Status: New Owner: ---- Labels: Type-Defect Priority-Medium New issue 1234 by fredrik.johansson: solve(4**x-x**4, x) (and similar) should give all solutions http://code.google.com/p/sympy/issues/detail?id=1234
The problem of solving 4^x = x^4 was just posed on the Wikipedia reference desk. I posted there some code for finding all the solutions with mpmath. With SymPy, one can find one solution like this: >>> solve(4**x-x**4, x) [-4*LambertW(-1/4*log(4))/log(4)] Four more solutions are: >>> p = -log(4)/4 >>> (LambertW(p)/p).evalf() 2.00000000000000 >>> (LambertW(-p)/p).evalf() -0.766664695962123 >>> (LambertW(I*p)/p).evalf() -0.270279229207913 + 0.869544816180665*I >>> (LambertW(-I*p)/p).evalf() -0.270279229207913 - 0.869544816180665*I Then, one obtains infinitely many solutions by replacing each LambertW(x) above with LambertW(x,k) for k = ...-2,-1,0,1,2,... (SymPy needs to be fixed to support the two-arg LambertW). What solve needs to do is, to begin with, to include all four branches when computing x^(1/4) in tsolve. Secondly, it would be nice it could return a solution containing the free parameter when one exists; something like Set(LambertW(-p,C1)/p, is_integer(C1)). -- 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 [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sympy-issues?hl=en -~----------~----~----~----~------~----~------~--~---
