‣ IsPolytope( M ) | ( category ) |
Returns: true or false
The GAP category of a polytope. Every polytope is a convex object.
Remember: Every cone is a convex object.
‣ IsNotEmpty( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is not empty.
‣ IsLatticePolytope( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is a lattice polytope, i.e. all its vertices are lattice points.
‣ IsVeryAmple( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is very ample.
‣ IsNormalPolytope( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is normal.
‣ IsSimplicial( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is simplicial.
‣ IsSimplePolytope( poly ) | ( property ) |
Returns: true or false
Checks if the polytope poly is simple.
‣ Vertices( poly ) | ( attribute ) |
Returns: a list
Returns the vertices of the polytope poly. For reasons, the corresponding tester is HasVerticesOfPolytopes
‣ LatticePoints( poly ) | ( attribute ) |
Returns: a list
Returns the lattice points of the polytope poly.
‣ FacetInequalities( poly ) | ( attribute ) |
Returns: a list
Returns the facet inequalities for the polytope poly.
‣ VerticesInFacets( poly ) | ( attribute ) |
Returns: a list
Returns the incidence matrix of vertices and facets of the polytope poly.
‣ AffineCone( poly ) | ( attribute ) |
Returns: a cone
Returns the affine cone of the polytope poly.
‣ NormalFan( poly ) | ( attribute ) |
Returns: a fan
Returns the normal fan of the polytope poly.
‣ RelativeInteriorLatticePoints( poly ) | ( attribute ) |
Returns: a list
Returns the lattice points in the relative interior of the polytope poly.
‣ *( polytope1, polytope2 ) | ( operation ) |
Returns: a polytope
Returns the Cartesian product of the polytopes polytope1 and polytope2.
‣ #( polytope1, polytope2 ) | ( operation ) |
Returns: a polytope
Returns the Minkowski sum of the polytopes polytope1 and polytope2.
‣ Polytope( points ) | ( operation ) |
Returns: a polytope
Returns a polytope that is the convex hull of the points points.
‣ PolytopeByInequalities( ineqs ) | ( operation ) |
Returns: a polytope
Returns a polytope defined by the inequalities ineqs.
gap> P := Polytope( [ [ 2, 0 ], [ 0, 2 ], [ -1, -1 ] ] ); <A polytope in |R^2> gap> IsVeryAmple( P ); true gap> LatticePoints( P ); [ [ -1, -1 ], [ 0, 0 ], [ 0, 1 ], [ 0, 2 ], [ 1, 0 ], [ 1, 1 ], [ 2, 0 ] ] gap> NFP := NormalFan( P ); <A complete fan in |R^2> gap> C1 := MaximalCones( NFP )[ 1 ]; <A cone in |R^2> gap> RayGenerators( C1 ); [ [ -1, -1 ], [ -1, 3 ] ] gap> IsRegularFan( NFP ); true
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