‣ IsFan( M ) | ( category ) |
Returns: true or false
The GAP category of a fan. Every fan is a convex object.
Remember: Every fan is a convex object.
‣ IsComplete( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is complete, i. e. if it's support is the whole space.
‣ IsPointed( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is pointed, which means that every cone it contains is strictly convex.
‣ IsSmooth( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is smooth, i. e. if every cone in the fan is smooth.
‣ IsRegularFan( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is regular, i. e. if it is the normal fan of a polytope.
‣ IsSimplicial( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is simplicial, i. e. if every cone in the fan is simplicial.
‣ HasConvexSupport( fan ) | ( property ) |
Returns: true or false
Checks if the fan fan is simplicial, i. e. if every cone in the fan is simplicial.
‣ Rays( fan ) | ( attribute ) |
Returns: a list
Returns the rays of the fan fan as a list of cones.
‣ RayGenerators( fan ) | ( attribute ) |
Returns: a list
Returns the generators rays of the fan fan as a list of of list of integers.
‣ RaysInMaximalCones( fan ) | ( attribute ) |
Returns: a list
Returns a list of lists, which represent an incidence matrix for the correspondence of the rays and the maximal cones of the fan fan. The ith list in the result represents the ith maximal cone of fan. In such a list, the jth entry is 1 if the jth ray is in the cone, 0 otherwise.
‣ MaximalCones( fan ) | ( attribute ) |
Returns: a list
Returns the maximal cones of the fan fan as a list of cones.
‣ *( fan1, fan2 ) | ( operation ) |
Returns: a fan
Returns the product of the fans fan1 and fan2.
‣ Fan( fan ) | ( operation ) |
Returns: a fan
Copy constructor for fans. For completeness reasons.
‣ Fan( rays, cones ) | ( operation ) |
Returns: a fan
Constructs the fan out of the given rays and a list of cones given by a lists of numbers of rays.
gap> F := Fan( [[-1,5],[0,1],[1,0],[0,-1]],[[1,2],[2,3],[3,4],[4,1]] ); <A fan in |R^2> gap> RayGenerators( F ); [ [ -1, 5 ], [ 0, 1 ], [ 1, 0 ], [ 0, -1 ] ] gap> RaysInMaximalCones( F ); [ [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 0, 0, 1 ] ] gap> IsRegularFan( F ); true gap> IsComplete( F ); true gap> IsSmooth( F ); true gap> F1 := MaximalCones( F )[ 1 ]; <A cone in |R^2> gap> DualCone( F1 ); <A cone in |R^2> gap> RayGenerators( F1 ); [ [ -1, 5 ], [ 0, 1 ] ] gap> F2 := StarSubdivisionOfIthMaximalCone( F, 1 ); <A fan in |R^2> gap> IsSmooth( F2 ); true gap> RayGenerators( F2 ); [ [ -1, 5 ], [ -1, 6 ], [ 0, -1 ], [ 0, 1 ], [ 1, 0 ] ]
generated by GAPDoc2HTML