That works.
Thanks!
Dave
On Feb 26, 5:31 pm, Alex Raichev <tortoise.s...@gmail.com> wrote:
> Hi Dave:
>
> I'm also just learning the basics of interacting with Singular through
> Sage. So probably someone else on the list can answer your question
> better than me. Still, i'll take a stab at it.
>
> Carrying on with your/Singular's notation, try
>
> sage: singular.setring(AC)
> sage: sol= singular('SOL').sage_structured_str_list()
>
> to save the output of SOL as a structured list of Sage strings. (I
> found this command by typing help(sage.interfaces.singular) and
> browsing the documentation page that popped up.) Now all you have to
> do is convert those Sage strings to Sage numbers with the eval()
> command. For instance,
>
> sage: a= eval(sol[1][1][1][1])
>
> Does that work?
>
> Alex
>
> P.S. I'll be jumping for joy if/when the Singular people fix the bug
> that's breaking the potentially super-useful variety() command.
>
> On Feb 27, 5:54 am,davidp<dav...@reed.edu> wrote:
>
> > Thanks for your response. I tried what you suggested and got the
> > error you anticipated. So it looks like I need to work within
> > Singular. The relevant page at the Singular site:
>
> >http://www.singular.uni-kl.de/Manual/latest/sing_1168.htm#SEC1227
>
> > Using the notation from the site just referenced, I end up with a
> > ring, AC, in which the solutions are supposed to be stored in 'SOL'.
> > I can execute singular.setring(AC), but cannot subsequently access the
> > solutions.
>
> > Thanks,
> > Dave
>
> > On Feb 25, 1:49 pm, Alex Raichev <tortoise.s...@gmail.com> wrote:
>
> > > 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-po...
>
> > > 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
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