Is %i an integer? - Adding more facts to the database

Oops,
forget this one, sorry
sqrt(rational)-> algebraic irrational
or replace by
sqrt(rational)-> algebraic

Eric


reyssat a ?crit :
> Richard Fateman a ?crit :
>   
>> I doubt that much can be done automatically with information that a 
>> constant is irrational or transcendental, so I think such information 
>> could be left out.
>>     
> Maybe you're right, but who knows how this information could be used ? 
> For instance one could imagine a different treatment of continued 
> fractions if one knows a priori that it doesn't stop in theory 
> (irrational numbers), or use a greater precision if some value, known to 
> be transcendental, is found to be almost zero.
> But one needs at least to implement some rules, like
> rational + irrational -> irrational
> non zero rational * irrational -> irrational
> non zero rational (or algebraic) polynomial applied to transcendental -> 
> transcendental
> sqrt(rational)-> algebraic irrational
> sqrt(transcendental) -> transcendental
>
>   
>> The last I heard, it was unknown whether e+pi was irrational.
>>
>> Though  either e+pi or e-pi is irrational.
>> (If they were both rational, then their sum would be rational, and 2e 
>> is not rational.)
>>     
> yes and even e*pi or e+pi  is irrational, and even transcendental  
> (otherwise e and pi would be algebraic)
>
> Eric
>   
>> RJF
>>
>>     
>
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