‣ Cdd_Canonicalize( P ) | ( attribute ) |
Returns: a CddPolyhedron
The function takes a polyhedron and reduces its defining inequalities (generators set) by deleting all redundant inequalities (generators).
gap> A:= Cdd_PolyhedronByInequalities( [ [ 0, 2, 6 ], [ 0, 1, 3 ], [1, 4, 10 ] ] ); <Polyhedron given by its H-representation> gap> B:= Cdd_Canonicalize( A ); <Polyhedron given by its H-representation> gap> Display( B ); H-representation begin 2 X 3 rational 0 1 3 1 4 10 end
‣ Cdd_V_Rep( P ) | ( attribute ) |
Returns: a CddPolyhedron
The function takes a polyhedron and returns its reduced \(V\)-representation.
‣ Cdd_H_Rep( P ) | ( attribute ) |
Returns: a CddPolyhedron
The function takes a polyhedron and returns its reduced \(H\)-representation.
gap> A:= Cdd_PolyhedronByInequalities( [ [ 0, 1, 1 ], [ 0, 5, 5 ] ] ); <Polyhedron given by its H-representation> gap> B:= Cdd_V_Rep( A ); <Polyhedron given by its V-representation> gap> Display( B ); V-representation linearity 1, [ 2 ] begin 2 X 3 rational 0 1 0 0 -1 1 end gap> C:= Cdd_H_Rep( B ); <Polyhedron given by its H-representation> gap> Display( C ); H-representation begin 1 X 3 rational 0 1 1 end gap> D:= Cdd_PolyhedronByInequalities( [ [ 0, 1, 1, 34, 22, 43 ], > [ 11, 2, 2, 54, 53, 221 ], [33, 23, 45, 2, 40, 11 ] ] ); <Polyhedron given by its H-representation> gap> Cdd_V_Rep( D ); <Polyhedron given by its V-representation> gap> Display( last ); V-representation linearity 2, [ 5, 6 ] begin 6 X 6 rational 1 -743/14 369/14 11/14 0 0 0 -1213 619 22 0 0 0 -1 1 0 0 0 0 764 -390 -11 0 0 0 -13526 6772 99 154 0 0 -116608 59496 1485 0 154 end
‣ Cdd_AmbientSpaceDimension( P ) | ( attribute ) |
Returns: The dimension of the ambient space of the polyhedron(i.e., the space that contains \(P\)).
‣ Cdd_Dimension( P ) | ( attribute ) |
Returns: The dimension of the polyhedron, where the dimension, \(\mathrm{dim}(P)\), of a polyhedron \(P\) is the maximum number of affinely independent points in \(P\) minus 1.
‣ Cdd_GeneratingVertices( P ) | ( attribute ) |
Returns: The reduced generating vertices of the polyhedron
‣ Cdd_GeneratingRays( P ) | ( attribute ) |
Returns: list
The output is the reduced generating rays of the polyhedron
‣ Cdd_Equalities( P ) | ( attribute ) |
Returns: a list
The output is the reduced equalities of the polyhedron.
‣ Cdd_Inequalities( P ) | ( attribute ) |
The output is the reduced inequalities of the polyhedron.
‣ Cdd_InteriorPoint( P ) | ( attribute ) |
Returns: a list
The output is an interior point in the polyhedron
‣ Cdd_Faces( P ) | ( attribute ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and returns a list. Every entry in this list is a again a list, contains the dimension and linearity of the face defined as a polyhedron over the same system of inequalities.
‣ Cdd_FacesWithFixedDimension( P, d ) | ( operation ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and a positive integer d. The output is a list. Every entry in this list is the linearity of an d- dimensional face of P defined as a polyhedron over the same system of inequalities.
‣ Cdd_FacesWithInteriorPoints( P ) | ( attribute ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and returns a list. Every entry in this list is a again a list, contains the dimension, linearity of the face defined as a polyhedron over the same system of inequalities and an interior point in the face.
‣ Cdd_FacesWithFixedDimensionAndInteriorPoints( P, d ) | ( operation ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and a positive integer d. The output is a list. Every entry in this list is a again a list, contains the linearity of the face defined as a polyhedron over the same system of inequalities and an interior point in this face.
‣ Cdd_Facets( P ) | ( attribute ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and returns a list. Every entry in this is the linearity of a facet defined as a polyhedron over the same system of inequalities.
‣ Cdd_Lines( P ) | ( attribute ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and returns a list. Every entry in this is the linearity of a ray (\(1\)-dimensional face) defined as a polyhedron over the same system of inequalities.
‣ Cdd_Vertices( P ) | ( attribute ) |
Returns: a list
This function takes a \(H\)-represented polyhedron P and returns a list. Every entry in this list is the linearity of a vertex defined as a polyhedron over the same system of inequalities.
‣ Cdd_IsEmpty( P ) | ( property ) |
Returns: true or false
The output is true if the polyhedron is empty and false otherwise
‣ Cdd_IsCone( P ) | ( property ) |
Returns: true or false
The output is true if the polyhedron is cone and false otherwise
‣ Cdd_IsPointed( P ) | ( property ) |
Returns: true or false
The output is true if the polyhedron is pointed and false otherwise
gap> poly:= Cdd_PolyhedronByInequalities( [ [ 1, 3, 4, 5, 7 ], [ 1, 3, 5, 12, 34 ], > [ 9, 3, 0, 2, 13 ] ], [ 1 ] ); <Polyhedron given by its H-representation> gap> Cdd_InteriorPoint( poly ); [ -194/75, 46/25, -3/25, 0 ] gap> Cdd_FacesWithInteriorPoints( poly ); [ [ 3, [ 1 ], [ -194/75, 46/25, -3/25, 0 ] ], [ 2, [ 1, 2 ], [ -62/25, 49/25, -7/25, 0 ] ], [ 1, [ 1, 2, 3 ], [ -209/75, 56/25, -8/25, 0 ] ], [ 2, [ 1, 3 ], [ -217/75, 53/25, -4/25, 0 ] ] ] gap> Cdd_Dimension( poly ); 3 gap> Cdd_IsPointed( poly ); false gap> Cdd_IsEmpty( poly ); false gap> Cdd_Faces( poly ); [ [ 3, [ 1 ] ], [ 2, [ 1, 2 ] ], [ 1, [ 1, 2, 3 ] ], [ 2, [ 1, 3 ] ] ] gap> poly1 := Cdd_ExtendLinearity( poly, [ 1, 2, 3 ] ); <Polyhedron given by its H-representation> gap> Display( poly1 ); H-representation linearity 3, [ 1, 2, 3 ] begin 3 X 5 rational 1 3 4 5 7 1 3 5 12 34 9 3 0 2 13 end gap> Cdd_Dimension( poly1 ); 1 gap> Cdd_Facets( poly ); [ [ 1, 2 ], [ 1, 3 ] ] gap> Cdd_GeneratingVertices( poly ); [ [ -209/75, 56/25, -8/25, 0 ] ] gap> Cdd_GeneratingRays( poly ); [ [ -97, 369, -342, 75 ], [ -8, -9, 12, 0 ], [ 23, -21, 3, 0 ], [ 97, -369, 342, -75 ] ] gap> Cdd_Inequalities( poly ); [ [ 1, 3, 5, 12, 34 ], [ 9, 3, 0, 2, 13 ] ] gap> Cdd_Equalities( poly ); [ [ 1, 3, 4, 5, 7 ] ] gap> P := Cdd_FourierProjection( poly, 2); <Polyhedron given by its H-representation> gap> Display( P ); H-representation linearity 1, [ 3 ] begin 3 X 5 rational 9 3 0 2 13 -1 -3 0 23 101 0 0 1 0 0 end
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