Solve large equation (Mathematica)

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Discussion Overview

The discussion revolves around solving a complex function of tau, denoted as f(tau), using Mathematica. Participants explore methods for taking the derivative of this function, setting it to zero, and solving for tau, while addressing concerns about the efficiency of the Solve function given the complexity of the expressions involved.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Anna expresses concern about the efficiency of the Solve function for a complicated expression and seeks assistance.
  • Some participants suggest that compact algebraic solutions may not exist for overly complex expressions and propose using numerical methods instead.
  • Anna insists on the need for an algebraic solution and inquires about the most efficient approach in Mathematica.
  • One participant advises allowing the computation to run despite its complexity and suggests expanding the function around a specific point.
  • Another participant notes that the goal may be to maximize or minimize the function, recommending the use of Maximize or Minimize functions instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to solve the problem. There are competing views on whether an algebraic solution is necessary and whether numerical methods or optimization functions would be more appropriate.

Contextual Notes

There is uncertainty regarding the assumptions about the complexity of the function and the definitions of the parameters w and v. The discussion does not resolve whether the use of Solve is indeed inefficient or if it is appropriate given the problem's complexity.

Anna Kaladze
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Hi All,

I have a big ugly function (please see the attached Mathematica file), of tau (f(tau)). The only parameters there in symbolic form are w and v. I need to take the derivative of this function with respect to tau, set it equal to zero and solve for tau. (Please see g(tau)). But Solve runs for a long time. Part of me says it is not surprising because the function is complicated, but part of me is saying I am doing something wrong which makes Solver run “inefficiently”, as in the past I was able to get a nice compact solution for tau albeit for somewhat less complex looking problems. Can you please help?

Thanks a lot.

Anna.
 

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Perhaps nice compact solutions simply don't exist if your expressions are too complicated. Do you really require an algebraic expression? If not, plug in your expressions for w and v, then use Solve/NSolve.
 
queenofbabes said:
Perhaps nice compact solutions simply don't exist if your expressions are too complicated. Do you really require an algebraic expression? If not, plug in your expressions for w and v, then use Solve/NSolve.

Yes, I require an algebraic solution. I wonder what would be the most efficient way to get in Mathematica.
 
Just let it run. If it is messy then it will take a long time.

Can you expand it about some point?
 
It appears that you are trying to maximize(or Minimize) the function. If so there is already the Maximize (and Minimize) functions.
 

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