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