MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Trouble using Eliminate and Reduce with big examples

  • To: mathgroup at smc.vnet.net
  • Subject: [mg117994] Trouble using Eliminate and Reduce with big examples
  • From: Johannes Gross <johannes.gross at gmx.li>
  • Date: Thu, 7 Apr 2011 08:07:23 -0400 (EDT)

Hi,

i am generating equation systems for dimensional analysis in engineering 
applications. When trying to replace the dimensional parameters by the 
dimensionless ones, i get problems with the Eliminate and Reduce 
functions in Mathematica.

Sometimes Eliminate works even for very big examples, sometimes it 
doesnt. Same with Reduce.

My equations are of the nature
f(x1, ... , xn)
pi0= f(x1,x2)
pi1= f(x3,x2,x4) etc.

i want to eliminate all xn variables and i know that its possible 
because i can do it by hand.

I think Mathematica has problems when case-by-case-analysis requires 
many cases. I tried to avoid this by telling that all variables are 
positive (e.g. Reduce[{a == x^2, x > 0, a > 0}, x]). It did not improve 
runtime.

Example 1:

Eliminate[{pe ==
    1/f 1.` (-0.35` c +
       1.4254109407099804` f ((R k c^2 Eb lm ll Tn (re -
                1.` sma)^2)/(f^2 etaG Dg^2 P etaT))^0.5`) (-0.25` + \
(0.5079490874739279` R k Eb lm ll Tn (re -
              1.` sma)^2)/(etaG Dg^2 P etaT))^0.5`, Pi0 == etaT,
   Pi1 == ll, Pi2 == f*c^-1*re^1, Pi3 == pe*re^-1, Pi4 == etaG,
   Pi5 == k*P^-1*c^1*re^-1*Tn^1, Pi6 == R*c^-1*re^1*Eb^1,
   Pi7 == sma*re^-1, Pi8 == lm, Pi9 == Dg*re^-1}, {etaT, ll, f, pe,
   etaG, k, R, sma, lm, Dg}]


Questions:

How can i tell mathematica to avoid case-by-case-analysis (because i 
only need the positive, real results)?
How can i eliminate variables in another way than by reduce or eliminate?
How might i improve runtime of reduce or eliminate in these cases?

Any answer to any of the questions is warmly welcome!

Thanks,

Johannes


  • Prev by Date: Re: Bug with map in conjuntion with plotstyle?
  • Next by Date: Re: Shadow problem of a variable defined in a function context inside different packages
  • Previous by thread: Re: Coefficents of terms in an expression containing the matching string
  • Next by thread: Re: Trouble using Eliminate and Reduce with big examples