`‣ IsProjectiveToricVariety` ( M ) | ( category ) |

Returns: `true`

or `false`

The **GAP** category of a projective toric variety.

Projective toric varieties have no additional properties. Remember that projective toric varieties are toric varieties, so every property of a toric variety is a property of an projective toric variety.

`‣ AffineCone` ( vari ) | ( attribute ) |

Returns: a variety

Returns the affine cone of the projective toric variety `vari`.

`‣ PolytopeOfVariety` ( vari ) | ( attribute ) |

Returns: a polytope

Returns the polytope corresponding to the projective toric variety `vari`, if it exists.

`‣ ProjectiveEmbedding` ( vari ) | ( attribute ) |

Returns: a list

Returns characters for a closed embedding in an projective space for the projective toric variety `vari`.

`‣ Polytope` ( vari ) | ( operation ) |

Returns: a polytope

Returns the polytope of the variety `vari`. Another name for PolytopeOfVariety for compatibility and shortness.

The constructors are the same as for toric varieties. Calling them with a polytope will result in an projective variety.

gap> P1P1 := Polytope( [[1,1],[1,-1],[-1,-1],[-1,1]] ); <A polytope in |R^2> gap> P1P1 := ToricVariety( P1P1 ); <A projective toric variety of dimension 2> gap> IsProjective( P1P1 ); true gap> IsComplete( P1P1 ); true gap> CoordinateRingOfTorus( P1P1, "x" ); Q[x1,x1_,x2,x2_]/( x2*x2_-1, x1*x1_-1 ) gap> IsVeryAmple( Polytope( P1P1 ) ); true gap> ProjectiveEmbedding( P1P1 ); [ |[ x1_*x2_ ]|, |[ x1_ ]|, |[ x1_*x2 ]|, |[ x2_ ]|, |[ 1 ]|, |[ x2 ]|, |[ x1*x2_ ]|, |[ x1 ]|, |[ x1*x2 ]| ] gap> Length( last ); 9

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