Help with a program...

[Rob_Holman]

Hi all:

I put together the following to find and show the intersection of two functions. What I'd LIKE to do is get the functions to be defined by input fields, so that I could make this a CDF or a widget that my students could use without having to edit the functions in the code itself. I've tried to do this a couple of different ways, and it hasn't worked. I've included my latest attempt as well.

First, the initial code:
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func1[x_] := (1/2) x^3 - 2 x;
func2[x_] := (-1/3) x^2 + 1;

points := Solve[func1[x] == func2[x], Reals];

graphplot :=
Plot[{func1[a], func2[a]}, {a, -10, 10}, PlotRange -> {-5, 20}];

solutions := Table[x /. points[[i]], {i, 1, k}];

k = Length[points];

Show[graphplot,
ListPlot[Tooltip[
Table[{solutions[[j]] // N, func1[solutions[[j]]] // N}, {j, 1,
k}]], PlotMarkers -> {Automatic, 8}]]

_________________________

Now, my most recent attempt at generating a document where the user can edit the functions without going into the code:
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Panel[DynamicModule[{f = Sin[x], g = x^2},
func1[x_] := Dynamic[f];
func2[x_] := Dynamic[g];

points := Solve[f == g, Reals] // N;

solutions := Table[x /. points[[i]], {i, 1, k}];

k = Length[points];

graphplot := Plot[{f, g}, {x, -10, 10}, PlotRange -> {-10, 20}];

Column[{InputField[Dynamic[f]], InputField[Dynamic[g]],
Dynamic[Show[graphplot,
ListPlot[
Tooltip[Table[{solutions[[j]] // N,
func1[solutions[[j]]] // N}, {j, 1, k}]],
PlotMarkers -> {Automatic, 14}]]]}]]]
____________________________________________

The problem I'm having is that I can't figure out how to dynamically define the two functions so that I can get them to accept input. It's easy to graph Sin[x] as a dynamically defined f, but I can't compute f[4], for example.

I fear that what I'm trying to do is more difficult than I realize, or that it requires expertise with the programming capabilities of Mathematica that I'm not quite ready to tackle yet. Anyone have a suggestion on how I could pull this off?

Thanks for the help.

Rob

[Michael_Morrison]

Hi Rob,

Yes, allowing open input fields like this does complicate things. However, you might be able to do this in a tricky way by using mesh functions (I found an example in the Documentation Center that I applied). Take a look at it here (it's the top example, called InputFieldIntersectionExample.nb):
http://members.wolfram.com/mmorrison/Fa ... ogram.html

Thanks,
Michael

[Rob_Holman]

Michael:

Thanks for the suggestion. I'll play around with it a little bit.

At first glance, the display is perfect, but I'd love to retain the tooltip functionality where hovering over the point will provide the coordinates. I'll see if I can figure out how to make that happen.

Thanks again for your help.

Rob

[Michael_Rogers]

Try Manipulate...

Manipulate[
points := Solve[f == g, Reals] // N;
solutions := {x, f} /. points;
Plot[{f, g}, {x, -10, 10}, PlotRange -> {-10, 20},
Epilog -> {ColorData[1][1], PointSize[Large],
Tooltip[Point[#], #] & /@ solutions}],
{{f, Sin[x]}, InputField}, {{g, x^2}, InputField},
TrackedSymbols -> True]

Note that Solve does not always find all the points of intersection (e.g. f = Sin[x], g = x/2 +x^2/8). I shortened some of the code. In particular, 1) you used k before it was initialized, which can lead to buggy behavior. 2) The variable points is initialized to approximate reals with "//N"; all the things computed from points will already be approximate (e.g. solutions) and further "//N" are unnecessary. 3) There seemed to be no need to hang onto the functions func1 and func2; f and g can be used as above. 4) I used Map (/@) and ReplaceAll (/.) in place of your use of Table. Solve returns a List of Rules, and these functions take advantage of it. But there is nothing wrong with using Table. 5) Ditto for Epilog instead of ListPlotPoint; a matter of taste, really.

Cheers!

[Rob_Holman]

Michael:

This is really great... exactly what I had in mind. Thank you!

Rob