Jason Grout wrote: > David Harvey wrote: >> Begin forwarded message: >> >>> *From: *Andrzej Chrzęszczyk <[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>> >>> *Date: *March 5, 2008 6:23:53 PM EST >>> *To: [EMAIL PROTECTED] <mailto:[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) >>> > > > According to http://www.ma.utexas.edu/maxima/maxima_11.html > > Function: RAT (exp, v1, ..., vn) > converts exp to CRE form by expanding and combining all terms over > a common denominator and cancelling out the greatest common divisor of > the numerator and denominator as well as converting floating point > numbers to rational numbers within a tolerance of RATEPSILON[2.0E-8]. > > and > > KEEPFLOAT[FALSE] if TRUE prevents floating point numbers from being > converted to rational numbers. > > > Maybe we should set the keepfloat thing or set ratepsilon to a much > smaller value?
Examples: sage: maxima_console() Maxima 5.13.0 http://maxima.sourceforge.net Using Lisp CLISP 2.41 (2006-10-13) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) keepfloat: true; (%o1) true (%i2) integrate(%e^(-x^2),x,0,0.1); (%o2) .05623145800914245 sqrt(%pi) (%i3) keepfloat: false; (%o3) false (%i4) ratepsilon: 1e-20; (%o4) 9.999999999999999E-21 (%i5) integrate(%e^(-x^2),x,0,0.1); `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced 0.1 by 1/10 = 0.1 `rat' replaced .05623145800914245 by 244715115/4351925482 = .05623145800914245 244715115 sqrt(%pi) (%o5) ------------------- 4351925482 Jason --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
