Here's the code and the sample expression in text:
>>> def combine_like_radicals(expr):
... from sympy.utilities.iterables import sift
... reps = {}
... for m in expr.atoms(Mul):
... rads = [p for p in m.atoms(Pow) if p.exp.is_Rational]
... sifted = sift(rads, lambda x: x.args[1].as_numer_denom())
... for k, v in sifted.items():
... if len(sifted[k]) > 1:
... e = Rational(*k)
... b = Mul(*[p.base for p in v])
... reps[Mul(*v)] = Pow(b, e, evaluate=False)
... return expr.xreplace(reps)
...
>>> sqrt(pi*x)+root(3*pi*x,3)
3**(1/3)*pi**(1/3)*x**(1/3) + sqrt(pi)*sqrt(x)
>>> combine_like_radicals(_)
sqrt(pi*x) + (3*pi*x)**(1/3)
On Wednesday, January 27, 2016 at 10:49:28 AM UTC-6, Chris Smith wrote:
>
> Paste of the result looks bad but it does something like you are asking.
>
> /c
>
> On Wednesday, January 27, 2016 at 10:48:53 AM UTC-6, Chris Smith wrote:
>
>> So you might try a helper function something like:
>>
>> >>> combine_like_radicals(sqrt(x)*sqrt(y) + root(2*pi*x,3))
>> xy − − √ +2πx − − − √ 3
>>
>> See http://codepad.org/lqcmqzwm for code snippet.
>>
>>
>>
>> On Thursday, January 21, 2016 at 2:55:32 PM UTC-6, Aaron Meurer wrote:
>>
>>> You can do it if you omit the assumptions. Otherwise, the only way is to
>>> use Pow(2*pi, Rational(1, 2), evaluate=False).
>>>
>>> Aaron Meurer
>>>
>>> On Wed, Jan 20, 2016 at 4:31 PM, Jonathan Crall <[email protected]>
>>> wrote:
>>>
>>>> I saw under
>>>> http://docs.sympy.org/dev/tutorial/simplification.html#powsimp
>>>> that it is impossible to combine radicals using powersimp:
>>>>
>>>> "This means that it will be impossible to undo this identity with
>>>> powsimp(), because even if powsimp() were to put the bases together,
>>>> they would be automatically split apart again."
>>>>
>>>> I was wondering if it was possible to do this any other way.
>>>>
>>>> For a toy example I have
>>>>
>>>> import sympy
>>>> L = sympy.symbols('L', real=True, finite=True, positive=True)
>>>> sympy.sqrt(L) * sympy.sqrt(pi)
>>>>
>>>> and I would like to have it return sympy.sqrt(L * pi)
>>>> Is there any way to do this?
>>>>
>>>> What I'd really like is if it combined these terms in this real
>>>> example:
>>>>
>>>> import simplify
>>>> import vtool as vt
>>>> import sympy
>>>> sigma, dist, L = sympy.symbols('sigma, distij, L', real=True,
>>>> finite=True, positive=True)
>>>> kernel = (1 / sympy.sqrt(sigma ** 2 * 2 * sympy.pi)) *
>>>> sympy.exp((-dist ** 2) / (2 * sigma ** 2))
>>>> phi = (1 / L) * kernel
>>>> logphi = sympy.simplify(sympy.log(phi))
>>>> logphi = sympy.logcombine(logphi)
>>>>
>>>> So I would get
>>>> -distij**2/(2*sigma**2) - log(sqrt(2 * pi)*L*sigma)
>>>>
>>>> instead of
>>>>
>>>> -distij**2/(2*sigma**2) - log(sqrt(2)*sqrt(pi)*L*sigma)
>>>>
>>>>
>>>>
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>>>>
>>>
>>>
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