4 Toric subvarieties 4.1 Toric subvarieties: Category and Representations 4.1-1 IsToricSubvariety IsToricSubvariety( M )  Category Returns: true or false The GAP category of a toric subvariety. Every toric subvariety is a toric variety, so every method applicable to toric varieties is also applicable to toric subvarieties. 4.2 Toric subvarieties: Properties 4.2-1 IsClosed IsClosed( vari )  property Returns: true or false Checks if the subvariety vari is a closed subset of its ambient variety. 4.2-2 IsOpen IsOpen( vari )  property Returns: true or false Checks if a subvariety is a closed subset. 4.2-3 IsWholeVariety IsWholeVariety( vari )  property Returns: true or false Returns true if the subvariety vari is the whole variety. 4.3 Toric subvarieties: Attributes 4.3-1 UnderlyingToricVariety UnderlyingToricVariety( vari )  attribute Returns: a variety Returns the toric variety which is represented by vari. This method implements the forgetful functor subvarieties -> varieties. 4.3-2 InclusionMorphism InclusionMorphism( vari )  attribute Returns: a morphism If the variety vari is an open subvariety, this method returns the inclusion morphism in its ambient variety. If not, it will fail. 4.3-3 AmbientToricVariety AmbientToricVariety( vari )  attribute Returns: a variety Returns the ambient toric variety of the subvariety vari 4.4 Toric subvarieties: Methods 4.4-1 ClosureOfTorusOrbitOfCone ClosureOfTorusOrbitOfCone( vari, cone )  operation Returns: a subvariety The method returns the closure of the orbit of the torus contained in vari which corresponds to the cone cone as a closed subvariety of vari. 4.5 Toric subvarieties: Constructors 4.5-1 ToricSubvariety ToricSubvariety( vari, ambvari )  operation Returns: a subvariety The method returns the closure of the orbit of the torus contained in vari which corresponds to the cone cone as a closed subvariety of vari.