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

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
>