# NConvex, single 11
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("nconvex11.tst");
# doc/_Chunks.xml:393-474
gap> P:= Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 2 ] ] );
<A polytope in |R^3>
gap> IsNormalPolytope( P );
false
gap> IsVeryAmple( P );
false
gap> Q:= Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 1 ] ] );
<A polytope in |R^3>
gap> IsNormalPolytope( Q );
true
gap> IsVeryAmple( Q );
true
gap> Q;
<A normal very ample polytope in |R^3 with 4 vertices>
gap> T:= Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 4 ] ] );
<A polytope in |R^3>
gap> I:= Polytope( [ [ 0, 0, 0 ], [ 0, 0, 1 ] ] );
<A polytope in |R^3>
gap> J:= T + I;
<A polytope in |R^3>
gap> IsVeryAmple( J );
true
gap> IsNormalPolytope( J );
false
gap> J;
<A very ample polytope in |R^3 with 8 vertices>
gap> # Example 2.2.20 Cox, Toric Varieties
> A:= [ [1,1,1,0,0,0], [1,1,0,1,0,0], [1,0,1,0,1,0], [ 1,0,0,1,0,1],
> [ 1,0,0,0,1,1], [ 0,1,1,0,0,1], [0,1,0,1,1,0], [0,1,0,0,1,1],
> [0,0,1,1,1,0], [0,0,1,1,0,1] ];
[ [ 1, 1, 1, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 0 ], [ 1, 0, 1, 0, 1, 0 ],
[ 1, 0, 0, 1, 0, 1 ], [ 1, 0, 0, 0, 1, 1 ], [ 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 1, 0 ],
[ 0, 0, 1, 1, 0, 1 ] ]
gap> H:= Polytope( A );
<A polytope in |R^6>
gap> IsVeryAmple( H );
true
gap> IsNormalPolytope( H );
false
gap> H;
<A very ample polytope in |R^6 with 10 vertices>
gap> l:= [ [ 0, 0, 1 ], [ 0, 0, 0 ], [ 1, 0, 0 ], [ 1, 0, 1 ], [ 0, 1, 0 ],
> [ 0, 1, 1 ], [ 1, 1, 4 ], [ 1, 1, 5 ] ];;
gap> P:= Polytope( l );
<A polytope in |R^3>
gap> IsNormalPolytope( P );
false
gap> lattic_points:= LatticePoints( P );
[ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 1, 0, 0 ], [ 1, 0, 1 ],
[ 1, 1, 4 ], [ 1, 1, 5 ] ]
gap> u:= Cartesian( lattic_points, lattic_points );;
gap> k:= Set( List( u, u-> u[1]+u[2] ) );
[ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 0, 1, 2 ],
[ 0, 2, 0 ], [ 0, 2, 1 ], [ 0, 2, 2 ], [ 1, 0, 0 ], [ 1, 0, 1 ], [ 1, 0, 2 ],
[ 1, 1, 0 ], [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 4 ], [ 1, 1, 5 ], [ 1, 1, 6 ],
[ 1, 2, 4 ], [ 1, 2, 5 ], [ 1, 2, 6 ], [ 2, 0, 0 ], [ 2, 0, 1 ], [ 2, 0, 2 ],
[ 2, 1, 4 ], [ 2, 1, 5 ], [ 2, 1, 6 ], [ 2, 2, 8 ], [ 2, 2, 9 ], [ 2, 2, 10 ] ]
gap> Q:= 2*P;
<A polytope in |R^3 with 8 vertices>
gap> LatticePoints( Q );
[ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 0, 1, 2 ],
[ 0, 2, 0 ], [ 0, 2, 1 ], [ 0, 2, 2 ], [ 1, 0, 0 ],
[ 1, 0, 1 ], [ 1, 0, 2 ], [ 1, 1, 0 ], [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 3 ],
[ 1, 1, 4 ], [ 1, 1, 5 ], [ 1, 1, 6 ], [ 1, 2, 4 ], [ 1, 2, 5 ], [ 1, 2, 6 ],
[ 2, 0, 0 ], [ 2, 0, 1 ], [ 2, 0, 2 ], [ 2, 1, 4 ],
[ 2, 1, 5 ], [ 2, 1, 6 ], [ 2, 2, 8 ], [ 2, 2, 9 ], [ 2, 2, 10 ] ]
gap> P:= Polytope( [ [ 1, 1 ], [ 1, -1 ], [ -1, 1 ], [ -1, -1 ] ] );
<A polytope in |R^2>
gap> Q:= PolarPolytope( P );
<A polytope in |R^2>
gap> Vertices( Q );
[ [ -1, 0 ], [ 0, -1 ], [ 0, 1 ], [ 1, 0 ] ]
gap> T := PolarPolytope( Q );
<A polytope in |R^2>
gap> Vertices( T );
[ [ -1, -1 ], [ -1, 1 ], [ 1, -1 ], [ 1, 1 ] ]
gap> P:= Polytope( [ [ 0, 0 ], [ 1, -1], [ -1, 1 ], [ -1, -1 ] ] );
<A polytope in |R^2>
gap> # PolarPolytope( P );;
#
gap> STOP_TEST("nconvex11.tst", 1);
