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)

Wouldnt it then be more consistent coerce RealFields to higher
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)


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