# [Maxima] solve(...) and unnecessary complex results

Stavros Macrakis macrakis at alum.mit.edu
Thu Feb 21 06:04:19 CST 2008

```The realroots function will find all real roots numerically.

Maxima is a symbolic math system, so normally performs exact symbolic
calculations.

-s

On 2/21/08, Paul Smith <phhs80 at gmail.com> wrote:
> 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
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