Subject: solve(...) and unnecessary complex results
From: Raymond Toy (RT/EUS)
Date: Wed, 20 Feb 2008 16:54:31 -0500
maxima-list at ssteiner.com wrote:
> Dear Maxima experts,
>
> If I make Maxima solve the following example equation it returns results which contain complex parts (%i) but I think the results should be "normal" real numbers.
>
> Example: solve( (0=x^3-4*x+2), x );
>
> Maxima returns:
> [x = (-sqrt(3)*%i/2-1/2)*(3^-(3/2)*sqrt(37)*%i-1)^(1/3)+4*(sqrt(3)*%i/2-\
> 1/2)/(3*(3^-(3/2)*sqrt(37)*%i-1)^(1/3)),x = (sqrt(3)*%i/2-1/2)*(3^-(3/2)*sqrt(\
> 37)*%i-1)^(1/3)+4*(-sqrt(3)*%i/2-1/2)/(3*(3^-(3/2)*sqrt(37)*%i-1)^(1/3)),x = (\
> 3^-(3/2)*sqrt(37)*%i-1)^(1/3)+4/(3*(3^-(3/2)*sqrt(37)*%i-1)^(1/3))]
>
> I think the correct results are -2,214; 0,539; 1,675
> How to make Maxima return these results (real numbers) instead of complicated terms containing complex numbers?
>
How about this:
solve(x^3-4*x+2,x)$
rectform(%)$
trigsimp(%);
[x = -(2*sqrt(3)*sin((atan(sqrt(37)/(3*sqrt(3)))-%pi)/3)
+2*cos((atan(sqrt(37)/(3*sqrt(3)))-%pi)/3))
/sqrt(3),
x = (2*sqrt(3)*sin((atan(sqrt(37)/(3*sqrt(3)))-%pi)/3)
-2*cos((atan(sqrt(37)/(3*sqrt(3)))-%pi)/3))
/sqrt(3),x = 4*cos((atan(sqrt(37)/(3*sqrt(3)))-%pi)/3)/sqrt(3)]
All the numbers are real now, but there are trig functions. I think
that's unavoidable.
Ray