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  1. Xref: sparky sci.math:10468 sci.math.symbolic:2242
  2. Newsgroups: sci.math,sci.math.symbolic
  3. Path: sparky!uunet!munnari.oz.au!metro!news
  4. From: king@physics.su.OZ.AU (Peter King)
  5. Subject: Solving Rate Equations
  6. Message-ID: <1992Aug20.224623.7856@ucc.su.OZ.AU>
  7. Sender: news@ucc.su.OZ.AU
  8. Nntp-Posting-Host: langmuir.physics.su.oz.au
  9. Organization: School of Physics, University of Sydney, Australia
  10. Date: Thu, 20 Aug 1992 22:46:23 GMT
  11. Lines: 35
  12.  
  13. I'm interested in solving the following equations (in Mathematica format)
  14. for a cw optically pumped laser:
  15.  
  16. eqns = {
  17.         wv N3 - wp (N0 - g0 / g2 N2) == 0
  18.         B21 n (N2 - g2 / g1 N1) - wr N1 == 0
  19.         wp (N0 - g0 / g2 N2) - wr N2 - B21 n (N2 - g2 / g1 N1) == 0
  20.         N0 + N1 + N2 + N3 == N
  21.         B21 n (N2 - g2 / g1 N1) - 2 Pi y n == 0
  22.        }
  23.  
  24. simultaneously.  In Mathematica I naively tried
  25.         Solve[eqns, {N0, N1, N2, N3, n}]
  26. and ran out of memory on a 40 Mb RAM workstation.  I've tried eliminating n
  27. from the last equation to reduce the system to 4 equations but then I can't
  28. find the solution to n without running out of memory.
  29.  
  30.         Does anyone know of any tricks/techniques/simplications I can make
  31. to solve this system?  Alternatively does anyone know of simple references
  32. to Groebner bases?
  33.  
  34.                                 thanks in advance
  35.  
  36.                                      Peter
  37.  
  38. --
  39. ********************************************************************************
  40. Peter King                               *         The home of TORTUS.
  41. Plasma Physics Department                *   T
  42. University of Sydney, NSW 2006           *   O
  43. AUSTRALIA                                *   Roid of
  44.     voice: 61 2 692 3371                 *   The 
  45.       FAX: 61 2 660 2903                 *   University of
  46.     email: king@physics.su.OZ.AU         *   Sydney
  47. ********************************************************************************
  48.