Comment #5 on issue 886 by Vinzent.Steinberg: simplify for general functions and derivatives fails http://code.google.com/p/sympy/issues/detail?id=886
>>> from sympy import * >>> var('x') x >>> f=Function('f') >>> f(x)*f(x).diff(x,2)/f(x).diff(x)**2 f(x)*D(f(x), x, x)/D(f(x), x)**2 >>> z=f(x)*f(x).diff(x,2)/f(x).diff(x)**2 >>> z.diff(x) D(f(x), x)*D(f(x), x, x)/D(f(x), x)**2 + f(x)*D(f(x), x, x, x)/D(f(x), x)**2 - 2*f(x)*D(f(x), x, x)*D(f(x), x, x)/(D(f(x), x)**2*D(f(x), x)) >>> simplify(z.diff(x)) (D(f(x), x)**6*D(f(x), x, x) - 2*f(x)*D(f(x), x, x)**2*D(f(x), x)**4 + f(x)*D(f(x), x)**3*D(f(x), x, x, x)*D(f(x), x)**2)/D(f(x), x)**7 It does not raise an exception, but it's still not what I want (as you can see, it can be further simplified). Here is the problem I wanted to solve: Cubic convergence of Halley's method ------------------------------------ Let phi(x) = x - f(x) / f'(x) * G(z) with z = f(x)*f''(x) / f'(x)**2 and G(0) = 1, G'(0) = 0.5. Assuming that phi(x*) = x* (x* is a fix point of phi) and f(x*) = 0 (the iteration x_{k+1} = phi(x_k) converges towards a root of f), prove the cubic convergence rate of this fix point iteration. The aim is to show that the first two derivatives of phi in x* are 0. (This proves that convergence is at least cubic, to prove that it's exactly cubic you'll need to show that the third derivative is not 0). You can do this by hand, but this is the kind of mathematical work you want to use a computer algebra system for. -- You received this message because you are listed in the owner or CC fields of this issue, or because you starred this issue. You may adjust your issue notification preferences at: http://code.google.com/hosting/settings --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy-issues" group. To post to this group, send email to sympy-issues@googlegroups.com To unsubscribe from this group, send email to sympy-issues+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sympy-issues?hl=en -~----------~----~----~----~------~----~------~--~---