Closed
Description
As discussed in https://groups.google.com/forum/#!topic/sage-devel/b1pWen3lrKA, the documentation of Fourier series as implemented in piecewise-defined functions needs some improvement. This ticket provides it, as well as a simplification of the user interface: the half-period is now an optional argument; if not provided, it is inferred from the domain of the piecewise-defined function:
sage: f = piecewise([((0, 2*pi), cos(x))])
sage: f.fourier_series_cosine_coefficient(1) # results in TypeError in Sage 8.0
1
sage: f.fourier_series_cosine_coefficient(1, pi) # compatible with Sage 8.0
1
The ticket also corrects two bugs:
- computation of Fourier coefficients when the domain width does not coincide with the period:
sage: f = piecewise([((0, 4*pi), cos(x))])
sage: f.fourier_series_cosine_coefficient(1, pi) # yields 2 in Sage 8.0
1
- despite what it claimed, the method
fourier_series_partial_sumdid not return SN(x) but SN-1(x) (this is because the summation was governed bysrange(1, N)instead ofsrange(1, N+1)); we have now
sage: f = piecewise([((0, 2*pi), cos(x))])
sage: f.fourier_series_partial_sum(1, pi) # yields 0 in Sage 8.0
cos(x)
CC: @wdjoyner
Component: documentation
Keywords: Fourier series, piecewise functions
Author: Eric Gourgoulhon
Branch/Commit: 8cb8a4d
Reviewer: Richard L Lozes
Issue created by migration from https://trac.sagemath.org/ticket/23672