Re: [Maxima-discuss] Simplification of a trigonometric or exponentialized term

[Raymond T. <toy...@gm...>]

>>>>> "Roland" == Roland Salz <sal...@gm...> writes:

    Roland> Thanks, Barton. That’s little better than what I had
    Roland> achieved in (%o20). I did not have the idea to use
    Roland> trigrat, because the expression resulting from your (%i3)
    Roland> does not have any trigonometric functions left, only
    Roland> square roots.

    Roland>  

    Roland> But your result is still far away from the simple
    Roland> expression c. I assume Maxima does not have any guideline
    Roland> regarding to which is the simplest version of this
    Roland> expression of nested square roots. And in order to verify
    Roland> identity of your (%o4) with my c, I would have to do it
    Roland> manually. Maxima does not simplfy, if I build the
    Roland> difference of the two, and I don’t see any way how to
    Roland> simplify this difference to zero. But the floats indicate
    Roland> clearly that the terms should be identical.

Here is one way.  Take Barton's result:

c: (sqrt(sqrt(5)+5)*(3*sqrt(2)*sqrt(5)-5*sqrt(2))*%i)/20
c^2;
ratsimp(sqrt(expand(%))),algebraic;

=> sqrt(5-2*sqrt(5))*%i/sqrt(5)

The c^2 and expand is a hack to get maxima to multiply the contents of
the sqrt together.  This really only works because the imagpart is
positive.  Otherwise, we probably would have gotten the wrong sign.

--
Ray