Regina Calculation Engine
|
A class that constraints the tableaux of normal surface matching equations to ensure that Euler characteristic is strictly positive. More...
#include <enumerate/ntreeconstraint.h>
Classes | |
struct | Coefficients |
Stores the extra coefficients in the tableaux associated with this constraint class (in this case, one extra integer per column). More... | |
Public Types | |
enum | { nConstraints = 1 } |
enum | { nConstraints } |
Static Public Member Functions | |
static bool | addRows (LPInitialTableaux< regina::LPConstraintEuler >::Col *col, const int *columnPerm, const NTriangulation *tri) |
template<typename Integer > | |
static void | constrain (LPData< regina::LPConstraintEuler, Integer > &lp, unsigned numCols) |
static bool | verify (const NNormalSurface *s) |
static bool | verify (const NAngleStructure *) |
static bool | supported (NormalCoords coords) |
static bool | addRows (LPInitialTableaux< LPConstraintBase >::Col *col, const int *columnPerm, const NTriangulation *tri) |
Explicitly constructs equations for the linear function(s) constrained by this class. More... | |
template<typename Integer > | |
static void | constrain (LPData< LPConstraintNone, Integer > &lp, unsigned numCols) |
Explicitly constraints each of these linear functions to an equality or inequality in the underlying tableaux. More... | |
A class that constraints the tableaux of normal surface matching equations to ensure that Euler characteristic is strictly positive.
There are many ways of writing Euler characteritic as a linear function. The function constructed here has integer coefficients, but otherwise has no special properties of note.
This constraint can work with either normal or almost normal coordinates. In the case of almost normal coordinates, the function is modified to measure Euler characteristic minus the number of octagons (a technique of Casson, also employed by Jaco and Rubinstein, that is used to ensure we do not have more than two octagons when searching for a normal or almost normal sphere in the 3-sphere recognition algorithm).
See the LPConstraintBase class notes for details on all member functions and structs.