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Suppose f(x):=when(x>-Pi and x<0,-1,when(x>=0 and x<Pi,1,0)).

Then Arg(fourier_cn(f(x),x,2*Pi,n,-Pi)) returns different answers accordingly to the assumption for n. With integer assumpton for n Arg(fourier_cn(...)) returns a correct answer, but without any assumption for n it returns the result which is like odd and even indexes swaped while substituting various integer values n.

Is it proper?

fourier_cn now auto-assumes that n is an integer.

(11-05-2019 04:08 PM)parisse Wrote: [ -> ]fourier_cn now auto-assumes that n is an integer.

That's right. In this case I get 1/2*Pi*sign((-1)^n-1) and subst(arg(1/2*Pi*sign((-1)^n-1)),n=1) returns -1/2*Pi.

But these steps cause the wrong answer:

1. assume(n,integer) returns [DOM_INT]

2. fourier_cn(f(x),x,2*Pi,n,-Pi) returns ((-1)^n*i-i)/(n*Pi)

3. purge(n) returns [DOM_INT]

4. simplify(arg(((-1)^n*i-i)/(n*Pi))) returns 1/2*(n*Pi-2*Pi*floor((n+1)/2)-Pi*sign(n)-Pi*sign(tan(n*Pi/2)))

5. subst(1/2*(n*Pi-2*Pi*floor((n+1)/2)-Pi*sign(n)-Pi*sign(tan(n*Pi/2))),n=1) returns undef and subst(1/2*(n*Pi-2*Pi*floor((n+1)/2)-Pi*sign(n)-Pi*sign(tan(n*Pi/2))),n=2) returns -1/2*Pi and so on.

That's because floor is discontinuous, and as explained above CAS assumes that parameter have generic values. It is therefore important to make assumptions like assume(m,integer); n:=2*m; before calling simplification.

(11-06-2019 08:44 PM)parisse Wrote: [ -> ]That's because floor is discontinuous, and as explained above CAS assumes that parameter have generic values. It is therefore important to make assumptions like assume(m,integer); n:=2*m; before calling simplification.

Thanks!