Regina Calculation Engine
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A comparison object that sorts hyperplanes by position vectors. More...
#include <enumerate/ordering.h>
Public Member Functions | |
PosOrder (const MatrixInt &matrix) | |
Creates a new helper object for comparing hyperplanes. More... | |
PosOrder (const PosOrder &)=default | |
Creates a clone of the given helper objet. More... | |
bool | operator() (long i, long j) const |
Determines whether the hyperplane described by row i of the matrix is smaller than the hyperplane described by row j. More... | |
PosOrder & | operator= (const PosOrder &)=delete |
A comparison object that sorts hyperplanes by position vectors.
This ordering is described in "Optimizing the double description method for normal surface enumeration", B.A. Burton, Mathematics of Computation 79 (2010), 453-484.
This comparison object is used to sort hyperplanes into a good order before enumerating vertex or fundamental normal surfaces A hyperplane is described by a row of the subspace matrix, as passed to an enumeration routine such as DoubleDescription::enumerateExtremalRays() or HilbertDual::enumerateHilbertBasis().
The ordering is defined as follows. For each hyperplane, we create a position vector (h_1, ..., h_f), where h_i is 0 if the hyperplane contains the ith coordinate axis, or 1 if not. We then compare these position vectors lexicographically.