On 03/14/2009 02:26 AM, Robert Bradshaw wrote: > On Mar 13, 2009, at 1:09 PM, John Cremona wrote: > >> 2009/3/13 Ralf Hemmecke <r...@hemmecke.de>: >> >>> Is there a function in Sage that really behaves like mathematical >>> equality? >> If you think about it, this would be rather hard to implement in >> general, in terms of complexity at least. > > Indeed, it is hard to nail down what one means by equality. For > example, is R[x] equal to R[y]. What about the commutative rings R > [x,y] and R[y,x]. What about sparse R[x] vs. dense R[x]. Do you > consider all vector spaces over K of the same dimension equal, or do > they have to have a specified basis? Nailing down questions like > these is unclear.
As I said, different type/parent must lead to a==b returning false. If you implement R[x] different from R[y] then no element from R[x] can be equal to an element from R[y]. If you implement R[x] and R[y] as just finite sequences over R then there is only one type and elements compare as the would as finite sequences. Now whether u==v for u\in R[x] and v\in R[y] returns true or false must clearly be written in the specification of the domain R[.]. Ralf --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
