Singular

4.22 cone

In the finite dimensional real vector space R^n, a convex rational polyhedral cone (in short "cone") is the convex set generated by finitely many half-lines generated by rational, and hence integer respectively, points. It may or may not contain a subspace of R^n (e.g. entire lines). The biggest subspace contained in a cone is called "lineality space". Modulo its lineality space, each cone is generated by a distinct minimal set of half lines, which are referred to as "rays". Moreover, a cone can be represented as a set of points satisfying certain homogeneous linear inequalities and equalities. And these two characterizations of cones are the two main ways of defining non-trivial cones in Singular (see coneViaRays, see coneViaNormals).

  cone c;                             // ambient dim 0, no equations,
                                      // no inequalities
  cone c = 17;                        // ambient dim 17, no equations,
                                      // no inequalities

4.22.1 coneViaRays
4.22.2 coneViaNormals
4.22.3 quickConeViaNormals
4.22.4 cone related functions