Affine diagram

For a rank-3 matroid we draw its affine diagram. The elements, numbered $1,\dots,n$, are points in the plane, and each nontrivial line (a rank-2 flat with at least 3 points) is drawn through its points.

• If the realization space is free (ideal $(0)$), we substitute small random integers for the variables until every inequation is nonzero, evaluate the realization matrix, and plot its columns in an affine chart. The result is an actual realization over $\mathbb R$, marked "(real realization)", and every line is straight.
• Otherwise we search for positions of the points that make as many lines as possible straight, while keeping points apart and keeping any three points that are not on a common line visibly non-collinear. A line that cannot be made straight is drawn as a circular arc (three points) or a smooth curve (more points) through its points, as in the usual pictures of the Fano plane. Such a diagram shows the incidences only, not a realization: the matroid may have no real realization at all, or one that the search did not find.

Parallel elements are drawn as one point labeled with all their numbers (e.g. "1,2"). Loops are not drawn; they are listed below the diagram.