Begin forwarded message: > From: Andrzej Chrzęszczyk <[EMAIL PROTECTED]> > Date: March 5, 2008 6:23:53 PM EST > To: [EMAIL PROTECTED] > Subject: sage-devel "exact" numerical integration > > Dear David > Try > > sage: maxima_console() > (%i1) integrate(%e^(-x^2),x,0,0.1); > ................................... > `rat' replaced .05623145800914245 by 2066/36741 = .05623145804414686 > 2066 sqrt(%pi) > (%o1) -------------- > 36741 > > then you will see that (behind the scene) > maxima replaces more accurate result .05623145804414686 sqrt(%pi) > by the less accurate one: 2066 sqrt(%pi)/36741 (default maxima > behaviour) > > Your exact calculations are OK but why do you mix the exact-inexact. > Pure numerical version using GSL: > > sage: numerical_integral(lambda x:e^(-x^2),0,-.1) > (-0.099667664290336327, 1.1065333570574191e-15) > > is in a good accordance with your exact calculations > > Andrzej Chrzeszczyk > > (I'm not in sage-devel so I'm using your e-mail adress, > I hope You will excuse me)
Okay, I can see this makes sense from within Maxima, since you get to see the "replacement" message. But in Sage, it's really terrible! When I do sage: f = e^(-x^2) sage: f.integral(x, 0, 0.1) 2066*sqrt(pi)/36741 I have absolutely no idea what is going on in the background. It could be maxima, or sympy, or some other library that someone plugged in, or who knows what. How am I supposed to tell that 2066*sqrt(pi)/36741 is not an exact answer? Since it contains sqrt(pi), it's very suggestive that it's supposed to be exact. Another example: if I do sage: f = x*e^(2*x) sage: f.integral(x, 0, 1) e^2/4 + 1/4 Is that an exact answer? Or it just "close enough" to e^2/4? What use is the answer if I can't tell? david --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
