On Thu, May 15, 2008 at 4:23 PM, David Joyner <[EMAIL PROTECTED]> wrote:
>
> I'm not disagreeing but want to point out one difference.
> RR is an ordered field and this fact is used to differentiate between
> i and -i. However, a finite field such as GF(5) is not, so there is
> some ambiguity to i. It seems to me that this should be resolved somehow.
>
In general in Sage when one explicitly does
R( foo )
then the rule is "make an element of R out of foo if at all possible".
The result
doesn't have to be at all canonical. In sharp contrast, when you do
R._coerce_(foo)
the rule is "make an element in R from foo *only* if you can do so in a
canonical way that extends to a morphism from the parent of foo".
The above discussion is about GF(5)(sqrt(-1)), and according to the
above general rule it is fine to define this. But definitely do not
define GF(5)._coerce_(sqrt(-1)).
Please see the programming guide, "The Sage Rules and Conventions for
Coercion and Arithmetic"
http://www.sagemath.org/doc/html/prog/node17.html
for more details.
William
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