Subject: solve(...) and unnecessary complex results
From: Billinghurst, David (RTATECH)
Date: Thu, 21 Feb 2008 09:10:22 +1100
> 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?
>
> Thank you!
> Sebastian
It is not always possible to express the solutions of a cubic equation
with three real roots in terms of radicals using just real numbers.
For more information, Google for "casus irreducibilis".
David
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