On Mar 13, 2009, at 6:54 PM, Ralf Hemmecke wrote: > 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[.].
I was going a bit off topic here and talking about comparing the actual Parents R[x,y] and R[y,x], etc. not their elements, because here the notion of == becomes much more murky. - Robert --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
