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### 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.

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