# HG changeset patch
# User Stepan Roucka <[EMAIL PROTECTED]>
# Date 1223756894 -7200
# Node ID 8b4b931bb77dee53e3d235592a7aa7c8c8ff96a6
# Parent 7f83ede93315ccf9c350629753d51ade7b960798
Implement simplification of reciprocal of power
In the rules for simplifying exponentiation implemented recently, I forgot
to implement one important relation for complex x and y:
1/x**y = x**(-y)
This patch adds this functionality. As a side effect it also fixes the problem
with failing heurisch test in issue 1130 so the xfail is removed.
One test in test_ccode is changed because of this simplification and unneeded
assumptions from docstrings are removed.
diff --git a/sympy/core/evalf.py b/sympy/core/evalf.py
--- a/sympy/core/evalf.py
+++ b/sympy/core/evalf.py
@@ -1003,7 +1003,7 @@ def N(x, n=15, **options):
Example:
>>> from sympy import Sum, Symbol, oo
- >>> k = Symbol("k", integer=True)
+ >>> k = Symbol("k")
>>> Sum(1/k**k, (k, 1, oo))
Sum(k**(-k), (k, 1, oo))
>>> N(Sum(1/k**k, (k, 1, oo)), 4)
diff --git a/sympy/core/power.py b/sympy/core/power.py
--- a/sympy/core/power.py
+++ b/sympy/core/power.py
@@ -81,6 +81,8 @@ class Pow(Basic):
return self._args[1]
def _eval_power(self, other):
+ if other == S.NegativeOne:
+ return Pow(self.base, self.exp * other)
if self.exp.is_integer and other.is_integer:
return Pow(self.base, self.exp * other)
if self.base.is_nonnegative and self.exp.is_real and other.is_real:
diff --git a/sympy/core/tests/test_eval_power.py
b/sympy/core/tests/test_eval_power.py
--- a/sympy/core/tests/test_eval_power.py
+++ b/sympy/core/tests/test_eval_power.py
@@ -55,3 +55,8 @@ def test_issue350():
def test_issue767():
assert --sqrt(sqrt(5)-1)==sqrt(sqrt(5)-1)
+
+def test_negative_one():
+ x = Symbol('x', complex=True)
+ y = Symbol('y', complex=True)
+ assert 1/x**y == x**(-y)
diff --git a/sympy/integrals/tests/test_risch.py
b/sympy/integrals/tests/test_risch.py
--- a/sympy/integrals/tests/test_risch.py
+++ b/sympy/integrals/tests/test_risch.py
@@ -106,7 +106,6 @@ def test_heurisch_symbolic_coeffs():
assert heurisch(1/(x+sqrt(2)), x) == log(x+sqrt(2))
assert trim(diff(heurisch(log(x+y+z), y), y)) == log(x+y+z)
[EMAIL PROTECTED]
def test_heurisch_symbolic_coeffs_1130():
assert heurisch(1/(x**2+y), x) == I*y**(-S.Half)*log(x +
(-y)**S.Half)/2 - \
I*y**(-S.Half)*log(x -
(-y)**S.Half)/2
diff --git a/sympy/printing/tests/test_ccode.py
b/sympy/printing/tests/test_ccode.py
--- a/sympy/printing/tests/test_ccode.py
+++ b/sympy/printing/tests/test_ccode.py
@@ -10,7 +10,7 @@ def test_Pow():
assert ccode(x**3) == "pow(x,3)"
assert ccode(x**(y**3)) == "pow(x,(pow(y,3)))"
assert ccode(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \
- "1/(pow((3.50000000000000*g(x)),(x - pow(y,x)))*(y + pow(x,2)))"
+ "1/(y + pow(x,2))*pow((3.50000000000000*g(x)),(-x + pow(y,x)))"
def test_Exp1():
assert ccode(exp(1)) == "exp(1)"
diff --git a/sympy/simplify/simplify.py b/sympy/simplify/simplify.py
--- a/sympy/simplify/simplify.py
+++ b/sympy/simplify/simplify.py
@@ -220,8 +220,6 @@ def together(expr, deep=False):
It also perfect possible to work with symbolic powers or
exponential functions or combinations of both:
- >>> x = Symbol('x', positive=True)
- >>> y = Symbol('y', real=True)
>>> together(1/x**y + 1/x**(y-1))
x**(-y)*(1 + x)
diff --git a/sympy/simplify/tests/test_simplify.py
b/sympy/simplify/tests/test_simplify.py
--- a/sympy/simplify/tests/test_simplify.py
+++ b/sympy/simplify/tests/test_simplify.py
@@ -165,6 +165,8 @@ def test_together():
assert together(Rational(1,2) + x/2) == (x+1)/2
+ assert together(1/x**y + 1/x**(y-1)) == x**(-y)*(1 + x)
+
def test_separate():
x, y, z = map(Symbol, 'xyz')
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