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Both sides previous revision Previous revision Next revision | Previous revisionLast revisionBoth sides next revision | ||
tutorial:coordinates [2012/05/16 11:26] – [Internal treatment of polytope generators (svn version only)] herr | user_guide:tutorials:coordinates [2019/01/25 13:40] – ↷ Page moved from user_guide:coordinates to user_guide:tutorials:coordinates oroehrig | ||
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Points from both sections can now be identified with infinite rays through the origin in //W//. Facets are identified with the a hyperplane containing the image of the facet in //V// and the origin in //W//. This hyperplane is represented by a normal vector. | Points from both sections can now be identified with infinite rays through the origin in //W//. Facets are identified with the a hyperplane containing the image of the facet in //V// and the origin in //W//. This hyperplane is represented by a normal vector. | ||
- | Note that a facet defining hyperplane is not uniquely determined if the polyhedron is not full-dimensional. {{ tutorial: | + | Note that a facet defining hyperplane is not uniquely determined if the polyhedron is not full-dimensional. {{ user_guide: |
A vertex is incident with a facet if and only if the scalar product of their representatives in //W// is zero. | A vertex is incident with a facet if and only if the scalar product of their representatives in //W// is zero. | ||
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0 0 0 1 | 0 0 0 1 | ||
</ | </ | ||
+ | |||
+ | Each line describes one linear inequality. | ||
Clearly, the polyhedron is unbounded. | Clearly, the polyhedron is unbounded. |