Enumerative Geometry

A p-plane 

in $\mbox{$C \! \! \! \rule[0.1ex]{0.05em}{1.25ex} \;$}\,^{m+p}$ is represented by an (m+p)-by-p matrix that has in its columns the generators of this plane. For numerical stability, we better apply the QR-algorithm to generate an orthogonal representation.

A localization pattern 

is used to specify the position of the zeros in the representation of a p-plane.