On Tue, Mar 10, 2009 at 2:31 PM, Fabian Seoane <fab...@fseoane.net> wrote:
>
> Ondrej Certik wrote:
>> Hi,
>>
>> sending a trivial patch to remove hacks from trigsimp.
>>
>
> removing hacks is always good news, but I do not agree that
> sin(x)**2/cos(x)**2 is a valid answer.
> By definition, trigsimp will try to return the simplest possible
> expression, and although 'the simplest possible
> expression' is a rather vague term, imho tan**2 is a better answer than
> sin(x)**2/cos(x)**2
>
> Related to this, I would expect the following to return True:
>
> In [2]: trigsimp(tan(x)) == trigsimp(sin(x)/cos(x))
> Out[2]: False
All of this is fixed in the attached patch. Please review.
Ondrej
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From bddf677be04b62d450229a622c8e8bd73d92e38d Mon Sep 17 00:00:00 2001
From: Ondrej Certik <ond...@certik.cz>
Date: Tue, 24 Mar 2009 21:13:59 -0700
Subject: [PATCH] trigsimp() two hacks removed and done right
Previously trigsimp() failed to simplify sin(x)/cos(x) to tan(x) and similar
things and also it required an ugly hack. Many of those are now fixed and tests
written.
Signed-off-by: Ondrej Certik <ond...@certik.cz>
---
sympy/simplify/simplify.py | 46 ++++++++++++++++++++++++--------
sympy/simplify/tests/test_simplify.py | 18 ++++++++++++-
2 files changed, 51 insertions(+), 13 deletions(-)
diff --git a/sympy/simplify/simplify.py b/sympy/simplify/simplify.py
index 2ab5cf3..1c0c42e 100644
--- a/sympy/simplify/simplify.py
+++ b/sympy/simplify/simplify.py
@@ -764,15 +764,39 @@ def trigsimp(expr, deep=False, recursive=False):
>>> trigsimp(log(e), deep=True)
log(2)
"""
+ from sympy.core.basic import S
+ sin, cos, tan, cot = C.sin, C.cos, C.tan, C.cot
if recursive:
w, g = cse(expr)
g = trigsimp_nonrecursive(g[0])
for sub in reversed(w):
g = g.subs(sub[0], sub[1])
g = trigsimp_nonrecursive(g)
- return(g)
+ result = g
else:
- return trigsimp_nonrecursive(expr, deep)
+ result = trigsimp_nonrecursive(expr, deep)
+
+ # do some final simplifications like sin/cos -> tan:
+ a,b,c = map(Wild, 'abc')
+ matchers = (
+ (a*sin(b)**c/cos(b)**c, a*tan(b)**c),
+ )
+ for pattern, simp in matchers:
+ res = result.match(pattern)
+ if res is not None:
+ # if c is missing or zero, do nothing:
+ if (not c in res) or res[c] == 0:
+ continue
+ # if "a" contains the argument of sin/cos "b", skip the
+ # simplification:
+ if res[a].has(res[b]):
+ continue
+ # simplify and finish:
+ result = simp.subs(res)
+ break
+
+ return result
+
def trigsimp_nonrecursive(expr, deep=False):
"""
@@ -796,28 +820,26 @@ def trigsimp_nonrecursive(expr, deep=False):
>>> e = 2*sin(x)**2 + 2*cos(x)**2
>>> trigsimp(e)
2
- >>> trigsimp(log(e))
+ >>> trigsimp_nonrecursive(log(e))
log(2*cos(x)**2 + 2*sin(x)**2)
- >>> trigsimp(log(e), deep=True)
+ >>> trigsimp_nonrecursive(log(e), deep=True)
log(2)
"""
from sympy.core.basic import S
sin, cos, tan, cot = C.sin, C.cos, C.tan, C.cot
- #XXX this stopped working:
- if expr == 1/cos(Symbol("x"))**2 - 1:
- return tan(Symbol("x"))**2
-
if expr.is_Function:
if deep:
- return expr.func( trigsimp(expr.args[0], deep) )
+ return expr.func( trigsimp_nonrecursive(expr.args[0], deep) )
elif expr.is_Mul:
ret = S.One
for x in expr.args:
- ret *= trigsimp(x, deep)
+ ret *= trigsimp_nonrecursive(x, deep)
+
return ret
elif expr.is_Pow:
- return Pow(trigsimp(expr.base, deep), trigsimp(expr.exp, deep))
+ return Pow(trigsimp_nonrecursive(expr.base, deep),
+ trigsimp_nonrecursive(expr.exp, deep))
elif expr.is_Add:
# TODO this needs to be faster
@@ -832,7 +854,7 @@ def trigsimp_nonrecursive(expr, deep=False):
# Scan for the terms we need
ret = S.Zero
for term in expr.args:
- term = trigsimp(term, deep)
+ term = trigsimp_nonrecursive(term, deep)
res = None
for pattern, result in matchers:
res = term.match(pattern)
diff --git a/sympy/simplify/tests/test_simplify.py b/sympy/simplify/tests/test_simplify.py
index b62ea40..b45ef5e 100644
--- a/sympy/simplify/tests/test_simplify.py
+++ b/sympy/simplify/tests/test_simplify.py
@@ -33,7 +33,7 @@ def test_ratsimp_X2():
assert e != 1
assert ratsimp(e) == 1
-def test_trigsimp():
+def test_trigsimp1():
x, y = symbols('x y')
assert trigsimp(1 - sin(x)**2) == cos(x)**2
@@ -53,11 +53,27 @@ def test_trigsimp():
assert trigsimp(cos(0.12345)**2 + sin(0.12345)**2) == 1
e = 2*sin(x)**2 + 2*cos(x)**2
assert trigsimp(log(e), deep=True) == log(2)
+
+def test_trigsimp2():
+ x, y = symbols('x y')
assert trigsimp(cos(x)**2*sin(y)**2 + cos(x)**2*cos(y)**2 + sin(x)**2,
recursive=True) == 1
assert trigsimp(sin(x)**2*sin(y)**2 + sin(x)**2*cos(y)**2 + cos(x)**2,
recursive=True) == 1
+def test_trigsimp3():
+ x, y = symbols('x y')
+ assert trigsimp(sin(x)/cos(x)) == tan(x)
+ assert trigsimp(sin(x)**2/cos(x)**2) == tan(x)**2
+ assert trigsimp(sin(x)**3/cos(x)**3) == tan(x)**3
+ assert trigsimp(sin(x)**10/cos(x)**10) == tan(x)**10
+
+ assert trigsimp(cos(x)/sin(x)) == 1/tan(x)
+ assert trigsimp(cos(x)**2/sin(x)**2) == 1/tan(x)**2
+ assert trigsimp(cos(x)**10/sin(x)**10) == 1/tan(x)**10
+
+ assert trigsimp(tan(x)) == trigsimp(sin(x)/cos(x))
+
@XFAIL
def test_factorial_simplify():
# There are more tests in test_factorials.py. These are just to
--
1.6.0.4
