On Apr 2, 2008, at 7:35 AM, Michel wrote: > > Hi, > > A short remark. It seems that taking the derivative of an element of a > fraction field is not supported at this point. This feels somewhat > inconsistent (tested with sage 2.10.4) > > sage: R=QQ['x'] > sage: x=R.gen() > sage: derivative(x^2,x) > 2*x > sage: derivative(1/x,x) > ---------------------------------------------------------------------- > ----- > <type 'exceptions.TypeError'> Traceback (most recent call > last) > <snip>
Looks like this was recently fixed: SAGE Version 2.11, Release Date: 2008-03-30 sage: R=QQ['x'] sage: x=R.gen() sage: derivative(1/x,x)-1/x^2 > More fundamentally, I wonder if it makes sense to define the general > concept of a derivation. > Derivations are given by their values on generators so they fit well > in the sage framework. > The advantage of having abstract derivations would be that one could > add them, take their > commutatior etc.... Yes. David Roe and I were talking about this the other day (in another context). It essentially boils down to the ability to do element -> [some abstract representation in terms of generators] -> [modified representation in terms of generators] -> element. We were talking about this in terms of morphisms, so the parents of the elements on the two sides may not be the same, and the representation needs to be in a form they both understand (e.g. based on the category) For algebras and rings, the representation would probably be a tree of binary operations, with leaf nodes being generators and elements of the base ring. Doing something more general requires more thought. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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 -~----------~----~----~----~------~----~------~--~---
