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Re: inconsistent refinement behavior


Refine treats Reals as a subset of Complexes, as expected:

In:	Assuming[Element[x, Reals], Refine[Element[x, Complexes]]]
Out:	True

Of course, the same holds for the other two examples:

In:	Assuming[x>0, Refine[Element[x, Complexes]]]
Out:	True

In:	Assuming[x>=0, Refine[Element[x, Complexes]]]
Out:	True

However, Refine recognizes that the stronger condition Element[x, Reals] 
holds for all three examples.

Alex


On Sun, 14 Jul 2013, Bill Rowe wrote:

> On 7/12/13 at 2:49 AM, akrasnov at cory.eecs.berkeley.edu (Alex Krasnov)
> wrote:
>
>> Firstly, x==0 also implicitly assumes that x is in Reals, since 0 is
>> in Reals, as the following examples demonstrate:
>
>> In:    Assuming[x==0, Refine[Element[x, Reals]]] Out:  True
>
>> In:    Assuming[{Element[x, Reals], x==0}, Refine[Infinity/x]]
>> Out:   ComplexInfinity
>
> No so. Consider
>
> In[1]:= Assuming[x == 0, Refine[Element[x, Complexes]]]
>
> Out[1]= True
>
>



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