There are many cases where you would *WANT* to coerce between polynomial rings with different orderings, think:
*Q1[x,y] with grevlex for heavy duty computations *Q2[x,y] wih elimination order for y to project on the x-line *Q3[x,y] with elimination order for x to project on the y-line (of course this only becomes important for higher dimensions) You would be going back and forth between these rings all the time and conceptually they would be representing the same ring for you - just equipped with other algorithmic properties. Hence, in that situation it would not be entirely undesirable to be able to coerce back and forth between Q1, Q2, Q3 and the match-up should prefer the corresponding names rather than the relative ordering (as far as that even can be done). Bases on that, I would say automatic coercion between polynomial rings should be allowed if the names of the variables (which are unalterable) can be matched up. Of course that would encourage people to make the names of variables in polynomial rings indistinguishable, which is not good, because it then becomes harder to recognise the parent from an element representation. I would actually be happy with virtually no automatic coercions between polynomial rings. For any set of rules I think you will be able to come up with an example where the system will do something the user did *not* intend. Requiring the user to be explicit by means of a homomorphism might avoid confusion. --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
