In keeping with Richard's suggestion, in Sage I think a good
_algebraic_ definition of 'real' is
bool(x/2+conjugate(x)/2 == x)
So
sage: def RN(x):
....: try:
....: return bool(x/2+conjugate(x)/2 == x)
....: except:
....: return false
which also works whenever conjugate is defined, including
sage: assume(x,'real')
sage: assume(y,'real')
sage: RN(sqrt(x^2+y^2))
True
On 19 September 2016 at 19:51, rjf <fate...@gmail.com> wrote:
> If arg(x) is 0 and x is a number, then it is a real number. Maxima calls
> this carg() for complex arg.
>
> Carg will also work for some things that are not of numeric type, but
> symbolic in some way.
> .
> Like sqrt(x^2+y^2) is real if domain=real
>
> Good luck
>
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