user_guide:tutorials:ilp_and_hilbertbases

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user_guide:ilp_and_hilbertbases [2019/01/25 09:27] – ↷ Page moved from tutorial:ilp_and_hilbertbases to user_guide:ilp_and_hilbertbases oroehriguser_guide:ilp_and_hilbertbases [2019/01/25 09:35] – ↷ Links adapted because of a move operation oroehrig
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 Now let us proceed with a somewhat more interesting example: The convex hull of 20 randomly chosen points on the 2-dimensional sphere. Now let us proceed with a somewhat more interesting example: The convex hull of 20 randomly chosen points on the 2-dimensional sphere.
-{{ :tutorial:ilp:rand_sphere.png?200|}}+{{ user_guide:ilp:rand_sphere.png?200|}}
 <code> <code>
 polytope > $rs = rand_sphere(3,20); polytope > $rs = rand_sphere(3,20);
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 To this end, we have to multiply every coordinate (except for the homogenising 1 in the beginning) of every vertex by lamda. Then we can create a new polytope by specifying its vertices. To this end, we have to multiply every coordinate (except for the homogenising 1 in the beginning) of every vertex by lamda. Then we can create a new polytope by specifying its vertices.
  
-{{ :tutorial:ilp:rand_sphere_lattice.png?200|}}+{{ user_guide:ilp:rand_sphere_lattice.png?200|}}
 <code> <code>
 polytope > $lambda=2; polytope > $lambda=2;
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 Now will construct the integer hull of ''$scaled_rs'' and visualise it: Now will construct the integer hull of ''$scaled_rs'' and visualise it:
  
-{{ :tutorial:ilp:ilp_lattice.png?200|}}+{{ user_guide:ilp:ilp_lattice.png?200|}}
 <code> <code>
 polytope > $integer_hull=new Polytope<Rational>(POINTS=>$scaled_rs->LATTICE_POINTS); polytope > $integer_hull=new Polytope<Rational>(POINTS=>$scaled_rs->LATTICE_POINTS);
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 Note that if we give ''POINTS'' (in contrast to ''VERTICES'') ''polymake'' constructs a polytope that is the convex hull of the given points regardless of whether they are vertices or not. I.e., redundacies are allowed here. Note that if we give ''POINTS'' (in contrast to ''VERTICES'') ''polymake'' constructs a polytope that is the convex hull of the given points regardless of whether they are vertices or not. I.e., redundacies are allowed here.
  
-If you specify ''VERTICES'' you have to make sure yourself that your points are actually vertices since ''polymake'' does not check this. You also need to specify the ''LINEALITY_SPACE'', see [[tutorial:apps_polytope | Tutorial on polytopes]].+If you specify ''VERTICES'' you have to make sure yourself that your points are actually vertices since ''polymake'' does not check this. You also need to specify the ''LINEALITY_SPACE'', see [[user_guide:tutorials:apps_polytope| Tutorial on polytopes]].
  
 ==== Linear Programming ==== ==== Linear Programming ====
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 polytope > $ilp=new Polytope<Rational>(VERTICES=>$integer_hull->VERTICES, LP=>$objective); polytope > $ilp=new Polytope<Rational>(VERTICES=>$integer_hull->VERTICES, LP=>$objective);
 </code> </code>
-{{ :tutorial:ilp:ilp_min_face.png?200|}} +{{ user_guide:ilp:ilp_min_face.png?200|}} 
-{{ :tutorial:ilp:ilp_max_face.png?200|}}+{{ user_guide:ilp:ilp_max_face.png?200|}}
  
 And now we can perform some computations: And now we can perform some computations:
  • user_guide/tutorials/ilp_and_hilbertbases.txt
  • Last modified: 2019/02/04 22:55
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