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CODE FOR THE TALK
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DEFINING A POLYTOPE, BASIC PROPERTIES

$points = new Matrix<Rational>([[1,0,0,0],[1,2,0,0],[1,0,2,0],[1,0,0,2]]);
$p = new Polytope<Rational>(POINTS=>$points);
print $p->VOLUME;
print $p->N_POINTS;
print $p->F_VECTOR;
print $p->N_LATTICE_POINTS;

$ineqs = new Matrix<Rational>([[0,1,0,0],[0,0,1,0],[0,0,0,1],[2,-1,-1,-1]]);
$p = new Polytope<Rational>(INEQUALITIES=>$ineqs);



CYCLIC POLYTOPE

$points = new Matrix<Rational>([[1,0.725426, 0.526243, 0.381751, 0.276932], [1,1.71403, 2.93789, 5.03562, 8.63119], [1,1.80351, 3.25263, 5.86615, 10.5796], [1,1.89725, 3.59956, 6.82927, 12.9568], [1,1.74107, 3.03134, 5.27779, 9.18902], [1,1.06607, 1.1365, 1.21158, 1.29162], [1,0.201847, 0.0407422, 0.00822368, 0.00165993], [1,1.25097, 1.56492, 1.95766, 2.44898]]);
$p = new Polytope<Rational>(POINTS=>$points);


REGULAR SUBDIVISION


$M = new Matrix<Rational>([[1,0,1],[1,1,1],[1,2,1],[1,3,1]]);
$w = new Vector<Rational>([4,2,1,2]);
$w = new Vector<Rational>([1,0,0,1]);
$w= new Vector<Rational>([3,2,1,2]);
$w = new Vector<Rational>([4,3,2,1]);
$F = regular_subdivision($M,$w);
print $F;

$M = new Matrix<Rational>([[1,2,0],[1,1,1],[1,0,2],[1,1,0],[1,0,1],[1,0,0]]);
$w = new Vector<Rational>([1,0,1,0,0,2]);
$w = new Vector<Rational>([3,0,3,1,1,0]);
$F = regular_subdivision($M,$w);
print $F;


TROPICAL

application “tropical”
$a = new TropicalNumber<Min>(4);
$c = new TropicalNumber<Min>("inf");
print $a * $a;

$M = new Matrix<TropicalNumber<Min> >([[0,1,2],[0,"inf",3],[0,0,"inf"]]);
 $v = new Vector<TropicalNumber<Min> >(1,1,2);
print $M * $v;
print tdet($M);