Let f be a polynomial in x and y giving an algebraic curve in the plane C^2 with a singularity at the point . The output of this procedure is called the singularity knot of this singularity. This knot is defined as follows: By identifying C^2 with R^4 the curve can be viewed as a two-dimensional surface over the real numbers. This procedure computes the intersection of this surface with a sphere in R^4 with radius epsilon and center 0. The intersection consists of a number of closed curves over the real numbers. After applying a projection from the sphere (which is three-dimensional over R) to R^3 these curves can be plotted by the tubeplot command in the plots package. Such a plot gives information about the singularity of f at the point 0. See also: E. Brieskorn, H. Knörrer: Ebene Algebraische Kurven, Birkhauser 1981.

The curve given by f need not be irreducible, but f must be square-free otherwise this procedure does not work.

If printlevel > 1 the number of branches will be printed to the screen. Each branch (i.e. place above the point 0) corresponds to one component in the knot.

epsilon=value -- the radius of the sphere. The default is 1. In some cases a smaller number must be chosen for the picture to be correct.

color=list -- specifying a list of colors results in a plot where each branch gets its own color.

The options for tubeplot can be used as well. In plot_knot these options have the following default values: numpoints=150, radius=0.05, tubepoints=5, scaling=constrained, and style=surface.