The issue is that sqrt(x)*sqrt(y) does not equal sqrt(x*y), unless x
and y are positive (see
http://docs.sympy.org/tutorial/tutorial/simplification.html#powers).
Unfortunately, your assumptions that A1 and A2 are real is not enough
for SymPy to deduce that the things under the square root are
positive.
One way to force it to happen is to use powsimp(force=True), like
powsimp(coef1*coef2, force=True). You can then expand that to get the
simplification you want.
Aaron Meurer
On Fri, Jun 21, 2013 at 1:29 PM, Anton Loukianov
<anton.loukia...@gmail.com> wrote:
> Hello,
>
> How do I expand products of square roots like this?
>
> import sympy as sp
> A1,A1 = sp.symbols('A1,A2', real=True, constant=True)
> coef1 = sp.sqrt(1/(A1**2 + A2**2 + sp.sqrt(A1**4 - A1**2*A2**2 + A2**4)))
> coef2 = sp.sqrt(1/(A1**2 + A2**2 - sp.sqrt(A1**4 - A1**2*A2**2 + A2**4)))
> sp.expand(coef1*coef2)
>
> I expected to get rid of the inner square root this way, but it doesn't seem
> to work.
>
> - Anton
>
>
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