Subject: How to plot a projective variety in Maxima?
From: Jaime Villate
Date: Fri, 12 Apr 2013 13:14:01 +0100
On 04/12/2013 04:07 AM, Jianrong Li wrote:
>
> I am trying to plot the projective variety defined by the homogeneous
> polynomials xz-y^2 = 0, yw-z^2 = 0, xw-yz = 0. I am trying to use
> implicit_plot function in Maxima. But it is not successful. How could
> I plot this variety? Thank you very much.
>
Perhaps this can be useful?:
(%i1) display2d: false$
(%i2) eq1: x*z-y^2$
(%i3) eq2: y*w-z^2$
(%i4) eq3: x*w-y*z$
(%i5) system: eliminate([eq1,eq2,eq3],[w]);
(%o5) [z*(x*z-y^2),x*z-y^2]
(%i6) answ: map(lambda([e],solve(e,z)),%);
(%o6) [[z = y^2/x,z = 0],[z = y^2/x]]
(%i7) ploteq (rhs(%[1][1]));
An you can then click in a few points and use the "save" icon when you
are happy with the result.
In to make ploteq work, you need to have xmaxima installed (see
http://maxima.sourceforge.net/docs/manual/en/maxima_22.html#SEC111)
Regards,
Jaime