Dear Gareth Russell: I say thanks to you too, I didn't notice that N is ised for the operator N[] whichis a built-in function. This is certainly another source of complications. Besides, the mismatch between number of equations and unknowns. Will check all these issues later on.

Thank you very much.

Gustavo Wouchuk

Fixing the RN error, and replacing N with n because N[] is a built-in function, Solve alone still produces no general solution, but adding MaxExtraConditions->All, after a pretty long time (minutes), produces a whole list. Which suggests you may get your answer if you can add some assumptions to your input.

Solve[{
  n^2 pia1 R == pib1/2,
  1/48 n - 3 R n^4 pia1 + R n^4 pia3 == -3 pib1 + pib3,
  (R n^6 pia1)/384 - (R n^6 pia3)/768 == pib1/384 - pib3/768,
  (R n^10 pia1)/1474560 - (R n^10 pia3)/2211840 == 
   pib1/1474560 - pib3/2211840,
  0 == newalb10 (pib1 + omb1 betr) + 
    2 epsb (pib3 ch3r/chr + omb3 sh3r/chr),
  0 == newala10 (pia1 - oma1 bett) + 
    2 epsa (pia3 ch3t/cht + omb3 sh3t/cht),
  (R n^10 pia1)/1474560 - (R n^10 pia3)/2211840 == 
   pib1/1474560 - pib3/2211840,
  -((R n^12 pia1)/176947200) + (R n^12 pia3)/
    247726080 == -(pib1/176947200) + pib3/247726080},
 {pia1, pib1, oma1, omb1, pia3, oma3, pib3}, 
 MaxExtraConditions -> All]

Ciao Gianluca, grazie dalla tua osservazione. Purtroppo, malgrado avessi cancellato la incognita doppia, non si è risolto il problema. Vedró di ridurre il numero sia di equazioni che d'incognite.

Dopo tutto Mathematica è uno strumento molto potente per la manipulazione simbolica. Ne trarrò profitto.

Buona sera,

Gustavo.

I have noticed now that your list of unknowns has a duplicate oma3:

{pia1, pib1, oma1, omb1, pia3, oma3, pib3, oma3}

Your system has 8 equations in 7 unknowns.

Caro Gisanluca,Grazie per la risposta. I have invented another arbytrary system in 8 unknowns and Mathematica handled it without problems. The serious problem is that I can not detect any syntax error in the system i am interested in.

Grazie tante,

Gustavo.