On Sat, May 31, 2008 at 11:14 AM, Henryk Trappmann
<[EMAIL PROTECTED]> wrote:
>
> On May 31, 3:59 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
>> However, there is a natural homomorphism from
>> RR to the symbolic ring.
>
> Hm, if this is the precondition then the coercion of say RealField(52)
> to RealField(2) is not valid, because it is no homomorphism at all.
> For example let R2 = RealField(2), then
> not R2(2.4+1.2)==R2(2.4)+R2(1.2)
>
Of course RealField(53) is not even a
ring -- it fails almost every axiom of a ring.
> Wouldnt it then be more consistent coerce RealFields to higher
> precision?
Suppose you write down an expression involving various digits of precision,
and in order to evaluate it Sage makes a sequence of *automatic*
coercions and outputs the result. Do you want an answer that has
many more digits of precision than have any chance of being
meaningful? E.g., would you really find it natural for
R(2)(0.5) + R(1000)(pi)
to implicitly output an answer with 1000 bits of precision?
> There really a homomorphism exists. Then there always would
> be a (desirable) difference between rounding and coercing. Rounding
> has to be explicit while coercing is automatic.
>
> Of course at this stage I also have to point out that the so called
> RealField is no field at all:
> not R2(3)+R2(2)-R2(2) == R2(3)
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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