Merge pull request #153 from skirpichev/fix-omg31

Fix wrong cancelation of expr with O terms in Add/Mul.flatten

sympy/core/add.py

@@ -91,6 +91,8 @@ def flatten(cls, seq):
         sympy.core.mul.Mul.flatten
 
         """
+        from sympy.series.order import Order
+
         rv = None
         if len(seq) == 2:
             a, b = seq
@@ -151,6 +153,9 @@ def flatten(cls, seq):
                 seq.extend(o.args)  # TODO zerocopy?
                 continue
 
+            elif o.has(Order):
+                c, s = S.One, o
+
             # Mul([...])
             elif o.is_Mul:
                 c, s = o.as_coeff_Mul()

sympy/core/function.py

@@ -429,16 +429,6 @@ def class_key(cls):
 
         return 4, i, name
 
-    @property
-    def is_commutative(self):
-        """
-        Returns whether the functon is commutative.
-        """
-        if all(getattr(t, 'is_commutative') for t in self.args):
-            return True
-        else:
-            return False
-
     def _eval_evalf(self, prec):
         # Lookup mpmath function based on name
         fname = self.func.__name__

sympy/core/mul.py

@@ -171,6 +171,8 @@ def flatten(cls, seq):
               you should only consider them when your code is highly performance
               sensitive.
         """
+        from sympy.series.order import Order
+
         rv = None
         if len(seq) == 2:
             a, b = seq
@@ -289,9 +291,12 @@ def flatten(cls, seq):
                 # o = b
                 b, e = o.as_base_exp()
 
+                if o.has(Order):
+                    b, e = o, S.One
+
                 #  y
                 # 3
-                if o.is_Pow:
+                elif o.is_Pow:
                     if b.is_Number:
 
                         # get all the factors with numeric base so they can be
@@ -343,7 +348,7 @@ def flatten(cls, seq):
                     # not an Add. This allow things like a**2*b**3 == a**5
                     # if a.is_commutative == False, but prohibits
                     # a**x*a**y and x**a*x**b from combining (x,y commute).
-                    if b1 == b2 and (not new_exp.is_Add):
+                    if b1 == b2 and (not new_exp.is_Add) and not (o.has(Order) or o1.has(Order)):
                         o12 = b1 ** new_exp
 
                         # now o12 could be a commutative object

sympy/core/tests/test_arit.py

@@ -2,7 +2,7 @@
 
 from sympy import (Basic, Symbol, sin, cos, exp, sqrt, Rational, Float, re, pi,
         sympify, Add, Mul, Pow, Mod, I, log, S, Max, symbols, oo, Integer,
-        sign, im, nan, Dummy, factorial, comp
+        sign, im, nan, Dummy, factorial, comp, O
 )
 from sympy.core.compatibility import long, range
 from sympy.utilities.iterables import cartes
@@ -1704,6 +1704,12 @@ def test_add_flatten():
     assert (1/a).simplify() == (1/b).simplify() == 0
 
 
+def test_omgissue_31():
+    assert sin(x + O(x**2)) - sin(x + O(x**2)) == \
+        Add(-sin(x + O(x**2)), sin(x + O(x**2)), evaluate=False)
+    assert sin(O(x))/sin(O(x)) == Mul(sin(O(x)), 1/sin(O(x)), evaluate=False)
+
+
 def test_issue_5160_6087_6089_6090():
     # issue 6087
     assert ((-2*x*y**y)**3.2).n(2) == (2**3.2*(-x*y**y)**3.2).n(2)