Since your belief about what the correct behavior is, is at best
arguable, and at worst, wrong, I would not expect it to
be "corrected"
Sqrt(anything) has TWO values.
Choosing one should depend on the choice of square root branch, e.g.
assume(sqrt(E))
assuming something about E doesn't say much.
e.g. even sqrt(9) is +-3.
who cares about the "sign" of 9.
In some engineering and physical circumstances, a branch of the sqrt
can be intuited. But the math issue is not resolved by "assume(x>0)" etc
On Saturday, June 15, 2013 8:31:02 AM UTC-7, Eric Gourgoulhon wrote:
>
> Hi,
>
> Here is some behavior of Sage which can be quite disturbing for a new user
> and probably would be considered as a bug:
>
> sage: assume(x<0)
> sage: sqrt(x^2).simplify_full()
> x
>
> It appears that the instruction "assume(x<0)" is not sufficient to enforce
> the desired behavior: x is still considered as a complex number and
> sqrt(x^2) returns *a* square root of x^2, not necessarily the positive one.
> To enforce x real, one should set:
>
> sage: maxima_calculus.eval('domain:real')
> 'real'
>
> Then the output of simplify_full() is correct:
>
> sage: sqrt(x^2).simplify_full()
> -x
>
> But the following problem remains:
>
> sage: sqrt((x-1)^2).simplify_full() # correct result:
> -x + 1
> sage: sqrt(x^2-2*x+1).simplify_full() # wrong result (and not consistent
> with the above):
> x - 1
>
> I know that the problem is due to Maxima function randcan and has been
> much discussed, in particular here:
> http://www.math.utexas.edu/pipermail/maxima/2011/026097.html
> What is the latest status of this ? In particular, is there any
> possibility to enforce the correct behavior by passing some options to
> Maxima ? (I've noticed that maxima_calculus.eval('radexpand:true') does not
> help).
> Thank you for your help.
>
> Eric.
>
>
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