Carl Love

Carl Love

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8 years, 17 days
Mt Laurel, New Jersey, United States
My name was formerly Carl Devore.

MaplePrimes Activity


These are replies submitted by Carl Love

Your last three equations are

phi[i]:= piecewise(...);

and likewise for phi[i+1/2] and phi[i+1]. I think that those should be

phi[j]:= r-> piecewise(...);

and likewise for phi[j+1/2] and phi[j+1]. Is that right? If I do that, then all the integrals in eq10 are evaluated. The resulting expression is large, but I can apply simplify(%) and it simplifies nicely all at once. The final expression fits on one screen. How much free memory do you have?

Are you saying that you want to take the tickmark positions that are chosen by default and make their labels shorter? Or are you saying that you want to choose both the positions of the tickmarks (as in your prior question) and the way their labels are printed? The latter is easier than the former.

Are you saying that you want to take the tickmark positions that are chosen by default and make their labels shorter? Or are you saying that you want to choose both the positions of the tickmarks (as in your prior question) and the way their labels are printed? The latter is easier than the former.

@sakhan I think that I may have missed part of the computation; maybe I got i's and j's mixed up. For whatever reason, my eq10 is only a half screen in size---not that complicated. Please upload the worksheet with all computations starting from the restart. Yes, I am sure that I can find a way to simplify each integral as it is done.

@sakhan I think that I may have missed part of the computation; maybe I got i's and j's mixed up. For whatever reason, my eq10 is only a half screen in size---not that complicated. Please upload the worksheet with all computations starting from the restart. Yes, I am sure that I can find a way to simplify each integral as it is done.

@Christopher2222 Ah, I guess by "caps" you meant what are called "whiskers" in a box-and-whiskers plot, the central vertical lines? Those are what I thought you meant by "tips". And I thought that by "caps" you meant what appears as horizontal lines in my plot.

So now I am guessing that you want the violin to have a cusp at the top and bottom, as in your original plot, with the top cusp at the highest data point and the bottom cusp at the lowest data point. Is that right? I believe we can achieve this with plottools:-homothety. And I guess that you want the scale of the vertical axis to stay the same. Is that correct?

@Christopher2222 Ah, I guess by "caps" you meant what are called "whiskers" in a box-and-whiskers plot, the central vertical lines? Those are what I thought you meant by "tips". And I thought that by "caps" you meant what appears as horizontal lines in my plot.

So now I am guessing that you want the violin to have a cusp at the top and bottom, as in your original plot, with the top cusp at the highest data point and the bottom cusp at the lowest data point. Is that right? I believe we can achieve this with plottools:-homothety. And I guess that you want the scale of the vertical axis to stay the same. Is that correct?

@Christopher2222 I totally agree that Maple should implement angled tickmark labels: It seems like a standard feature of plotting software (mostly for histograms). As a stopgap measure until something like that is implemented, would it be useful to you to have a Pareto plot with one- or two-letter tickmark labels along the horizontal axis and a legend that matches the short labels to the actual labels?

I just want to clarify for less-experienced readers that the "labels" to which you refer are tickmark labels. Usually, the unqualified word "labels" in the context of Maple plots means axes labels, which can indeed be written horizontally or vertically.

@Carl Love Further observations and suggestions:

  1. Instead of making a series approximation to the Wronskian, how about first testing via plots that your approximation to the HeunG functions is correct.
  2. The Maple kernel can easily handle far more terms than the 20 you've been using. I've been using 50 terms and it's still essentially instantaneous. Just make sure that you don't try to display a huge number of terms on the screen; you'll blow away the GUI. Make sure to end your commands with colons. Applying the simplify command will drastically reduce the size of these expressions.
  3. You seem to be mixing series expanded at t=0 and t=1. I don't kow why that's valid.
  4. What happens to the t in wronski?
  5. How does your approximation account for the HeunGPrime?

You haven't said that you've tried doing any of this in Maple. So try it first, and post a followup comment.

A slightly better workaround: Change Pi to pi, then reverse that after the symbolic summation.

A slightly better workaround: Change Pi to pi, then reverse that after the symbolic summation.

@digerdiga I know nothing about Heun functions, but I've been looking at this. Try comparing plots of Re, Im, and abs, in addition to argument. This might lead you to the wrongski in your wronski.

These are just my raw observations; they may be of no significance:

The series expansion has a singularity at p = 0. Other than that, both the Re and Im of the series expansion look simple functions of the form exp(a*p)*sin(b*p+c) for different a and c, but the same b.

@Markiyan Hirnyk I understand your solution mathematically, but what is the physical significance of any value of n other than 2 or possibly 3? And wouldn't the value of n be determined completely by the dimensions of k? Each ODE has dimensions of acceleration, L/T^2 (probably specifically meter/second^2 since g is given as 10).

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