The future of FourierTrigSeries package
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In this post I would like to kindly ask users of this package (if there are any) for a feedback. Please, add a comment to share your experience with FourierTrigSeries package (how do you use it) and suggest new features or report bugs.
FourierTrigSeries package is a Maple package which provides new data structure for the representation of trigonometric series and also several procedures to manipulate with trigonometric series and to compute Fourier series. The last version 0.41 was released in February 2008 and after this version there is no progress in development. The only new thing is a README file included in zip archive because I found (and I was very surprised) that I didn't write such a file before.
I hope your feedback will help me with further development of the package. Thank you.
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Comments
suggestion
For instance, it would be useful a command to change the index for cases like the example in ?FourierTrigSeries[ExploreFourierSeriesCoefficients], where the function signum(sin(2*x)) has symmetries that make some coefficients vanish, rewriting the series to look like:
(by the way, there is no command to convert this sum to a sin series).
Thank you for the comment. I
Thank you for the comment. I know about this issue but at the moment I don't know how to solve it. The problem is that such a series doesn't fit into the internal data structure which is used to represent trigonometric series. The "general" coefficient is expected to be a single equation which is used to derrive all the remaining sin(n*x) or cos(n*x) terms. This makes easy to Add two series. If there would be a possibility how to specify different values for this "general" coefficient dependent on the value of "k" (e.g. using IF statement), it would be very difficult to Add this series to another series which is not fully "compatible" (doesn't have the same conditions for the value of "general" coefficient).
Please, let me know If you have any suggestions how to deal with this problem.
normal form
Sure, algebraic operations should be made for a "normal" representation, with terms like sin(n*x) or cos(n*x), say. What I mean is to include a facility to transform between this normal form and an alternative one.
So, to add a series in non-normal representation you convert it first to the
normal one.