[Maxima] Finding roots of sextic in radicals
nikos.ap at gmail.com
Fri Jan 25 11:53:45 CST 2008
"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
> sin(atan(x)) already returns x/sqrt(1-x^2).
> 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,
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