Finding roots of sextic in radicals



"Raymond Toy (RT/EUS)" <raymond.toy at ericsson.com> writes:

> 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).
>

Great!

> But the expressions aren't sin(atan(x)).  They're sin(atan(x)/3).  

Indeed.  I should have been more carefull.

> To simplify that, I think you need to solve a cubic, which will
> probably give another expression containing sin's.
>

Right!  If a = sin(x/3) and c =sin(x) then a is the soloution of the
equation: 3a - 4a^3 = c,

Sorry for the noise,
Nikos