Solver misses real solutions



On 10/13/2013 09:00 PM, Stavros Macrakis wrote:
>
>  I'll guess that these are 
http://en.m.wikipedia.org/wiki/Casus_irreducibilis, where an exact real 
solution can only be expressed with complex expressions. For approximate 
(numeric) results, you can use realroots.
>
>  -s

Yes, that's it. If the solution set is three irrational (real) numbers, 
then a solution using radicals only requires complex radicals. Maybe 
Maxima and Mathematica prefer this form because it seems more consistent 
to use radicals if possible (or maybe it's accidental). I suppose Maxima 
could use a function to convert to trig functions. I don't know if 
something similar applies to quartic equations and some solutions of 
higher order equations.

>  On Oct 13, 2013 1:12 PM, "Joerg Rauh" <jrgrauh at yahoo.com> wrote:
>
>  ("5.28.0-2","2012-08-27 23:16:48","i686-pc-mingw32","GNU Common Lisp 
(GCL)","GCL 2.6.8")
>
>  Dear Maxima Supporter,
>  out of wxMaxima 12.04.0 I had Maxima solve for x:
>  ((40-3*x)*(20-2*x)*x)/2-500
>  Here are the results:
> 
[x=(-(sqrt(3)*%i)/2-1/2)*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+(1300*((sqrt(3)*%i)/2-1/2))/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))+70/9,
> 
x=((sqrt(3)*%i)/2-1/2)*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+(1300*(-(sqrt(3)*%i)/2-1/2))/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))+70/9,
> 
x=((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+1300/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))
>
>  It missed the real results: x=1.7407 and x=6.23415, which I found here:
> 
http://www.wolframalpha.com/input/?i=solve%28%28%2840-3*x%29%2F2%29*%2820-2*x%29*x-500%2Cx%29
>
>  Is there anything I can do differently to make it find the real solutions?
>  Thank you and kind regards
>
>  Joerg
>
>  _______________________________________________
>  Maxima mailing list
>  Maxima at math.utexas.edu
>  http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
>
>  _______________________________________________
>  Maxima mailing list
>  Maxima at math.utexas.edu
>  http://www.math.utexas.edu/mailman/listinfo/maxima