Yesterday I ran into some trouble when trying to integrate a simple
integral that should return atan(x). I also found an open bug about
this topic: http://code.google.com/p/sympy/issues/detail?id=636&q=atan
.
So, I took a peek into sympy/simplify/simplify.py's trigsimp function.
So I tried to add the specific form with imaginary units into matchers
list under ifelse expr.is_Add but it doesn't seem to work :(
diff --git a/sympy/simplify/simplify.py b/sympy/simplify/simplify.py
index b2816f3..916e608 100644
--- a/sympy/simplify/simplify.py
+++ b/sympy/simplify/simplify.py
@@ -762,11 +762,16 @@ def trigsimp(expr, deep=False):
log(2)
"""
from sympy.core.basic import S
- sin, cos, tan, cot = C.sin, C.cos, C.tan, C.cot
+ from sympy import log
+ I = S.ImaginaryUnit
+ sin, cos, tan, cot, atan = C.sin, C.cos, C.tan, C.cot, C.atan
#XXX this stopped working:
if expr == 1/cos(Symbol("x"))**2 - 1:
return tan(Symbol("x"))**2
+# This works :)
+# if expr == (((I*log(Symbol("x") + I))/Rational(2) - (I*log(Symbol
("x") - I))/Rational(2))):
+# return atan(Symbol("x"))
if expr.is_Function:
if deep:
@@ -786,7 +791,8 @@ def trigsimp(expr, deep=False):
matchers = (
(a*sin(b)**2, a - a*cos(b)**2),
(a*tan(b)**2, a*(1/cos(b))**2 - a),
- (a*cot(b)**2, a*(1/sin(b))**2 - a)
+ (a*cot(b)**2, a*(1/sin(b))**2 - a),
+ (((I*log(a)+I)/Rational(2))-((I*log(a)-I)/Rational(2)),
atan(a)),
)
# Scan for the terms we need
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