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.

To those who are interested:

New version of FourierTrigSeries package was released. This release fixes a bug in ExploreFourierSeriesCoefficients procedure.

FourierTrigSeries package provides new data structure for the representation of trigonometric series and also several procedures to manipulate with trigonometric series and to compute Fourier series.

Visit the homepage and see some examples. Try also the online Fourier series calculator.

I have just released the new version of the FourierTrigSeries package. Some bugs were fixed and new procedures were added. This package provides new data structure for the representation of trigonometric series and also several procedures to manipulate with trigonometric series and to compute Fourier series.

Previous package name FourierSeries was changed to FourierTrigSeries to be distinguished from the FourierSeries package made by Wilhelm Werner.

I am using Maple to solve some inequalities where the solution I get is a RealRange or a real constant. And I want to get an union of these values. I wrote a short procedure which does the work. But is there a better way to do this (there must be :-) )?


> RealRangeUnion:=proc(L::list) local L2, rel, rel2, eq, sol, x;
> assume(x, real);
> L2:=map(a->`if`(a::realcons, x = a, x in a), L);
> rel:=convert(L2, relation);
> rel2:=convert(Or(op(rel)), relation);
> eq:=piecewise(rel2,1,0);
> sol:=solve(1=eq,x);
> RETURN(sol);
> end proc:
>
> L:=[RealRange(Open(-2),-1), RealRange(Open(0),1), RealRange(1/2,2), -3, -2];

Yet another Fourier series package? This package provides new data structure for the representation of trigonometric series and few procedures to work with trigonometric series and to compute Fourier series. Some procedures and data structure are similar to OrthogonalSeries package (but not the same).

UPDATE!!! I found that my blogpost appers in Maple reporter. You should know, that this blogpost was just a question about how to solve my problem better. Alec Mihailovs gave me and aswer and his solution of testing nested objects is much better. If you still want to use my piece of code, you should remove "set object" form "convertAMVStolist" procedure and replace all occurrences of "hastype" with "type" (as mentioned in comments below).

This piece of code should be able to test two objects (not of every type) for equivalence (like testeq() does). The benefit is, that it should be able to test also nested objects. Is there any other and more simple way how to do that? How to test nested objects in sets?

I have noticed that my text that was converted from MW to HTML is not properly displayed.

If you look at the end of the text, you will se the command

> f:=x->piecewise(x FSeries:=FSeriesOfFunction(f,-Pi..Pi);

which is not correct. The part "FSeries:=FSeriesOfFunction(f,-Pi..Pi);" is the next command.

View the original worksheet via the MapleNet to see the difference.

The problem is in the symbol "lower than" (which appears in definition of the piecewise continous function), because the publication system (or what) thinks that it is the begining of an unsupported HTML tag and the "tag" is removed. The solution is to substitute "lower than" for "&lt ;" (without the white space before the semicolon) and maybe the same with the "grater than" symbol.

by Karel Srot, Department of mathematics at Masaryk University, Czech Republic,

karels@mail.muni.cz, © 2005 Karel Srot

NOTE: This worksheet solves some examples using the package Fourier. This package provides procedures for computing Fourier series of real functions, drawing plots and animations. Especially animations illustrates the convergence of Fourier series in a comprehensive form. The usage of procedures from package Fourier is described in its help file.

The recent czech/english version of the package Fourier (as well as some exported examples) can be found at www.math.muni.cz/~xsrot/frady. Unfortunately, this website is only in czech at the present.