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I'm trying to get this piece of code to work:

Panel[
 DynamicModule[{f = x, g = -x},
  xmax = 10;
  Column[{
   InputField[Dynamic[f], ContinuousAction -> True], 
   InputField[Dynamic[g]], 
   Dynamic[ Show[Plot[{f, g}, {x, -xmax, xmax}, AspectRatio -> 1,
                              PlotRange -> {{-xmax, xmax}, {-xmax, xmax}}]
                ]
          ]
        }]
              ]
     ]

This works and updates dynamically the graphs of f and g. Now, I would like to add the intersections, dynamically, if any (so with a IF testing), and I tried different things, without success:

solution = Dynamic[Solve[f == g, {x,y}]

gives me indeed the dynamically updated solution. But I can't use this information to plot points, nor even get Length[solution] update dynamically...

Any help with this?

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2
  • $\begingroup$ This is the static version of your question. Take a look there. solution definition looks strange, use solution:=... and use Dynamic at the end in the plotting procedure. p.s. isn't Show redundant? $\endgroup$
    – Kuba
    Commented Sep 4, 2013 at 18:04
  • $\begingroup$ Thank you for this static version, it's very helpful! $\endgroup$
    – Gabriel
    Commented Sep 4, 2013 at 20:05

1 Answer 1

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This solution is only for simple cases where the intersection is a point. And not adapted for cases with periodical functions when the output of the Solve contains a conditional expression (sometimes).

Panel[DynamicModule[{f = x, g = -x, xmax = 20},

  Column[{
    InputField[Dynamic[f], ContinuousAction -> True],
    InputField[Dynamic[g]],
    Dynamic @ Plot[{f, g}, {x, -xmax, xmax}, AspectRatio -> 1, PlotRange -> xmax, 
                                             Epilog -> {[email protected], Point[pt]}]
        }]
  , Initialization :> (pt := ({x, f} /. NSolve[f == g, x, Reals]) /. {x, f} -> {})
      ]]

enter image description here

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2
  • $\begingroup$ I like this answer a lot, thank you very much. One question though, what do you mean by "/. {x, f} -> {}" ? Would this be equivalent to {x, f} /. NSolve[f == g, x, Reals])[[1]] ? Thank you! $\endgroup$
    – Gabriel
    Commented Sep 4, 2013 at 20:04
  • $\begingroup$ @Gabriel when there is no solution there is no replacement rules so in this case {x,f} is switching to {} because it will not cause any error in Epilog. I'm glad it is helpful. $\endgroup$
    – Kuba
    Commented Sep 4, 2013 at 20:10

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