‣ IsCone( M ) | ( category ) |
Returns: true or false
The GAP category of a cone.
Remember: Every cone is a convex object.
‣ IsRay( cone ) | ( property ) |
Returns: true or false
Checks if the cone cone is a ray, i.e. if it has only one ray generator.
‣ DualCone( cone ) | ( attribute ) |
Returns: a cone
Returns the dual cone of the cone cone.
‣ HilbertBasis( cone ) | ( attribute ) |
Returns: a list
Returns a Hilbert Basis of the cone cone.
‣ RaysInFacets( cone ) | ( attribute ) |
Returns: a list
Returns an incidence matrix for the rays in the facets of the cone cone. The ith entry of the result corresponds to the ith facet, the jth entry of this is 1 if the jth ray is in th ith facet, 0 otherwise.
‣ Facets( cone ) | ( attribute ) |
Returns: a list
Returns a list of the facets of the cone cone as homalg cones.
‣ GridGeneratedByCone( cone ) | ( attribute ) |
Returns: a homalg module
Returns the grid generated by the lattice points of the cone cone as a homalg module.
‣ FactorGrid( cone ) | ( attribute ) |
Returns: a homalg module
Returns the factor of the containing grid of the cone cone and the grid generated by cone.
‣ GridGeneratedByOrthogonalCone( cone ) | ( attribute ) |
Returns: a homalg module
Returns the grid generated by the lattice points of the orthogonal cone of the cone cone.
‣ DefiningInequalities( cone ) | ( attribute ) |
Returns: a list
Returns a list of the defining inequalities of the cone cone.
‣ IsContainedInFan( cone ) | ( attribute ) |
Returns: a fan
If the cone cone is constructed as part of a fan, this method returns the fan.
‣ FactorGridMorphism( cone ) | ( attribute ) |
Returns: a morphism
Returns the morphism to the factor grid of the cone cone.
‣ IntersectionOfCones( cone1, cone2 ) | ( operation ) |
Returns: a cone
If the cones cone1 and cone2 share a face, the method returns their intersection,
‣ Contains( cone1, cone2 ) | ( operation ) |
Returns: true or false
Returns true if the cone cone1 contains the cone cone2, false otherwise.
‣ StarFan( cone ) | ( operation ) |
Returns: a fan
Returns the star fan of the cone cone, as described in cox, 3.2.7
‣ StarFan( cone, fan ) | ( operation ) |
Returns: a fan
Returns the star fan of the fan fan along the cone cone, as described in cox, 3.2.7
‣ StarSubdivisionOfIthMaximalCone( fan, numb ) | ( operation ) |
Returns: a fan
Returns the star subdivision of the fan fan on the numbth maximal cone as in cox, 3.3.13.
‣ Cone( cone ) | ( operation ) |
Returns: a cone
Returns a cone generated by the rays in cone.
gap> C := Cone([[1,2,3],[2,1,1],[1,0,0],[0,1,1]]); <A cone in |R^3> gap> Length( RayGenerators( C ) ); 3 gap> IsSmooth( C ); true gap> Length( HilbertBasis( C ) ); 3 gap> IsSimplicial( C ); true gap> DC := DualCone( C ); <A cone in |R^3> gap> Length( HilbertBasis( DC ) ); 3
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