Partial sums are off for Fourier series of piecewise functions

[novoselt]

Doing

f = Piecewise([[(-pi, pi), x]])
print f.fourier_series_partial_sum(2, pi)
print f.fourier_series_partial_sum(3, pi)

we get

2*sin(x)
-sin(2*x) + 2*sin(x)

while according to the documentation we should get the second output with the first command.

Update: Same output with the new piecewise from #14801. Does it agree with the documentation there?

UPDATE: this is fixed in Sage 8.1 (see #23672):

sage: f = piecewise([[(-pi, pi), x]])
sage: f.fourier_series_partial_sum(2, pi)
-sin(2*x) + 2*sin(x)

Depends on #14801

CC: @wdjoyner @jasongrout @jondo @kcrisman @vbraun @slel @mkoeppe @eviatarbach @rwst @novoselt

Component: calculus

Keywords: sd31

Work Issues: other instances of the typo

Author: David Joyner

Issue created by migration from https://trac.sagemath.org/ticket/8603

[kcrisman]

comment:1

This is still true, and syntax is also deprecated.

sage: f = Piecewise([[(-pi, pi), x]])
sage: print f.fourier_series_partial_sum(2, pi)
/Applications/MathApps/sage/local/lib/python2.6/site-packages/sage/functions/piecewise.py:1095: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
  a0 = self.fourier_series_cosine_coefficient(0,L)
/Applications/MathApps/sage/local/lib/python2.6/site-packages/sage/functions/piecewise.py:1099: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
  for n in srange(1,N)])
2*sin(x)
sage: print f.fourier_series_partial_sum(3, pi)
-sin(2*x) + 2*sin(x)

[novoselt]

Changed keywords from none to sd31

[novoselt]

comment:2

On a related note: what is the purpose of plot methods for Fourier partial sums? They don't do anything except for passing arguments to the usual global plot function, so they seem redundant to me and perhaps can be removed (after deprecation period).

[kcrisman]

comment:3

You may be right. I'd have to look at it. Remember, these are all really old, so they probably at the time bypassed the non-existent 'plot' function, and then were subsequently changed, perhaps.

[wdjoyner]

one line change in docstring

[wdjoyner]

comment:4

Attachment: trac_8603-fourier-sum-docstring.patch.gz

This fixes the documentation of fourier_series_partial_sum, replacing

 f(x) \sim \frac{a_0}{2} + \sum_{n=1}^N [a_n\cos(\frac{n\pi x}{L}) +
b_n\sin(\frac{n\pi x}{L})],

by

 f(x) \sim \frac{a_0}{2} + \sum_{n=1}^{N-1} [a_n\cos(\frac{n\pi x}{L})
+ b_n\sin(\frac{n\pi x}{L})],

[kcrisman]

comment:5

Thanks, David; I don't have time to review this now, but appreciate it.

Andrey and I were discussing this at Sage Days 31, and thought that maybe changing the behavior instead to match Taylor series would be good, but if this was in fact what you had intended all along, then this solution is better.