Cones
Creating cones a Cone Object The function takes a list of lists [L_1, L_2, ...] where each L_j represents an inequality and returns the cone defined by them. For example the j'th entry L_j = [a_{j1},a_{j2},...,a_{jn}] corresponds to the inequality \sum_{i=1}^n a_{ji}x_i \geq 0. a Cone Object The function takes two lists. The first list is the equalities and the second is the inequalities and returns the cone defined by them. a Cone Object The function takes a list in which every entry represents a ray in the ambient vector space and returns the cone defined by them. a Cone Object This function takes a cone defined in CddInterface and converts it to a cone in NConvex
Attributes of Cones a list Returns the list of the defining inequalities of the cone C. a list Returns the list of the equalities in the defining inequalities of the cone C. a cone Returns the dual cone of the cone C. a list of cones Returns the list of all faces of the cone C. a list of cones Returns the list of all facets of the cone C. a list Returns a list whose i'th entry is the number of faces of dimension i. a list Returns a relative interior point (or ray) in the cone C. a list Returns the Hilbert basis of the cone C a list Returns the Hilbert basis of the dual cone of the cone C a list Returns a basis of the lineality space of the cone C. a cdd object Converts the cone to a cdd object. The operations of CddInterface can then be applied on this convex object. an normaliz object Converts the cone to a normaliz object. The operations of NormalizInterface can then be applied on this convex object. an integer The dimension of the ambient space of the cone, i.e., the space that contains the cone. a list See LatticePointsGenerators for polyhedrons. Please note that any cone is a polyhedron. a homalg module Returns the homalg \mathbb{Z}-module that is generated by the ray generators of the cone. a homalg module Returns the homalg \mathbb{Z}-module that is presented by the matrix whose raws are the ray generators of the cone. a homalg morphism Returns an epimorphism from a free \mathbb{Z}-module to FactorGrid(C). a homalg module Returns the homalg \mathbb{Z}-module that is by generated the ray generators of the orthogonal cone on C.
Properties of Cones true or false Returns if the cone C is regular or not. true or false Returns if the cone C is ray or not. true or false Returns whether the cone is the zero cone or not.
Operations on cones a cone Returns the projection of the cone on the space (O, x_1,...,x_{m-1}, x_{m+1},...,x_n ). a cone Returns the intersection. a cone The input is a list of cones and the output is their intersection. a true or false Returns if the cone C1 contains the cone C2. a true or false Checks whether the input point (or ray) L is in the relative interior of the cone C. <#Include Label="example1"> a list It returns a list of inequalities that define the cone.