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Topic: inconsistent refinement behavior
Replies: 2   Last Post: Jul 17, 2013 1:45 AM

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Alex Krasnov

Posts: 12
Registered: 7/12/13
Re: inconsistent refinement behavior
Posted: Jul 16, 2013 5:53 AM
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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.


On Sun, 14 Jul 2013, Bill Rowe wrote:

> On 7/12/13 at 2:49 AM, (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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