On Fri, 13 Oct 2006 12:44:23 -0700, Martin Albrecht <[EMAIL PROTECTED]> wrote:
>> I haven't thought about this too carefully, so maybe someone will >> indulge me by shooting it down. >> >> > An alternative is that we could define == to be "there exists a >> > 'natural' >> > SAGE >> > map in both direction", i.e., _coerce_ is defined to work in both >> > direction. >> > I.e., two objects are considered "==" if canonical coercion works in >> > both >> > direction. >> > The result would be that if X == Y and x in X and y in Y, then x+y is >> > defined >> > only if X is Y. > > But this assumes that the create-only-one-instance-of-a-category > infrastructure is in place, right? It is. David Kohel and I implemented this nearly a year ago when he visited me in San Diego. For example, sage: Rings() Category of rings sage: Rings() is Rings() True And again, I think the idea to make the map that sends generators to generators (in order!) canonical is a great idea, at least in some cases. It would be nice to use Conway polynomials to define canonical consistent embeddings between finite fields of different cardinalities (when they exist), but such maps don't send generators to generators. Another problematic example is that QQ canonically maps into CC (in the category of fields), but the generator of QQ is 1 and the generator of CC is sqrt(-1). So we shouldn't require that all canonical maps sends generators to generators, though a morphism that sends gens to gens in order should be considered canonical. William > > sage: k1, x = GF(2**8).objgen() > sage: k2, y = GF(2**8).objgen() > sage: k1 == k2 > True > sage: k1 is k2 # this would be True under the assumption > False > sage: x+y # this would work under the assumption > ArithmeticError, "x.parent() is not y.parent()" --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
