 LIB "polymake.lib";
==> Welcome to polymake version
==> Copyright (c) 19972015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
ring r=0,(x,y),dp;
// the Newton polygon of the following polynomial
// has precisely one interior point
poly f=x22y11+x19y10+x17y9+x16y9+x12y7+x9y6+x7y5+x2y3;
list polygon=newtonPolytopeLP(f);
// its lattice points are
polygon;
==> [1]:
==> 22,11
==> [2]:
==> 19,10
==> [3]:
==> 17,9
==> [4]:
==> 16,9
==> [5]:
==> 12,7
==> [6]:
==> 9,6
==> [7]:
==> 7,5
==> [8]:
==> 2,3
// find its normal form
list nf=ellipticNF(polygon);
// the vertices of the normal form are
nf[1];
==> [1]:
==> 4,0
==> [2]:
==> 0,0
==> [3]:
==> 0,2
// it has been transformed by the unimodular affine transformation A*x+v
// with matrix A
nf[2];
==> 3,7,
==> 2,5
// and translation vector v
nf[3];
==> 15,11
// the 3rd lattice point ...
polygon[3];
==> 17,9
// ... has been transformed to
nf[4][3];
==> 3,0
