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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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      • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
    • Re: "Assuming"
      • From: "Mariano Suárez-Alvarez" <mariano.suarezalvarez@gmail.com>
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