Hi Burcin,
Many thanks for theses details about sage. I try to understand what you prefer, and why. > The main reason I left this simplification "exp(a)^2 to exp(2*a)" while > fixing #6948 was that MMA does things this way. All right : MMA is good. > Another consideration was that before performing any nontrivial operation on > symbolic expressions (integration, > transforms, etc.), we would have to perform some normalization, and this > seemed like a normal form as it is. It's often true, but on the other hand I'm quite sure the main Risch algorithm for integration looks at independant algebraic functions and transforms exp(2x) and exp(3x) to y^2 and y^3 with y=exp(x) : the opposite transform. This almost canonical transform can also be the first call in sum, diffenrentiate, and so. (I'm not sure about integrate). An other point : I see that sage is very lazy over expressions : (1+1/x) / (2+1/x) remains. So I don't find very logically consistent to be hurry with exp(a)^2 and to be lazy with fractions. With rational expressions the single functions expand and factor transform (a-b)*(a+b) and a^2-b^2, and sage remains both expressions in their input forms. And I look at exp by analogies. Thanks a lot for your workaround for tests, but I expect an easiest way for students. As a workaround, you can do the following to replace exp(x) with y in the example above: sage: t = exp(2*x)/(exp(3*x)+1) sage: w = SR.wild() sage: match_list = t.find(exp(w*x)); match_list ... The way with hold(exp(a))^5 expressions is less symetric in the mind but lets also possible a lot of computations in both way. An expand(exp(2*a)) may return hold(exp(a))^2 even if the next eval go back to exp(2*a). > If you think it'll help, I can probably prepare a pynac package that > disables the automatic simplification of exp powers. I don't have time > to submit that to Sage (say, as an alternative solution to #6948), but > it's not hard to do this for experimental purposes. > Your offer is superb and I keep it in my mind. But I'll continue to play with the standard sage, and learn it. Even if I feel we should come back to this point later. 3 more practice questions. 1/ I see you have already patched the exp(a)^b problem. I use sage-4.1.1 and run sage -upgrade, but I don't get any update. Of corse I can wait the next sage, but is there a way to get a new-and-unstable sage ? 2/ expand(x^(a+b)) = x^a * x^b but expand(x^(2*a)) remains x^(2*a). I dislike (expand(x^(a+b)).subs(b=a). The + morphism transform implies the Integer*a and the -a related properties. 3/ How in sage can I test if a sub-expression I get with expr.operands()[0 or 1 or 2] is a integer, a single variable, a real expression in its tree. Many thanks for your patience with me. Francois --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
