On Mon, Oct 27, 2008 at 7:48 AM, Martin Rubey <[EMAIL PROTECTED]> wrote: > > How come that solve doesn't solve this? > > sage: solve(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x) > [x == -sqrt(sqrt(4*x^2 + 1) - 1), x == sqrt(sqrt(4*x^2 + 1) - 1)] > > sage: axiom.solve(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x) > > +-+ +-+ > [x= 0,x= \|2 ,x= - \|2 ]
Sage's solve command is simply a light wrapper around Maxima's, and Maxima doesn't solve the above: ------------------ teragon:Desktop wstein$ sage -maxima Maxima 5.16.3 http://maxima.sourceforge.net Using Lisp CLISP 2.46 (2008-07-02) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) solve(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x); 2 2 (%o1) [x = - sqrt(sqrt(4 x + 1) - 1), x = sqrt(sqrt(4 x + 1) - 1)] ------------------ In the long run in Sage some of us will likely have to write a new solve command from scratch, which is much more sophisticated than Maxima's, and will certainly benefit from knowledge about what's in Fricas. > Furthermore, is there a way to convince integrate to do > > sage: integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x,0,sqrt(2)) > integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x, 0, sqrt(2)) > > sage: axiom.integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), "x=0..sqrt(2)", > '"noPole"') > > 1 > - > 2 Exactly the same answer as to your previous question. > a third question: how do I get a power series expansion of, say, x^(1/3)? > > sage: axiom.series(sin(x)^(1/3),x=0) > > 1 7 > - - > 3 1 3 4 > x - -- x + O(x ) > 18 > > > (I know how to do it with FriCAS, but I'd like to know how I can show my > students how to do these things with sage. Actually, sage-3.1.2, that is > what's installed.) Is this what you want? sage: (sin(x)^(1/3)).taylor(x,0,10) x^(1/3) - x^(7/3)/18 - x^(13/3)/3240 - 53*x^(19/3)/1224720 - 191*x^(25/3)/62985600 -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
