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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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  4 Toric subvarieties

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  4.1 Toric subvarieties: Category and Representations

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  4.1-1 IsToricSubvariety

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  IsToricSubvariety( M )  Category

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  Returns:  true or false

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  The  GAP  category  of a toric subvariety. Every toric subvariety is a toric

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  variety, so every method applicable to toric varieties is also applicable to

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  toric subvarieties.

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  4.2 Toric subvarieties: Properties

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  4.2-1 IsClosed

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  IsClosed( vari )  property

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  Returns:  true or false

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  Checks if the subvariety vari is a closed subset of its ambient variety.

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  4.2-2 IsOpen

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  IsOpen( vari )  property

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  Returns:  true or false

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  Checks if a subvariety is a closed subset.

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  4.2-3 IsWholeVariety

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  IsWholeVariety( vari )  property

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  Returns:  true or false

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  Returns true if the subvariety vari is the whole variety.

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  4.3 Toric subvarieties: Attributes

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  4.3-1 UnderlyingToricVariety

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  UnderlyingToricVariety( vari )  attribute

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  Returns:  a variety

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  Returns  the  toric  variety  which  is  represented  by  vari.  This method

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  implements the forgetful functor subvarieties -> varieties.

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  4.3-2 InclusionMorphism

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  InclusionMorphism( vari )  attribute

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  Returns:  a morphism

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  If the variety vari is an open subvariety, this method returns the inclusion

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  morphism in its ambient variety. If not, it will fail.

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  4.3-3 AmbientToricVariety

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  AmbientToricVariety( vari )  attribute

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  Returns:  a variety

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  Returns the ambient toric variety of the subvariety vari

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  4.4 Toric subvarieties: Methods

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  4.4-1 ClosureOfTorusOrbitOfCone

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  ClosureOfTorusOrbitOfCone( vari, cone )  operation

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  Returns:  a subvariety

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  The  method  returns the closure of the orbit of the torus contained in vari

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  which corresponds to the cone cone as a closed subvariety of vari.

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  4.5 Toric subvarieties: Constructors

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  4.5-1 ToricSubvariety

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  ToricSubvariety( vari, ambvari )  operation

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  Returns:  a subvariety

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  The  method  returns the closure of the orbit of the torus contained in vari

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  which corresponds to the cone cone as a closed subvariety of vari.

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