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

Am Sonntag, den 28.06.2009, 19:36 -0400 schrieb Stavros Macrakis:
> On Sun, Jun 28, 2009 at 5:53 PM, Leo Butler <l.butler at ed.ac.uk> wrote:
>         ...It seems to me that there is a convention and it is
>         reasonable:
>         if x is declared to be in a set, but not explicitly declared
>         to be
>         in a subset, then it is assumed not to be in the subset.
> 
> I think that would be a terrible convention and it conflicts with
> standard mathematics: writing x ? C never implies x ? R in
> mathematics.

But this "terrible" convention is implemented in Maxima:

(%i1) declare(x,real);
(%o1)                                done

A symbol declared to be real is complex, or real:

(%i5) featurep(x,complex);
(%o5)                                true
(%i6) featurep(x,real);
(%o6)                                true

but not a rational, or an integer:

(%i7) featurep(x,rational);
(%o7)                                false
(%i8) featurep(x,integer);
(%o8)                                false

Now the other way:

(%i12) declare(n,integer);
(%o12)                               done

A symbol declared to be an integer is an integer, a rational, a real, or
a complex:

(%i13) featurep(n,integer);
(%o13)                               true
(%i14) featurep(n,rational);
(%o14)                               true
(%i15) featurep(n,real);
(%o15)                               true
(%i16) featurep(n,complex);
(%o16)                               true

Dieter Kaiser