
4.22 coneIn order to use convex objects in Singular, Singular has to be build from sources together with gfanlib, a C++ library for convex geometry by Anders N. Jensen. Please check the readme file for installation instructions. 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 halflines, which in turn are generated by rational, and hence integer, points. It may or may not contain whole 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". Alternatively, a cone can be represented as a set of points satisfying a system homogeneous rational, and hence integer, linear inequalities and equations. These two characterizations of cones are the two main ways of defining cones in Singular (see coneViaPoints, see coneViaInequalities).
