core: change semantics of the dir kwarg of Expr.series()

Closes #1236

diofant/core/expr.py

@@ -2317,7 +2317,7 @@ def is_comparable(self):
     # ####### SERIES, LEADING TERM, LIMIT, ORDER METHODS ####### #
     ##############################################################
 
-    def series(self, x=None, x0=0, n=6, dir='+', logx=None):
+    def series(self, x=None, x0=0, n=6, dir=None, logx=None):
         """Series expansion of "self" around ``x = x0`` yielding either terms of
         the series one by one (the lazy series given when n=None), else
         all the terms at once when n != None.
@@ -2346,15 +2346,15 @@ def series(self, x=None, x0=0, n=6, dir='+', logx=None):
         >>> [next(term) for i in range(2)]
         [1, -x**2/2]
 
-        For ``dir=+`` (default) the series is calculated from the right and
-        for ``dir=-`` the series from the left.  For infinite ``x0`` (``oo``
+        For ``dir=-1`` (default) the series is calculated from the right and
+        for ``dir=+1`` the series from the left.  For infinite ``x0`` (``oo``
         or ``-oo``), the ``dir`` argument is determined from the direction
-        of the infinity (i.e. ``dir="-"`` for ``oo``).  For smooth functions
+        of the infinity (i.e. ``dir=+1`` for ``oo``).  For smooth functions
         this flag will not alter the results.
 
-        >>> abs(x).series(dir='+')
+        >>> abs(x).series(dir=-1)
         x
-        >>> abs(x).series(dir='-')
+        >>> abs(x).series(dir=+1)
         -x
 
         For rational expressions this method may return original expression.
@@ -2365,6 +2365,7 @@ def series(self, x=None, x0=0, n=6, dir='+', logx=None):
         """
         from .function import expand_mul
         from .symbol import Dummy, Symbol
+        from ..functions import sign
         from ..series import Order
         from ..simplify import collect
 
@@ -2385,31 +2386,30 @@ def series(self, x=None, x0=0, n=6, dir='+', logx=None):
             else:
                 return self
 
-        if len(dir) != 1 or dir not in '+-':
-            raise ValueError("Dir must be '+' or '-'")
-
-        if x0 == oo:
-            return self.aseries(x, n)
-        elif x0 == -oo:
-            return self.subs({x: -x}).aseries(x, n).subs({x: -x})
-
-        # use rep to shift origin to x0 and change sign (if dir is negative)
-        # and undo the process with rep2
-        if x0 or dir == '-':
-            if dir == '-':
-                rep = -x + x0
-                rep2 = -x
-                rep2b = x0
-            else:
-                rep = x + x0
-                rep2 = x
-                rep2b = -x0
-            s = self.subs({x: rep}).series(x, x0=0, n=n, dir='+', logx=logx)
+        x0 = sympify(x0)
+
+        if x0.is_infinite:
+            dir = sign(x0).simplify()
+        elif dir is None:
+            dir = Rational(-1)
+        else:
+            dir = sympify(dir)
+            dir = dir/abs(dir)
+
+        if not (isinstance(dir, Expr) and dir.is_nonzero):
+            raise ValueError('Direction must be a nonzero Expr, got {dir}')
+
+        if x0.is_infinite:
+            return self.subs({x: dir*x}).aseries(x, n).subs({x: x/dir})
+
+        # use rep to shift origin to x0 and change dir to 1, then undo
+        if x0 or dir != -1:
+            s = self.subs({x: x0 - dir*x}).series(x, x0=0, n=n, dir=-1, logx=logx)
             if n is None:  # lseries...
-                return (si.subs({x: rep2 + rep2b}) for si in s)  # pragma: no branch
-            return s.subs({x: rep2 + rep2b})
+                return (si.subs({x: x0/dir - x/dir}) for si in s)  # pragma: no branch
+            return s.subs({x: x0/dir - x/dir})
 
-        # from here on it's x0=0 and dir='+' handling
+        # from here on it's x0=0 and dir=1 handling
 
         if x.is_positive is x.is_negative is None or x.is_Symbol is not True:
             # replace x with an x that has a positive assumption

diofant/series/series.py

@@ -1,7 +1,7 @@
 from ..core.sympify import sympify
 
 
-def series(expr, x=None, x0=0, n=6, dir='+'):
+def series(expr, x=None, x0=0, n=6, dir=None):
     """Series expansion of ``expr`` in ``x`` around point ``x0``.
 
     See Also

diofant/tests/functions/test_trigonometric.py

@@ -1050,10 +1050,10 @@ def test_aseries():
     def t(n, v, d, e):
         assert abs(n(1/v).evalf(strict=False) -
                    n(1/x).series(x, dir=d).removeO().subs({x: v})) < e
-    t(atan, 0.1, '+', 1e-5)
-    t(atan, -0.1, '-', 1e-5)
-    t(acot, 0.1, '+', 1e-5)
-    t(acot, -0.1, '-', 1e-5)
+    t(atan, 0.1, -1, 1e-5)
+    t(atan, -0.1, +1, 1e-5)
+    t(acot, 0.1, -1, 1e-5)
+    t(acot, -0.1, +1, 1e-5)
     pytest.raises(PoleError, lambda: atan(y/x).series(x, n=1))
     pytest.raises(PoleError, lambda: acot(y/x).series(x, n=1))
 

diofant/tests/series/test_aseries.py

@@ -1,7 +1,7 @@
 import pytest
 
-from diofant import (O, PoleError, Rational, Symbol, cos, exp, log, oo, sin,
-                     sqrt, symbols)
+from diofant import (I, O, PoleError, Rational, Symbol, cos, exp, log, oo, pi,
+                     sin, sqrt, symbols)
 from diofant.abc import x
 
 
@@ -72,3 +72,7 @@ def test_issue_1231():
                                 log(x) + O(x**(-6), (x, oo)))
     assert e.series(x, -oo) == (3/(32*x**4) - 1/(4*x**2) - log(2) -
                                 log(-x) + O(x**(-6), (x, -oo)))
+    assert e.series(x, x0=+I*oo) == (-3/(32*x**4) + 1/(4*x**2) + I*pi/2 +
+                                     log(2) + log(-I*x) + O(x**(-6), (x, oo*I)))
+    assert e.series(x, x0=-I*oo) == (+3/(32*x**4) - 1/(4*x**2) - I*pi/2 -
+                                     log(2) - log(+I*x) + O(x**(-6), (x, -oo*I)))

diofant/tests/series/test_nseries.py

@@ -2,7 +2,7 @@
 
 from diofant import (Derivative, E, I, O, PoleError, Rational, Symbol, acosh,
                      acoth, asin, asinh, atanh, besselk, cbrt, ceiling, cos,
-                     cosh, cot, coth, exp, floor, limit, ln, log, pi, sign,
+                     cosh, cot, coth, exp, floor, limit, ln, log, oo, pi, sign,
                      sin, sinh, sqrt, tan, tanh)
 from diofant.abc import a, b, l, w, x, y, z
 
@@ -110,6 +110,12 @@ def test_log3():
     assert e.series(x, n=4, logx=l) == 1/(-l + log(-1))
 
 
+def test_log4():
+    assert (log(1 + x).series(x, x0=I*oo) ==
+            1/(5*x**5) - 1/(4*x**4) + 1/(3*x**3) - 1/(2*x**2) + 1/x +
+            I*pi/2 + log(-I*x) + O(x**(-6), (x, oo*I)))
+
+
 def test_x0():
     # issue sympy/sympy#5654
     assert ((1/(x**2 + a**2)**2).series(x, x0=I*a, n=0) ==
@@ -457,13 +463,13 @@ def test_abs():
 
 
 def test_dir():
-    assert abs(x).series(x, 0, dir='+') == x
-    assert abs(x).series(x, 0, dir='-') == -x
-    assert floor(x + 2).series(x, 0, dir='+') == 2
-    assert floor(x + 2).series(x, 0, dir='-') == 1
-    assert floor(x + 2.2).series(x, 0, dir='-') == 2
-    assert ceiling(x + 2.2).series(x, 0, dir='-') == 3
-    assert sin(x + y).series(x, 0, dir='-') == sin(x + y).series(x, 0, dir='+')
+    assert abs(x).series(x, 0, dir=-1) == x
+    assert abs(x).series(x, 0, dir=+1) == -x
+    assert floor(x + 2).series(x, 0, dir=-1) == 2
+    assert floor(x + 2).series(x, 0, dir=+1) == 1
+    assert floor(x + 2.2).series(x, 0, dir=+1) == 2
+    assert ceiling(x + 2.2).series(x, 0, dir=+1) == 3
+    assert sin(x + y).series(x, 0, dir=+1) == sin(x + y).series(x, 0, dir=-1)
 
 
 def test_sympyissue_3504():

diofant/tests/series/test_series.py

@@ -57,10 +57,10 @@ def test_simple():
     assert (cos(x).series(x, 1) -
             cos(x + 1).series(x).subs({x: x - 1})).removeO() == 0
 
-    assert abs(x).series(x, oo, n=5, dir='+') == x
-    assert abs(x).series(x, -oo, n=5, dir='-') == -x
-    assert abs(-x).series(x, oo, n=5, dir='+') == x
-    assert abs(-x).series(x, -oo, n=5, dir='-') == -x
+    assert abs(x).series(x, oo, n=5, dir=-1) == x
+    assert abs(x).series(x, -oo, n=5, dir=+1) == -x
+    assert abs(-x).series(x, oo, n=5, dir=-1) == x
+    assert abs(-x).series(x, -oo, n=5, dir=+1) == -x
 
     # issue sympy/sympy#7203
     assert series(cos(x), x, pi, 3) == -1 + (x - pi)**2/2 + O((x - pi)**3,
@@ -73,11 +73,11 @@ def test_sympyissue_5223():
 
     e = cos(x).series(x, 1, n=None)
     assert [next(e) for i in range(2)] == [cos(1), -((x - 1)*sin(1))]
-    e = cos(x).series(x, 1, n=None, dir='-')
+    e = cos(x).series(x, 1, n=None, dir=+1)
     assert [next(e) for i in range(2)] == [cos(1), (1 - x)*sin(1)]
     # the following test is exact so no need for x -> x - 1 replacement
-    assert abs(x).series(x, 1, dir='-') == x
-    assert exp(x).series(x, 1, dir='-', n=3).removeO() == \
+    assert abs(x).series(x, 1, dir=+1) == x
+    assert exp(x).series(x, 1, dir=+1, n=3).removeO() == \
         E - E*(-x + 1) + E*(-x + 1)**2/2
 
     assert next(Derivative(cos(x), x).series(n=None)) == Derivative(1, x)
@@ -106,7 +106,7 @@ def test_sympyissue_5223():
 
 
 def test_sympyissue_3978():
-    assert f(x).series(x, 0, 3, dir='-') == \
+    assert f(x).series(x, 0, 3, dir=+1) == \
         f(0) + x*Subs(Derivative(f(x), x), (x, 0)) + \
         x**2*Subs(Derivative(f(x), x, x), (x, 0))/2 + O(x**3)
     assert f(x).series(x, 0, 3) == \