SymPy is reluctant to do manipulations with the squareroots because they are
not valid for complex x and y (this is assumed by default). If you assume that
they are real, or even better, positive, it will work better (for example, you
can then split sqrt(x*y) => sqrt(x)*sqrt(y) or reduce sqrt(x**2) => x).
In [10]: x, y = symbols('x y', real=True)
In [11]: a = (1 + x**2/y**2)**(S(1)/2)
In [12]: b = x**2 + y**2
In [13]: f = -1/(a*b) + 3*y/(x**2*a**3*b)
In [14]: f
Out[14]:
1 3⋅y
- ──────────────────────── + ────────────────────────
⎽⎽⎽⎽⎽⎽⎽⎽ 3/2
╱ 2 ⎛ 2⎞
╱ x ⎛ 2 2⎞ 2 ⎜ x ⎟ ⎛ 2 2⎞
╱ 1 + ── ⋅⎝x + y ⎠ x ⋅⎜1 + ──⎟ ⋅⎝x + y ⎠
╱ 2 ⎜ 2⎟
╲╱ y ⎝ y ⎠
In [15]: simplify(f)
Out[15]:
⎽⎽⎽⎽⎽⎽⎽⎽⎽
╱ 2 2 ⎛ 2 2 3 4⎞
╲╱ x + y ⋅⎝- x ⋅y + 3⋅y - x ⎠⋅│y│
──────────────────────────────────────
2 ⎛ 4 2 2 4 6 6⎞
x ⋅⎝3⋅x ⋅y + 3⋅x ⋅y + x + y ⎠
(note this was technically in polys12, but I think it will work the same or
similarly in master).
Aaron Meurer
On Apr 5, 2011, at 12:42 PM, Dave wrote:
>
>
> On Apr 5, 1:33 pm, Mateusz Paprocki <matt...@gmail.com> wrote:
>> Hi,
>>
>> On 5 April 2011 19:23, Ondrej Certik <ond...@certik.cz> wrote:
>>
>>
>>
>>> Hi Dave!
>>
>>> On Tue, Apr 5, 2011 at 5:36 AM, Dave <dspg...@netscape.net> wrote:
>>>> Hello,
>>>> I'm relatively new to SymPy. I'm using it to verify some of my
>>
>>> Welcome to SymPy!
>>
>>>> algebraic manipulations. I have the following expression I'm trying to
>>>> simplify:
>>>> 1 3*Y
>>>> - ------------------------ + ------------------------
>>>> ________ 3/2
>>>> / 2 / 2\
>>>> / Y / 2 2\ 2 | Y | / 2 2\
>>>> / 1 + -- *\X + Y / X *|1 + --| *\X + Y /
>>>> / 2 | 2|
>>>> \/ X \ X /
>>
>>>> Hopefully the above expression looks okay if you view it in a fixed
>>>> font.
>
> Hi Guys,
> Thanks for the input. I don't mind leaving the expression as a sum of
> 2 terms, but rather trying to simplify the sqrt()(x^2+y^2) in each
> denominator. As an example you could change (x^2+y^2) to x^2*(1 +y^2/
> x^2) and then combine the sqrt() functions.
>
> I know it's a bit much to expect sympy to do it automatically, and I
> don't mind telling sympy what I'd like to do, but I haven't really
> found the proper commands to use.
>
> I did have some success using subs with a 3rd symbol. For example
> f.subs(sqrt(1+y**2/x**2),z)
> f.subs(x**2+y**2,x**2*z**2)
> f.subs(z,sqrt(1+y**2/x**2))
>
> This gives me what I was looking for, but in the 2nd statement I have
> to explicitly know what the substitution is - if I made a mistake
> there, then the resulting expression would be wrong :(
>
> I also tried using as_coefficient() from mul but it wouldn't extract
> x**2 or 1/x**2.
>
> Cheers,
> Dave
>
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