How can i use the Solve function to find the actual equation for a

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Discussion Overview

The discussion revolves around the use of the Solve function in a mathematical context to find fixed points of the function f(x) = ur(1-u). Participants explore the formulation of the equation for fixed points and the implications of different approaches to solving it.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about using the Solve function to determine the equation for a fixed point of the function f(x) = ur(1-u).
  • Another participant provides a definition of the function and explains the syntax of the Solve function, indicating that f[f[u]] == u represents the equation for a fixed point.
  • A question is raised regarding the choice of using f[f[u]] == u instead of f[u] == u, with a suggestion that the former might yield complex solutions.
  • A participant acknowledges a mistake in their initial approach, clarifying that using f[u] == u should suffice to find all solutions, including complex ones.
  • One participant expresses gratitude for the clarification, indicating some confusion about the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of using f[f[u]] == u versus f[u] == u, as the discussion reveals differing perspectives on the implications of each approach.

Contextual Notes

There is a lack of clarity regarding the implications of using nested functions versus single applications in the context of fixed points, and the discussion does not resolve whether one method is superior to the other.

Who May Find This Useful

This discussion may be useful for individuals interested in mathematical functions, fixed point theory, and the application of the Solve function in computational contexts.

peter.a
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How can i use the Solve function to find the actual equation for a fixed point?
For the function f(x)=ur(1-u)
 
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f[u_] := u r (1 - u)
Solve[f[f] == u, u]

the u_ means to use it as an input variable, the " := " means not to evaluate it until its used. So i just nested it once, f[f] == u should be the equation for a fixed point of f.
Solve[EQUATION,VARIABLE] is its use.

or SOLVE[{EQ1,EQ2},{V1,V2}] for multivariate solutions.

I assume "u" was the variable in this case as f(x) = u r (1- u) has no x in it.
 


why have you done f[f==u and not f==u?
is this because then it also gives the complex solutions?
 


Ah that was a mistake. I was thinking of attractive fixed point functions.

Yeah Solve[f==u,u] should be enough. It will give all solutions, include any complex ones.
 


Thanks for clearing that up, because i was getting confused
 

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