series of expression with big-O ignore the big-O

[ThibaultLejemble]

It seems that when an expression involves a big-O, then its series expansion does note take into account this big-O.

The example below shows the expansion of 1/(1+x) and 1/(1+x+O(x**n)) at point 0 and order 4, which I believe should be different

from sympy import *

x = Symbol('x')

f = 1 / (1 - x)
g = 1 / (1 - x + O(x**2))

# Ok: 1 + x + x**2 + x**3 + x**4 + O(x**5)
print(series(f, x, 0, 4)) 

# Wrong: 1 + x + x**2 + x**3 + x**4 + O(x**5) 
# Expected: 1 + x + O(x**2)
print(series(g, x, 0, 4))

It seems that the O(x**5) is ignored right?

[oscarbenjamin]

Yes, it looks like it is ignored:

In [15]: series(1/(1 - x + O(x**2)))
Out[15]: 
         2    3    4    5    ⎛ 6⎞
1 + x + x  + x  + x  + x  + O⎝x ⎠

[oscarbenjamin]

Possibly related to gh-24477

[anutosh491]

Well I fixed the Pow._eval_nseries function locally which was responsible for this . So now I get

>>> (1/(1 - x + O(x**2))).nseries(x)
1 + x + O(x**2)

But for fixing the series method , I am unsure about the current framework we have

sympy/sympy/core/expr.py

Lines 3046 to 3064 in 3878065

	elif ngot < n:
	# increase the requested number of terms to get the desired
	# number keep increasing (up to 9) until the received order
	# is different than the original order and then predict how
	# many additional terms are needed
	from sympy.functions.elementary.integers import ceiling
	for more in range(1, 9):
	s1 = self._eval_nseries(x, n=n + more, logx=logx, cdir=cdir)
	newn = s1.getn()
	if newn != ngot:
	ndo = n + ceiling((n - ngot)*more/(newn - ngot))
	s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir)
	while s1.getn() < n:
	s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir)
	ndo += 1
	break
	else:
	raise ValueError('Could not calculate %s terms for %s'
	% (str(n), self))

Now that series internally uses nseries , we get the correct answer through nseries but then the series method compulsorily forces the presence of n (in this case 6 ) terms . I am not sure why this is being done though

Do we expect series(1/(1 - x + O(x**2))) to compulsorily have 6 terms or could we stop at 3 (after O(x**2)) . @jksuom what are your thoughts here ?