Kurt Pagani wrote:
>
> 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)
>
FourierSeries represent explicit (expanded) thing. You want notation
involving operators like summation, currently only Expression can
handle operators.
>
> (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 :)
Well, for Foures series complex approach is much simpler than real.
But in general 'integrate' spends serious effort to make result
more pretty, while 'complexIntegrate' may produce somewhat ugly
results. Of course extra work done by 'integrate' takes time
and sometimes may backfire leading to bigger expressions.
--
Waldek Hebisch
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/fricas-devel.
For more options, visit https://groups.google.com/d/optout.
