Syntax Problem?

Questions
,
1

Is somebody able to explain why line 87 works and 85 does not?

Capture.PNG
Capture.PNG685×891 22.5 KB

2

Hi,

I guess that the problem is the delayed evaluation of \psi. (BTW, it is quite cumbersome to retype everything if you paste an image into your post. The code would be much easier to debug.

a[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Sin[
\*FractionBox[\(Pi\ n\), \(2\)] x]\), \(2\)] \[DifferentialD]x\)\))^-1

b[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Cos[
\*FractionBox[\(Pi\ n\), \(2\)] x]\), \(2\)] \[DifferentialD]x\)\))^-1

\[Phi]odd[x_, n_] := b[n] Cos[(Pi n)/2 x]

\[Phi]even[x_, n_] := a[n] Sin[(Pi n)/2 x]

\[Psi][x_, \[Alpha]_, \[Beta]_] := -\[Alpha] \[Phi]odd[x, 
    1] + \[Beta] \[Phi]even[x, 2]

As you say, if you plot

Plot[{\[Psi][x, 2^-0.5, 2^-0.5], \[Psi][x, 3^-0.5, (2/3)^-0.5]}, {x, -1, 1}]

that does not work. You can either prefix everything with Evaluate:

Plot[Evaluate@{\[Psi][x, 2^-0.5, 2^-0.5], \[Psi][x, 3^-0.5, (2/3)^-0.5]}, {x, -1, 1}]

or modify the definition of \psi like so:

\[Psi][x_, \[Alpha]_, \[Beta]_] = -\[Alpha] \[Phi]odd[x, 1] + \[Beta] \[Phi]even[x, 2]

Now, it’s not a delayed definition anymore. Now the plot command works without the Evaluate.

Cheers,

Marco

3

Hi thanks for the fast Answer Evaluate@ seems to do do the trick.
Sorry for the Picture next time I’ll post the code.
So when do I have to put an Evaluate@ in this situation the problem seems to be at the Integrals.

4

Hi,

well, yes. In particular I think that the integration variable of the integrals causes problems. Because of the delayed evaluation it leaves the Integrals as they are. When you plot wrt x then that causes a problem. If you rename the integration variables you also circumvent the problem (but the whole thing gets very slow):

a[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Sin[
\*FractionBox[\(Pi\ n\), \(2\)] y]\), \(2\)] \[DifferentialD]y\)\))^-1

b[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Cos[
\*FractionBox[\(Pi\ n\), \(2\)] y]\), \(2\)] \[DifferentialD]y\)\))^-1

\[Phi]odd[x_, n_] := b[n] Cos[(Pi n)/2 x]

\[Phi]even[x_, n_] := a[n] Sin[(Pi n)/2 x]

\[Psi][x_, \[Alpha]_, \[Beta]_] := -\[Alpha] \[Phi]odd[x, 
    1] + \[Beta] \[Phi]even[x, 2]

Plot[{\[Psi][x, 2^-0.5, 2^-0.5], \[Psi][x, 
   3^-0.5, (2/3)^-0.5]}, {x, -1, 1}]

will give the correct plot with no error messages, but it will run for a while.

Cheers,

M.