Subject: solve(...) and unnecessary complex results
From: Paul Smith
Date: Thu, 21 Feb 2008 11:02:52 +0000
On Wed, Feb 20, 2008 at 9:32 PM, <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?
You can also solve the problem numerically:
1. with plot2d identify small intervals containing the solutions;
2. use find_root to determine the numeric solutions.
Paul