Hi Richard,

I do get your point that we don't have to make the same mistake with other 
systems, but I do think there is a benefit for consistency, if they have a 
purpose in doing that design. For most systems, sqrt() returns the 
principal/positive square root, so there is only one unique value. If we'd 
like a function to return all square roots, we can create another function 
dedicated to do that with a new name.

My two cents,

Shawn

On Friday, December 5, 2014 6:48:32 PM UTC-5, Richard Fateman wrote:
>
> You are heading into erroneous waters.
> It doesn't matter that 3>0.  sqrt(9) has two values,  +3 and -3.
> Just because some other systems make this mistake does not mean
> sympy should do this.
>
> If you want to say something about the choice of branch for sqrt(x^2),
> you have to say something about sqrt(x^2), not x.
>
> It may be sensible if you mean to restrict the square root function.
> But not that way.
> Good luck
>
>
> On Friday, December 5, 2014 1:49:35 PM UTC-8, Aaron Meurer wrote:
>>
>> They need to be positive. Even for integer x, sqrt(x**2) != x if x is 
>> negative. 
>>
>> Aaron Meurer 
>>
>> On Fri, Dec 5, 2014 at 3:34 PM, Francesco Bonazzi 
>> <[email protected]> wrote: 
>> > newvars =symbols('x a b', integer=True) 
>> > e.xreplace(dict(zip([x,a,b], newvars))) 
>> > 
>> > I did not test this. 
>> > 
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