Hi Dave: Once you have your zero-dimensional ideal K within a Sage ring, you could try the variety() command
K.variety(ring=QQbar) or K.variety(ring=CC) to get its solutions as algebraic numbers or complex floating point numbers, respectively. See 'variety()' under http://www.sagemath.org/doc/ref/module-sage.rings.polynomial.multi-polynomial-ideal.html for more details. Problem is, variety() sometimes fails: http://sagetrac.org/sage_trac/ticket/4622 . Alex On Feb 25, 7:27 am, davidp <dav...@reed.edu> wrote: > Hi, > > I have the following homogeneous Singular ideal defining a finite set > of points in projective space. I would like to get numerical > approximations for these points. > > sage: S.ring() > > // characteristic : 0 > // number of vars : 4 > // block 1 : ordering dp > // : names x_3 x_2 x_1 x_0 > // block 2 : ordering C > sage: S.ideal() > > x_1^3-x_3*x_2*x_0, > x_3*x_2*x_1-x_0^3, > x_2^3-x_3*x_1*x_0, > x_3^3-x_2*x_1*x_0, > x_2^2*x_1^2-x_3^2*x_0^2, > x_3^2*x_1^2-x_2^2*x_0^2, > x_3^2*x_2^2-x_1^2*x_0^2 > sage: type(S.ideal()) > <class 'sage.interfaces.singular.SingularElement'> > > One way to go might be to map to a new ring, setting x_0 = 1, then use > the nice Singular algorithm for finding the solutions: > > http://www.singular.uni-kl.de/Manual/3-0-4/sing_582.htm > > I couldn't figure out how to get the Singular "map" function to work > with Sage, so I just converted equations using string commands (saved > in "y" in the following code) then tried: > > sage: R = singular.ring(0,'(x_3,x_2,x_1)','lp') > sage: J = singular.ideal(y) > sage: J > > -x_3*x_2+x_1^3, > x_3*x_2*x_1-1, > -x_3*x_1+x_2^3, > x_3^3-x_2*x_1, > -x_3^2+x_2^2*x_1^2, > x_3^2*x_1^2-x_2^2, > x_3^2*x_2^2-x_1^2 > sage: K = J.groebner() > sage: M = K.solve(10,1) > > I'm not sure where to go from there. Of course, I might be taking the > wrong approach altogether. > > Any advice would be appreciated. > > Thanks, > Dave --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
