Toppling the numeric tower

[Guido van Rossum]

David Eppstein <eppstein at ics.uci.edu> writes:

> In article <cp7kwv7iag.fsf at cj20424-a.reston1.va.home.com>,
>  Guido van Rossum <guido at python.org> wrote:
> 
> > > (2) should isintegral() return true for algebraic integers that are not 
> > > rational integers?
> > 
> > Sorry, you lost me there.  What are these?
> 
> Roots of polynomials with integer coefficients, leading coefficient = 1.
> E.g. the golden ratio 1+sqrt(5)/2 is a root of the polynomial
> x^2-x-1, so it is an algebraic integer.  When mathematicians want to 
> specify that a number is what you would call an integer, in the context of 
> algebraic numbers, they say "rational integer" to be more specific.

Neat.  Then to answer the question, I would think that isintegral()
should not include the algebraic integers, since to most folks those
aren't integers at all (they're definitely not part of the set Z).

--Guido van Rossum (home page: http://www.python.org/~guido/)