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Re: Re: "Assuming"
Mariano Suárez-Alvarez wrote:
> On Feb 23, 7:34 am, Daniel Lichtblau <d... at wolfram.com> wrote:
> [...]
>>[From David Cantrell:]
>>
>>>>[...] But I do know of a case where
>>>>Mathematica goes even further, removing a singularity at which the
>>>>function
>>>>is defined as a number:
>>
>>>>In[17]:= FullSimplify[UnitStep[-x^2]]
>>>>Out[17]= 0
>>
>>>>despite the fact that correctly
>>
>>>>In[18]:= UnitStep[-x^2] /. x -> 0
>>>>Out[18]= 1
>>
>>>>Perhaps the simplification above is considered a bug, perhaps not.
>>
>>>>David
>>
>>A feature, really. That is, it's wrong, but FullSimplify can make
>>mistakes on measure zero sets. We do not generally regard this
>>phenomenon as a bug, though we reconsider on case by case basis.
>
>
> How does that `measure zero' allowance work in a context
> of something like
>
> Assuming[Element[x, Integers], FullSimplify[something]]
>
> ?
>
> -- m
I've seen cases where the FullSimplify[something] result differs from
something on a finite set of integers. This motivated me several months
ago to alter assumptions of integrality, to reality (realness?
realhood?), in processing of Integrate.
Daniel Lichtblau
Wolfram Research
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