Merge pull request #19916 from sachin-4099/gsoc#14

[GSoC] Functions: Fixes limit evaluations related to trigonometric functions

sympy/functions/elementary/trigonometric.py

@@ -1,6 +1,6 @@
 from sympy.core.add import Add
 from sympy.core.basic import sympify, cacheit
-from sympy.core.function import Function, ArgumentIndexError, expand_mul
+from sympy.core.function import Function, ArgumentIndexError, PoleError, expand_mul
 from sympy.core.logic import fuzzy_not, fuzzy_or, FuzzyBool
 from sympy.core.numbers import igcdex, Rational, pi
 from sympy.core.relational import Ne
@@ -388,6 +388,14 @@ def taylor_term(n, x, *previous_terms):
             else:
                 return (-1)**(n//2)*x**(n)/factorial(n)
 
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        if logx is not None:
+            arg = arg.subs(log(x), logx)
+        if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity):
+            raise PoleError("Cannot expand %s around 0" % (self))
+        return Function._eval_nseries(self, x, n=n, logx=logx, cdir=cdir)
+
     def _eval_rewrite_as_exp(self, arg, **kwargs):
         I = S.ImaginaryUnit
         if isinstance(arg, TrigonometricFunction) or isinstance(arg, HyperbolicFunction):
@@ -576,6 +584,9 @@ def eval(cls, arg):
         elif isinstance(arg, SetExpr):
             return arg._eval_func(cls)
 
+        if arg.is_extended_real and arg.is_finite is False:
+            return AccumBounds(-1, 1)
+
         if arg.could_extract_minus_sign():
             return cls(-arg)
 
@@ -708,6 +719,14 @@ def taylor_term(n, x, *previous_terms):
             else:
                 return (-1)**(n//2)*x**(n)/factorial(n)
 
+    def _eval_nseries(self, x, n, logx, cdir=0):
+        arg = self.args[0]
+        if logx is not None:
+            arg = arg.subs(log(x), logx)
+        if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity):
+            raise PoleError("Cannot expand %s around 0" % (self))
+        return Function._eval_nseries(self, x, n=n, logx=logx, cdir=cdir)
+
     def _eval_rewrite_as_exp(self, arg, **kwargs):
         I = S.ImaginaryUnit
         if isinstance(arg, TrigonometricFunction) or isinstance(arg, HyperbolicFunction):

sympy/series/tests/test_limits.py

@@ -859,6 +859,12 @@ def test_issue_15055():
     assert limit(n**3*((-n - 1)*sin(1/n) + (n + 2)*sin(1/(n + 1)))/(-n + 1), n, oo) == 1
 
 
+def test_issue_16708():
+    m, vi = symbols('m vi', positive=True)
+    B, ti, d = symbols('B ti d')
+    assert limit((B*ti*vi - sqrt(m)*sqrt(-2*B*d*vi + m*(vi)**2) + m*vi)/(B*vi), B, 0) == (d + ti*vi)/vi
+
+
 def test_issue_19739():
     assert limit((-S(1)/4)**x, x, oo) == 0
 
@@ -867,7 +873,13 @@ def test_issue_19766():
     assert limit(2**(-x)*sqrt(4**(x + 1) + 1), x, oo) == 2
 
 
-def test_issue_16708():
-    m, vi = symbols('m vi', positive=True)
-    B, ti, d = symbols('B ti d')
-    assert limit((B*ti*vi - sqrt(m)*sqrt(-2*B*d*vi + m*(vi)**2) + m*vi)/(B*vi), B, 0) == (d + ti*vi)/vi
+def test_issue_19770():
+    m = Symbol('m')
+    # the result is not 0 for non-real m
+    assert limit(cos(m*x)/x, x, oo) == Limit(cos(m*x)/x, x, oo, dir='-')
+    m = Symbol('m', real=True)
+    # can be improved to give the correct result 0
+    assert limit(cos(m*x)/x, x, oo) == Limit(cos(m*x)/x, x, oo, dir='-')
+    m = Symbol('m', nonzero=True)
+    assert limit(cos(m*x), x, oo) == AccumBounds(-1, 1)
+    assert limit(cos(m*x)/x, x, oo) == 0