[Maxima] Finding roots of sextic in radicals

[Raymond Toy (RT/EUS)]

Nikos Apostolakis wrote:
> Actually in z3, all sines and cosines occur in the form
> sin(atan(expr)) and cos(atan(expr)) where expr are some expresions
> involving square roots.  So using pythagorean theorem one can in 
> principle get an expression involving only radicals from that. 
> 
> So I guess the next question is: is there a global variable that
> setting it true will cause maxima to simplify sin(atan(x)) to
> x/sqrt(1-x^2)?

sin(atan(x)) already returns x/sqrt(1-x^2).

But the expressions aren't sin(atan(x)).  They're sin(atan(x)/3).  To 
simplify that, I think you need to solve a cubic, which will probably 
give another expression containing sin's.

Ray