On 11/11/2008 11:38 AM, Martin Rubey wrote: > Robert Bradshaw <[EMAIL PROTECTED]> writes: > >> In Sage, we use the term "coercion" to denote a canonical (using the >> term a bit loosely), implicit map between Parents (or objects of a >> concrete category). E.g. from ZZ to F5 would be a "coercion," but >> there is a "conversion" and not a "coercion" the other direction. >> Coercions are invoked to do arithmetic, but conversions are not.
> Just for the record, this is *exactly* the same definition as in FriCAS. Exactly. > (in case you wonder, the notation "Object::SomeType" is syntactic sugar for > "coerce(Object)@SomeType", where @ is a language builtin, that selects the > function according to return type. And, as Robert kindly explained (thank you), it is written "SomeType(Object)" in Sage. The only difference between Sage and Aldor/panAxiom is that Sage checks whether the Object can be coerced to SomeType at runtime whereas Aldor and SPAD allow to check at compile time. And I don't say that "some string"::Integer is impossible to succeed, it is only a question whether the compiler sees (has in scope) a function coerce: String->Integer that would do the job... of course at compile time. (By the way, if one defines this coerce to be the length of the string and takes + as the concatenation of strings then this coerce is even a homomorphism from the String monoid into the integers considered as an additive monoid.) Ralf --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
