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| user_guide:lattice_polytopes_tutorial [2019/01/25 09:27] – ↷ Page moved from tutorial:lattice_polytopes_tutorial to user_guide:lattice_polytopes_tutorial oroehrig | user_guide:tutorials:lattice_polytopes_tutorial [2019/01/25 09:38] – ↷ Page moved from user_guide:lattice_polytopes_tutorial to user_guide:tutorials:lattice_polytopes_tutorial oroehrig |
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| ====== Tutorial for Lattice Polytopes ====== | ====== Tutorial for Lattice Polytopes ====== |
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| This page gives a small introduction to lattice polytopes in ''polymake'', some useful external software, and usage hints for it. For a list of methods and properties applicable to lattice polytopes see [[user_guide:lattice_polytopes_doc|here]]. For an introduction to the ''polymake'' package see [[tutorial/start|here]]. \\ | This page gives a small introduction to lattice polytopes in ''polymake'', some useful external software, and usage hints for it. For a list of methods and properties applicable to lattice polytopes see [[user_guide:lattice_polytopes_doc|here]]. For an introduction to the ''polymake'' package see [[user_guide:start|here]]. \\ |
| ''polymake'' always assumes that the lattice used to define a lattice polytope is the standard lattice Z<sup>d</sup>. Some rules also require that the polytope is full dimensional. There are user functions that transform a polytope sitting in some affine subspace of R<sup>d</sup> into a full dimensional polytope, either in the induced lattice or the lattice spanned by the vertices, see below. \\ | ''polymake'' always assumes that the lattice used to define a lattice polytope is the standard lattice Z<sup>d</sup>. Some rules also require that the polytope is full dimensional. There are user functions that transform a polytope sitting in some affine subspace of R<sup>d</sup> into a full dimensional polytope, either in the induced lattice or the lattice spanned by the vertices, see below. \\ |
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| </code> | </code> |
| The output may look similar to the following. \\ | The output may look similar to the following. \\ |
| {{:tutorial:cube-in-lattice.gif?298}} | {{user_guide:cube-in-lattice.gif?298}} |
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| The command ''LATTICE_COLORED'' sorted the lattice points into three classes before visualization: lattice points in the interior of the polytope, lattice points on the boundary, and vertices that are not in the lattice. These classes are then visualized with different colors (where we only see two in the above picture, as all vertices of the cube are in the lattice). If you don't need this distinction, ''VISUAL->LATTICE'' avoids the additional computations. | The command ''LATTICE_COLORED'' sorted the lattice points into three classes before visualization: lattice points in the interior of the polytope, lattice points on the boundary, and vertices that are not in the lattice. These classes are then visualized with different colors (where we only see two in the above picture, as all vertices of the cube are in the lattice). If you don't need this distinction, ''VISUAL->LATTICE'' avoids the additional computations. |