  
  [1X6 [33X[0;0YProjective toric varieties[133X[101X
  
  
  [1X6.1 [33X[0;0YProjective toric varieties: Category and Representations[133X[101X
  
  [1X6.1-1 IsProjectiveToricVariety[101X
  
  [29X[2XIsProjectiveToricVariety[102X( [3XM[103X ) [32X Category
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe [5XGAP[105X category of a projective toric variety.[133X
  
  
  [1X6.2 [33X[0;0YProjective toric varieties: Properties[133X[101X
  
  [33X[0;0YProjective  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.[133X
  
  
  [1X6.3 [33X[0;0YProjective toric varieties: Attributes[133X[101X
  
  [1X6.3-1 AffineCone[101X
  
  [29X[2XAffineCone[102X( [3Xvari[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya variety[133X
  
  [33X[0;0YReturns the affine cone of the projective toric variety [3Xvari[103X.[133X
  
  [1X6.3-2 PolytopeOfVariety[101X
  
  [29X[2XPolytopeOfVariety[102X( [3Xvari[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya polytope[133X
  
  [33X[0;0YReturns  the polytope corresponding to the projective toric variety [3Xvari[103X, if
  it exists.[133X
  
  [1X6.3-3 ProjectiveEmbedding[101X
  
  [29X[2XProjectiveEmbedding[102X( [3Xvari[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya list[133X
  
  [33X[0;0YReturns  characters  for  a  closed embedding in an projective space for the
  projective toric variety [3Xvari[103X.[133X
  
  
  [1X6.4 [33X[0;0YProjective toric varieties: Methods[133X[101X
  
  [1X6.4-1 Polytope[101X
  
  [29X[2XPolytope[102X( [3Xvari[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ya polytope[133X
  
  [33X[0;0YReturns the polytope of the variety [3Xvari[103X. Another name for PolytopeOfVariety
  for compatibility and shortness.[133X
  
  
  [1X6.5 [33X[0;0YProjective toric varieties: Constructors[133X[101X
  
  [33X[0;0YThe  constructors  are  the same as for toric varieties. Calling them with a
  polytope will result in an projective variety.[133X
  
  
  [1X6.6 [33X[0;0YProjective toric varieties: Examples[133X[101X
  
  
  [1X6.6-1 [33X[0;0YPxP1 created by a polytope[133X[101X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XP1P1 := Polytope( [[1,1],[1,-1],[-1,-1],[-1,1]] );[127X[104X
    [4X[28X<A polytope in |R^2>[128X[104X
    [4X[25Xgap>[125X [27XP1P1 := ToricVariety( P1P1 );[127X[104X
    [4X[28X<A projective toric variety of dimension 2>[128X[104X
    [4X[25Xgap>[125X [27XIsProjective( P1P1 );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XIsComplete( P1P1 );[127X[104X
    [4X[28Xtrue [128X[104X
    [4X[25Xgap>[125X [27XCoordinateRingOfTorus( P1P1, "x" );[127X[104X
    [4X[28XQ[x1,x1_,x2,x2_]/( x2*x2_-1, x1*x1_-1 )[128X[104X
    [4X[25Xgap>[125X [27XIsVeryAmple( Polytope( P1P1 ) );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XProjectiveEmbedding( P1P1 );[127X[104X
    [4X[28X[ |[ x1_*x2_ ]|, |[ x1_ ]|, |[ x1_*x2 ]|, |[ x2_ ]|,[128X[104X
    [4X[28X|[ 1 ]|, |[ x2 ]|, |[ x1*x2_ ]|, |[ x1 ]|, |[ x1*x2 ]| ][128X[104X
    [4X[25Xgap>[125X [27XLength( last );[127X[104X
    [4X[28X9[128X[104X
  [4X[32X[104X
  
