Algebraic curves in TikZ or Asymptote

Question

I want to draw algebraic curves in asymptote, but I do not know how this works. Has anyone an example?

If we want to plot for example k[x,y]/\langle x^2+y^2-1\rangle, where can I input the equation x^2-y^2-1=0? Here it is obvious that it is just a circle, but if we have several equations, this will not be so easy. Is there any command for this?

Thanks a lot for any help.

Welcome to TeX.SX! Did you try to search this site for examples? E.g., http://tex.stackexchange.com/questions/33607/easy-curves-in-tikz might be a good starting point. If things like that do not solve your problem, you should post a minimal working example (MWE) to illustrate where you are having problems exactly. This will raise your chances of getting suitable help significantly. — cryingshadow, Dec 27 '15 at 14:50
This might even be more suitable for your needs: http://tex.stackexchange.com/questions/105570/how-to-plot-functions-like-x-fy-using-tikz — cryingshadow, Dec 27 '15 at 14:52
See also Plot Tikz graph defined with two variables, ie 4=x^2+y^2 — Torbjørn T., Dec 27 '15 at 20:20
Please clarify what you mean by "several equations." If you are looking at algebraic curves in k^2, then every curve is a hypersurface and thus can be defined by a single equation. — Charles Staats, Dec 31 '15 at 17:19

score 6 · Answer 1 · edited Jan 02 '16 at 02:47

Perhaps information on Asymptote with the contour module are on Stackexchange. Indeed Asymptote provides the contour module (also the excellent smoothcontour3 module for implicitly defined 3D surfaces). For the question please consider the basic example

import contour;
import graph;
size(10cm);
real f(real x , real y)
{
  return x**3+y**3-3*x*y;
}
real [] c={-.5 , 0., .5}; // c should be an array
draw(contour(f,(-2,-2),(2,2),c));
xaxis("$x$",LeftTicks);
yaxis("$y$",RightTicks(trailingzero));

and the result

Other examples are available in the Asymptote documentation, with color, labels, or different pen...

O.G.

Algebraic curves in TikZ or Asymptote

1 Answers1