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Avoid indeterminate result after simplifying a function?

Dear Mathematica team:

When executing the following calculation (a simplification, see attached file) in general I get "indeterminate" for the function "Pc" if I did it in an anaytic way.

Simplify::infd: Expression ((-(((CBdp (fsc-fsw1) LPc-CXdw2 fsc (-1+CBdp+CBdp fsw1+LPc)) (CBdp (-fstr+fsw1) LPc+CXdr fstr (-1+CBdp+CBdp fsw1+LPc)) LXm Rm \[Alpha])/((1+Times[<<2>>]) LXm Rm+CBdp (Times[<<2>>]+Times[<<3>>]+Times[<<2>>])))-((CBdp (-fsc+fsw1) LPc+CXdw2 fsc (-1+CBdp+CBdp fsw1+LPc)) <<3>> \[Alpha])/(-(-1+LPc) LXm Rm+CBdp (Times[<<2>>]+Times[<<3>>]+Times[<<2>>]))) ((<<1>>+<<1>>) <<4>> \[Alpha]+<<7>>))/(fsw2 (fsr-fsz) (-(((CBdp (Times[<<2>>]+fsw1) LPc+CXdw2 fsc (-1+CBdp+Times[<<2>>]+LPc)) <<3>> \[Alpha])/(Plus[<<2>>] LXm Rm+CBdp Plus[<<3>>]))-((CBdp (<<1>>) LPc+<<1>>) <<4>>)/(-Plus[<<2>>] LXm Rm+<<1>>))^2) simplified to Indeterminate.

However, after substituting the values below, I get a meaningful result for "Pc". How is that possible?

{fsm, fsw1, fsr, fstr, fsz, fsw2, fsc} = {0.05, 10^6, 1.5, 0.1, 10^5, 
  10^7, 0.75}
{LXm, Sm, CXdw2, LPc, Rm, Rn, CBdp, \[Alpha]} = {0.6*10^-2, 100, 
  10^-6, 0.8, 0.75, 0.9, 0.15, 0.25}

Pc -> (6.09873*10^-28 + 
    CXdr (-6.42908*10^-27 + 
       f (-2.0817*10^-25 + 
          f (7.49617*10^-28 - 1.24079*10^-32 f - 2.03291*10^-27 Pr) - 
          5.08226*10^-29 Pr)) + 
    CXdr^2 (-1.21975*10^-27 + 
       f (-5.20425*10^-26 + 
          f (9.37013*10^-29 - 1.55099*10^-33 f - 4.57405*10^-28 Pr) - 
          1.27057*10^-29 Pr)) + 
    CXdr^3 (-5.08227*10^-29 + 
       f (-3.25265*10^-27 + f (-9.69366*10^-35 - 2.54114*10^-29 Pr) - 
          7.94105*10^-31 Pr)) + 
    f (1.98526*10^-31 + 
       f (-6.30088*10^-34 + 5.91654*10^-39 f + 1.55099*10^-33 Pr) + 
       7.75493*10^-34 Pr))/((-4.3274*10^-34 + 
      CXdr^3 (9.01541*10^-31 + 1.26218*10^-29 f) + 
      CXdr^2 (1.44247*10^-29 + 2.01948*10^-28 f) + 
      CXdr (5.76985*10^-29 + 8.07793*10^-28 f) - 8.07794*10^-34 f) f)

Maybe I should seach the domain of the function? If yes, how could I do it with such a lenghty formula? I have no idea where the underlying infinity that is causing the problem is happening.

Thank you in advance,

Alberto Silva

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2 Replies

It seems that Pc is a fraction whose numerator and denominator both simplify to zero. It is a simple algebraic simplification, you can do it with ExpandAll, you don't need Simplify.

POSTED BY: Gianluca Gorni

The reason I want to simplify it is that is a lenghtly, ugly, expression I got after solving a large system of equations.

However, "ExpandAll" didn't work either, as I got now, somewhere in the expression, an infinity (1/0) instead of "indeterminate". It would be great if I could find where the "(1/0)" term is located, so I can find where the problem is.

At first I thought that the solution was wrong due to bad input (i.e. I make some mistake in the original equations) but then I found that the singular (or indeterminate) expression disappears after substituting numerical values, so probably the problem can be solved with some rearrangement of the solutions, but I have no idea how to do that.

Any idea?

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