it got imagpart exact. Macsyma doesn't, e.g., force 3.1... + .69b-105*%i to real.) But note that the convergence is *cubic* if we just subst realparts: (c190) subst(realpart(d185),x,d184)
Does this just throw away the imaginary part at each iteration? (c190) (et seq.) do, yes. (d245) *is* the iteration, minus discarding the imagpart, which I do manually.
x 1 (d245) (%i - -) (----------- + 1) + x n %i x n (---- + 1) n
Am I reading it right? (i-x/n) * (1/ (i*x/n +1)^n +1) + x Yep. Try it! --rwg CATATONIC TOCCATINA