Differences

This shows you the differences between two versions of the page.

--- tutorial:coordinates [2012/07/07 14:40] – joswig
+++ user_guide:tutorials:coordinates [2019/01/25 13:40] – ↷ Page moved from user_guide:coordinates to user_guide:tutorials:coordinates oroehrig
@@ Line 11: / Line 11: @@
 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:coord.gif?326|}}
+Note that a facet defining hyperplane is not uniquely determined if the polyhedron is not full-dimensional. {{ user_guide:coord.gif?326|}}
 A vertex is incident with a facet if and only if the scalar product of their representatives in //W// is zero.
@@ Line 40: / Line 40: @@
 </code>
-Each line describes one linear inequality.  The encoding is as follows (a_0,a_1,...,a_d) is the inequality a_0 + a_1 x_1 + ... + a_d x_d >= 0.
+Each line describes one linear inequality.  The encoding is as follows: (a_0,a_1,...,a_d) is the inequality a_0 + a_1 x_1 + ... + a_d x_d >= 0.  This way a point in (oriented) homogeneous coordinates satisfies an inequality if and only if the scalar product of the point with the inequality gives a non-negative value. (Use the command ''print_constraints($m)'' to display the inequalities of the matrix ''$m'' in a nice way.)
 Clearly, the polyhedron is unbounded.