Re: inconsistent refinement behavior

• To: mathgroup at smc.vnet.net
• Subject: [mg131375] Re: inconsistent refinement behavior
• From: Alex Krasnov <akrasnov at cory.eecs.berkeley.edu>
• Date: Tue, 16 Jul 2013 05:56:45 -0400 (EDT)
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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.

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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