;### CONSTRUCTING A POLYTOPE
$orig_points=new Matrix([[1,2,0],[0,1,2],[2,0,1],[1,1,1],[1,0,2],[2,1,0],[0,2,1]]);
;### Loading data from file? -> see tutorial "Save and load data in polymake"
;### homogenization: prepend ones-vector
$fst_col=ones_vector($orig_points->rows); print $fst_col;
$homog_points=$fst_col|$orig_points; print $homog_points;
$p=new Polytope(POINTS=>$homog_points);
print $p->VERTICES;
print "Number of points: ".$p->N_POINTS.", number of vertices: ".$p->N_VERTICES;
$p->VISUAL;
$p->VISUAL(VertexThickness=>3,VertexColor=>"green",FacetColor=>"blue");
;### more information about visualization: tutorial VIS and wiki page
print "Ambient dimension: ".$p->AMBIENT_DIM.", dimension of the polytope: ".$p->DIM;
$p_proj=projection_full($p);
print $p_proj->VERTICES;  
;
;### CONVEX HULL COMPUTATIONS
$pyr=pyramid(n_gon);
print $pyr->list_properties;
print join(", ", $pyr->list_properties);
$schedule=$pyr->get_schedule("FACETS");
print join("\n", $schedule->list);
prefer "lrs";
$schedule=$pyr->get_schedule("FACETS"); print join("\n", $schedule->list);
print $p->FACETS;
;
;### COMPUTING LATTICE POINTS
$schedule=$pyr->get_schedule("LATTICE_POINTS"); print join("\n", $schedule->list);
print $pyr->LATTICE_POINTS;
$pyr->VISUAL->LATTICE;
;
;### PERL SYNTAX FOR POLYMAKE
;### STANDARD DATA STRUCTURES
i=5;
$i=5;
@array=("a","b","c"); print scalar(@array);
push(@array,"d"); print "@array"; 
$first_entry=$array[0]; print $first_entry;
print join("\n",@array);

@array2=(3,1,4,2);
print sort(@array2);
%hash=();
$hash{"zero"}=0;
$hash{"four"}=4;
print keys %hash;
print join(", ",keys %hash);
print join(", ",values %hash);
%hash=("one",1,"two",2);
%hash=("one"=>1,"two"=>2);
;
;### "SMALL OBJECTS": DATA STRUCTURES INHERITED FROM C++
;### ARRAY
$arr1=new Array<String>(\@array); print $arr1;
$arr2=new Array<Int>([3,2,5]); print $arr2; 
$arr3=new Array<Int>(0,1,2,3); print $arr3; 
$arr4=new Array<Int>(0..4); print $arr4;
@arr4=@{$arr4}; print @arr4;
;### SET
$set=new Set<Int>(3,2,5); print $set;
;### MATRIX
$mat=new Matrix<Rational>([[2,1,4,0,0,1],[3,1,5,2,1,2],[1,0,4,0,6,0]]); print $mat;
$mat->row(1)->[1]=7; print $mat;
$mat->(1,2)=8; print $mat;
print 4*unit_matrix<Rational>(6);
$scaled_unitmat=new Matrix(4*unit_matrix<Rational>(6)); print $scaled_unitmat;
$append=$mat/$scaled_unitmat; print $append;
$z_vec=zero_vector($append->rows);
$extend=($z_vec|$append); print $extend;
print $set;
$cols235=$extend->minor(All,$set); print $cols235;
;### TEMPLATES
$template_Ex=new Array<Set<Int>>((new Set<Int>(5,2,6)),$set); print $template_Ex;
;
;### "BIG OBJECTS": OBJECTS WITH PROPERTIES
$p=new Polytope<Rational>(POINTS=>cube(4)->VERTICES);
$lp=new LinearProgram<Rational>(LINEAR_OBJECTIVE=>[0,1,1,1,1]);
$p->LP=$lp;
print $p->LP->MAXIMAL_VALUE;
;