On Feb 18, 2008 7:16 PM, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> > (%i29) log2(x) := log(x)/log(2)
> > (%i84) eq1 : y = 64*n*log2(n)$
> > (%i85) eq2 : y = 8*n^2$
> >
>
> Maxima cannot solve this system of equations symbolically because it is not
> solvable in closed form. Using the eliminate function, you can reduce it to
> an equation in n only:
>
> eq12: eliminate([eq1,eq2],[y]); => [8*n*(8*log(n)-log(2)*n)]
>
> If you use solve on the result, you get
>
> sols: solve(eq12,n) => [n = 0,n = 8*log(n)/log(2)]
>
> The first solution is correct (despite the log(n) term...); the second is a
> transcendental equation and can't be solved symbolically using the usual
> elementary functions. At this point, you can use find_root:
>
> find_root(sols[2],n,.1,10) => 1.10
> find_root(sols[2],n,10,100) => 43.56
>
> I believe someone is working on a more automated root-finder, but this
> should work for now.
Maple gives all symbolic solutions expressed through Lambert W
functions. Although one can argue that a solution expressed as a
Lambert W function is not a closed-form solution, Maple solution
informs us about the number of solutions of the problem (very helpful
piece of information). Maybe Maxima could be improved regarding the
possibility of giving also the solution of this sort of problems
expressed through Lambert W functions, so that the user could learn
the number of the solutions of his problem.
Paul