I'm unable to create a reasonable example:
FCI==>FourierComponent(Integer)
FSI ==> FourierSeries(EXPR INT,INT)
(1) -> sin(5)$FCI
(1) sin[5]
Type: FourierComponent(Integer)
(2) -> makeCos(5,z)$FSI
(2) zcos[5]
Type: FourierSeries(Expression(Integer),Integer)
What puzzles me is the E: Join(*OrderedSet*
<http://fricas.github.io/api/OrderedSet.html#l-ordered-set>, *AbelianGroup*
<http://fricas.github.io/api/AbelianGroup.html#l-abelian-group>) in
FourierSeries(R,E). What could be a set such that the domain might be used
to get the following:
fourierPartialSumX(N,sin,0..2*%pi)
n x n x
N sin(2n %pi)sin(---) N (cos(2n %pi) - 1)cos(---)
--+ 2 --+ 2
(1) > ------------------- + > -------------------------
--+ 2 --+ 2
n = 1 (n - 1)%pi n = 1 (n - 1)%pi
Type:
Expression(Integer)
(2) -> fourierSum('N,sin(z),z=0..%pi)
N - 2%i n %pi 2%i n z
--+ (- %e - 1)%e
(2) > ------------------------------
--+ 2
n = - N (4n - 1)%pi
Type: Expression(Complex(Integer))
Certainly, it might be of the form {y: y=n*x, n\in Integer}, where 'x' some
fixed symbol or expression. Nevertheless I can't see much utility in it.
BTW complexIntegrate performs incredibly much better, so (2) above is
definitely the preferred way to compute Fourier coefficients. That was a
really good hint :)
On Friday, 11 November 2016 18:15:29 UTC+1, Waldek Hebisch wrote:
>
> Kurt Pagani wrote:
> >
> > BTW do you have any idea what FourierSeries(R, E) and FourierComponent E
> are
> > for? I can't recognize any functionality regarding to compute Fourier
> > coefficients nor series.
>
> Essentially it implements trigonometric polynomials (that is _finite_
> Fouries series), but its is a bit more general because there are no
> restriction on frequencies.
>
> --
> Waldek Hebisch
>
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