Comment #4 on issue 3627 by [email protected]: Order malfunctions with
sin(x)
http://code.google.com/p/sympy/issues/detail?id=3627
This issue is really twisted. I'll try to explain why the endless recursion
is happening.(You should import calculate_series from gruntz)
Let's try this-
calculate_series(sin(x)**1.2, x)
Now, in the calculate_series function, it tries to get at least one term of
the required expansion. So, it calls nseries and provides the number of
terms to which the series is to be calculated.
nseries returns a series with an order term. Now, if there is only the
order term in the series, then, calculate_series again calls nseries. This
time, the series is calculated to twice as many terms as last time.
Again, calculate_series checks if the returned series has any terms other
than the order terms. If so, calculate_series will just return the smallest
term in the series. Otherwise, it will again call nseries asking it to give
the series to twice as many terms as last time.I hope you are with me till
here.
In the current case, (sin(x)**1.2).nseries(x, n=4) is called. Inside
nseries, it generates a term like:t = (x + O(x**3))**1.2This term is to be
added to O(x**4), that is:t = t+ O(x**4)Now, when adding an order term to
an expression, SymPy checks whether the other term (in this case 't') also
has an odder term or not. So here, SymPy checks whether t has an order term
or not.
So, we need to determine whether t has an order term. If t is a
simple 'Add' object, then it's straightforward to determine this. In our
case, t is a 'Pow' object.
Now, the Order function (that calculates order) works by finding the
leading term. So, it calls the function compute_leading_term() but this
function in turn calls to calculate_series(). And the recursion continues
on and on.I am still trying to see how this can be fixed. Any ideas?
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