Fix issue #879: series of undefined functions.

[renatocoutinho]

No description provided.

[asmeurer]

You might also add a test for a subclass of Function, like

class TestFunction(Function):
    pass

TestFunction(x).series(x)

[asmeurer]

Shouldn't this just go in the UndefinedFunction class?

[renatocoutinho]

UndefinedFunction is actually a metaclass, so I would have to mess with it a bit. OTOH, would it be really better to repeat most of the series logic in a different place? The algorithm as it is looks fine, I have to special-case it just because f(x).nargs == 1 but f.nargs is None.

[asmeurer]

I guess AppliedUndef then?

[asmeurer]

Actually, from what you say, it sounds like what you really should be testing for is the nargs is None case.

[asmeurer]

So this seems to be wrong anyway. Try f(x, y).series(x).

[asmeurer]

Yet f(x, y).series(y) gives the right thing.

[asmeurer]

By the way, great to have you contributing again!

[jrioux]

SymPy Bot Summary: 🔴 Failed after merging renatocoutinho/879b (3e9f0ad) into master (6faba52).
@renatocoutinho: Please fix the test failures.
✳️ PyPy 2.0.0-beta-1; 2.7.3-final-42: pass
✳️ Python 2.7.2-final-0: pass
🔴 Python 3.2.1-final-0: fail
✳️ Sphinx 1.1.3: pass
Docs build command: make clean && make html-errors && make latex && cd _build/latex && xelatex sympy-*.tex

[jrioux]

SymPy Bot Summary: ✳️ Passed after merging renatocoutinho/879b (ca49718) into master (f556486).
✳️ PyPy 2.0.0-beta-1; 2.7.3-final-42: pass
✳️ Python 2.7.2-final-0: pass
✳️ Python 3.2.1-final-0: pass
✳️ Sphinx 1.1.3: pass
Docs build command: make clean && make html-errors && make latex && cd _build/latex && xelatex sympy-*.tex

[asmeurer]

SymPy Bot Summary: ✳️ Passed after merging renatocoutinho/879b (ca49718) into master (b498c0f).
✳️ Python 2.5.6-final-0: pass
✳️ Python 2.6.8-final-0: pass
✳️ Python 2.7.3-final-0: pass
✳️ Python 3.2.3-final-0: pass
✳️ Sphinx 1.1.3: pass

[smichr]

>>> f, g = map(Function, 'fg')
>>> f(x).series(x, a, 3).subs(f, sin).doit()
sin(a) + x*cos(a) - x**2*sin(a)/2 + O(x**3)

And I was expecting sin(a) + (x-a)*cos(a) - (x-a)**2/2*sin(a) + O(x**3). I know that this is because of the reasons noted in the series docstring. But I wonder if we could just use Subs on the O term, too:

if series_result.has(O):
  if series_result.is_Add:
    e, o = series_result.as_independent(O)
    if not e.has(O):
      return e.subs(x, x - x0) + Subs(o, x, x - x0)
return series_result

for example

>>> def go():
...     if series_result.has(O):
...       if series_result.is_Add:
...         e, o = series_result.as_independent(O)
...         if not e.has(O):
...           return e.subs(x, x - x0) + Subs(o, x, x - x0)
...     return series_result
...
>>> x0=a; series_result = sin(x).series(x,x0,n=3)
>>> go()
-(-a + x)**2*sin(a)/2 + (-a + x)*cos(a) + sin(a) + Subs(O(x**3), (x,), (-a + x,))
>>> x0=a;series_result = (x**2).series(x,x0,n=3)
>>> go()
a**2 + 2*a*(-a + x) + (-a + x)**2
>>> series_result
a**2 + 2*a*(-a + x) + (-a + x)**2

[smichr]

• rebase
• respond to suggestion about putting O in Subs

[asmeurer]

• Make sure functions of multiple variables work and are tested.

[danieljfarrell]

Can I check the status of this pull request, when do you think it will be added to master?

[asmeurer]

SymPy Bot Summary: ❗ There were merge conflicts (could not merge renatocoutinho/879b (ca49718) into master (ec1ac09)); could not test the branch.
@renatocoutinho: Please rebase or merge your branch with master. See the report for a list of the merge conflicts.

[asmeurer]

Unless I misunderstand this issue, I think the O Subs thing can be postponed. I tested this branch, and it seems to work for functions of multiple variables. It just needs to be tested.

So if someone wants to pick up work here, what needs to be done is to merge the branch with master, and add tests for functions of multiple variables. I think @renatocoutinho is busy, so if you want to pick up the work, just make a new branch based off this one and make a new pull request.

[asmeurer]

SymPy Bot Summary: ❗ There were merge conflicts (could not merge renatocoutinho/879b (ca49718) into master (71a8f17)); could not test the branch.
@renatocoutinho: Please rebase or merge your branch with master. See the report for a list of the merge conflicts.

[asmeurer]

See #2224.