algsys and real solutions

Mathematica provides these answers, but only teta is likely to be real.

{{teta -> 0.7149967367564205 - 3.197442310920451*^-14* I,
 alpha -> 2.9108200822019925 +  0.8604727214413472*I, 
  beta -> -2.9108200822020556 + 0.8604727214413*I}, 

 {teta -> 0.7149967367564205 + 3.197442310920451*^-14* I, 
alpha -> 2.9108200822019925 -  0.8604727214413472*I, 
  beta -> -2.9108200822020556 - 0.8604727214413*I}, 

 {teta -> 1.8925016316217953 - 1.6468675090842353*I, 
  alpha -> 2.102721744570885 - 1.3266245243852706*I, 
  beta -> 0.5135418267729412 + 0.39710396729601977*I}, 

 {teta -> 1.8925016316217953 + 1.6468675090842353*I, 
  alpha -> 2.102721744570885 + 1.3266245243852706*I, 
  beta -> 0.5135418267729412 - 0.39710396729601977*I}, 

 {teta -> 1.8925016316218155 - 1.6468675090842426*I, 
  alpha -> -0.5135418267729636 - 0.39710396729603836* I,
 beta -> -2.102721744570886 +     1.326624524385275*I}, 

 {teta -> 1.8925016316218155 + 1.6468675090842426*I, 
  alpha -> -0.5135418267729636 + 0.39710396729603836*  I, 
  beta -> -2.102721744570886 -     1.326624524385275*I}}

The exact symbolic solution from Mathematica is quite long and involves
roots of polynomials of degree 6.



> -----Original Message-----
> From: maxima-admin at math.utexas.edu [mailto:maxima-admin at math.utexas.edu]
> On Behalf Of Michel Gosse
> Sent: Friday, August 18, 2006 1:35 AM
> To: maxima at math.utexas.edu
> Subject: algsys and real solutions
> 
> Hello
> 
> Solving the above system with algsys, i obtain only complex solutions. How
> can
> i obtain the real solutions of this system ?
> 
> eq1: alpha * beta * teta / ( (alpha-1)*(beta+1) ) - 1.5
> eq2: alpha * beta * teta^2 / ( (alpha-2)*(beta+2) ) - 3
> eq3: alpha * beta * teta^3 / ( (alpha-3)*(beta+3) ) - 4.5
> 
> algsys([eq1,eq2,eq3],[alpha,beta,teta]) returns no real solutions.
> 
> Best regards
> 
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