It is possible to combine terms under a radical?

[Jonathan Crall]

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)

[Aaron Meurer]

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

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[Chris Smith]

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.

[Chris Smith]

Paste of the result looks bad but it does something like you are asking.

/c

[Chris Smith]

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)