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user_guide:apps_polytope [2019/01/25 09:27] – ↷ Page moved from tutorial:apps_polytope to user_guide:apps_polytope oroehrig | user_guide:tutorials:apps_polytope [2019/01/29 21:46] – external edit 127.0.0.1 | ||
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====== Tutorial on Polytopes ====== | ====== Tutorial on Polytopes ====== | ||
- | **This tutorial is also available as a {{ :tutorial: | + | **This tutorial is also available as a {{ user_guide: |
A // | A // | ||
- | This tutorial first shows basic ways of defining a polytope from scratch. For larger input (e.g. from a file generated by some other program) have a look at [[tutorial:data|how to load data]] in '' | + | This tutorial first shows basic ways of defining a polytope from scratch. For larger input (e.g. from a file generated by some other program) have a look at [[..:howto:data|how to load data]] in '' |
The second part demonstrates some of the tool '' | The second part demonstrates some of the tool '' | ||
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==== V-Description ==== | ==== V-Description ==== | ||
- | To define a polytope as the convex hull of finitely many points, you can pass a matrix of coordinates to the constructor. Since '' | + | To define a polytope as the convex hull of finitely many points, you can pass a matrix of coordinates to the constructor. Since '' |
< | < | ||
polytope > $p = new Polytope(POINTS=> | polytope > $p = new Polytope(POINTS=> | ||
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polytope > $p2-> | polytope > $p2-> | ||
</ | </ | ||
- | See [[tutorial:visual_tutorial# | + | See [[visual_tutorial# |
If you are sure that all the points really are //extreme points// (vertices) and your description of the lineality space is complete, you can define the polytope via the properties '' | If you are sure that all the points really are //extreme points// (vertices) and your description of the lineality space is complete, you can define the polytope via the properties '' | ||
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It is also possible to define a polytope as an intersection of finitely many halfspaces, i.e., a matrix of inequalities.\\ | It is also possible to define a polytope as an intersection of finitely many halfspaces, i.e., a matrix of inequalities.\\ | ||
- | An inequality a< | + | An inequality a< |
< | < | ||
polytope > $p4 = new Polytope(INEQUALITIES=> | polytope > $p4 = new Polytope(INEQUALITIES=> |