Updates:
Status: Duplicate
Mergedinto: 1374
Comment #3 on issue 3611 by [email protected]: sqrt(x) should be the same
as x ** 0.5
http://code.google.com/p/sympy/issues/detail?id=3611
Don't worry, not saying hello is not considered rude. See
http://producingoss.com/en/communications.html#rudeness.
The reason is that in a multiplication, the powers cancel, so that it
becomes x**(0.), which is just x**0 == 1 (see issue 3446, issue 2340, and
probably several others).
The Add one is the other issue I noted (issue 1374). The worst part is:
In [28]: S.Half == 0.5
Out[28]: True
In [29]: x**S.Half == x**0.5
Out[29]: True
In [30]: x**S.Half + x**0.5
Out[30]:
0.5 ___
x + ╲╱ x
Meaning that the seemingly obvious invariant x == y implies x - y == 0 does
not actually hold here.
Let's keep those other issues for the equality of sqrt(x) and x**0.5, since
there's already a lot of discussion about them there (particularly on issue
1374). For the integral, it looks like it's already been fixed in master:
In [32]: integrate (exp (x ** .5), x)
Out[32]:
⎛ 0.5⎞ ⎛ 0.5⎞
0.5 ⎝x ⎠ ⎝x ⎠
2.0⋅x ⋅ℯ - 2.0⋅ℯ
In [33]: integrate (exp (x ** .5), x, meijerg=True)
Out[33]:
2.0⋅ⅈ⋅π │ -4.0⋅ⅈ⋅π│ ⎛ 0.5 ⅈ⋅π⎞
2.0⋅ℯ ⋅│ℯ │⋅γ⎝2.0, x ⋅ℯ ⎠
So I am closing this.
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