On Mar 1, 3:02 am, Alex Ghitza <aghi...@gmail.com> wrote: > On Sun, 28 Feb 2010 23:02:08 -0800 (PST), Sharpie <ch...@sharpsteen.net> > wrote: > > However, tonight I have been trying to solve an open channel flow > > problem which requires me to find the roots of: > > > y^3 - 1.39027132807289 * y^2 + 0.090610488164005 == 0 > > > find_root() does return the correct answers-- but in this case both > > positive roots are of interest so it would be nice to recover them > > both at the same time. > > Hi, > > How about this: > > sage: R.<y> = RR[] > sage: f = y^3 - 1.39027132807289 * y^2 + 0.090610488164005 > sage: f.roots() > [(-0.236040904804615, 1), (0.286518993973450, 1), (1.33979323890405, 1)] > > Is this what you were hoping for? > > Best, > Alex > > -- > Alex Ghitza --http://aghitza.org/ > Lecturer in Mathematics -- The University of Melbourne -- Australia
Thanks for the reply Alex. I think I understand that by choosing a variable of the appropriate type, in this case one that is restricted to the real numbers, the roots can be determined in a straight-forward manner. I had some more problems, but finally figured out how to coerce a expression of type symbolic to the real ring through a somewhat convoluted application of multiplication, full_simplify() and polynomial(). The cubic is the result of balancing a system of conservation equations and then substituting in known information: y2 = var( 'y2' ) f = 1.54027132807289 == y2 + 0.0906104881640050/y2^2 + 0.150000000000000 # Multiply to eliminate fractions. f = f * y2^2 f.full_simplify().polynomial(RR).roots() [(-0.236040904804615, 1), (0.286518993973450, 1), (1.33979323890405, 1)] That gives the correct answer-- but it seems pretty darn inelegant, distracted and burdensome to explain when presented in a homework report. I experimented with the "domain=" argument to var() to see if it could help, but I didn't notice any changes. If someone could suggest a way the above code could be cleaned up, I would be very grateful! -Charlie -- 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 URL: http://www.sagemath.org
