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D.13.1 gfan_lib

Interface to gfan and gfanlib for computations in convex geometry
Anders N. Jensen, email: jensen@imf.au.dk
Yue Ren, email: ren@mathematik.uni-kl.de
Frank Seelisch


D.13.1.1 fullSpace  cone, the ambient space of dimension n
D.13.1.2 origin  cone, the origin in an ambient space of dimension n
D.13.1.3 positiveOrthant  cone, the positive orthant of dimension n
D.13.1.4 ambientDimension  the dimension of the ambient space the input lives in
D.13.1.5 canonicalizeCone  a unique representation of the cone c
D.13.1.6 codimension  the codimension of the input
D.13.1.7 coneViaPoints  define a cone
D.13.1.8 coneViaInequalities  define a cone
D.13.1.9 coneLink  the link of c around w
D.13.1.10 containsAsFace  is d a face of c
D.13.1.11 containsInSupport  is d contained in c
D.13.1.12 containsPositiveVector  contains a vector with only positive entries?
D.13.1.13 containsRelatively  p in c?
D.13.1.14 convexHull  convex hull
D.13.1.15 convexIntersection  convex hull
D.13.1.16 dimension  dimension of c
D.13.1.17 dualCone  the dual of c
D.13.1.18 equations  defining equations of c
D.13.1.19 faceContaining  the face of c containing w in its relative interior
D.13.1.20 facets  the facets of c
D.13.1.21 generatorsOfLinealitySpace  generators of the lineality space of c
D.13.1.22 generatorsOfSpan  generators of the span of c
D.13.1.23 getLinearForms  linear forms previously stored in c
D.13.1.24 getMultiplicity  multiplicity previously stored in c
D.13.1.25 inequalities  inequalities of c
D.13.1.26 isFullSpace  is the entire ambient space?
D.13.1.27 isOrigin  is the origin?
D.13.1.28 isSimplicial  is simplicial?
D.13.1.29 linealityDimension  the dimension of the lineality space of c
D.13.1.30 linealitySpace  the lineality space of c
D.13.1.31 negatedCone  the negative of c
D.13.1.32 polytopeViaInequalities  
D.13.1.33 polytopeViaPoints  
D.13.1.34 quotientLatticeBasis  basis of Z^n intersected with the span of c modulo Z^n intersected with the lineality space of c
D.13.1.35 randomPoint  a random point in the relative interior of c
D.13.1.36 rays  generators of the rays of c
D.13.1.37 relativeInteriorPoint  point in the relative interior of c
D.13.1.38 semigroupGenerator  generator of Z^n intersected with c modulo Z^n intersected with the lineality space of c
D.13.1.39 setLinearForms  stores linear forms in c
D.13.1.40 setMultiplicity  stores a multiplicity in c
D.13.1.41 span  unique irredundant equations of c
D.13.1.42 uniquePoint  a unique point in c stable under reflections at coordinate hyperplanes
D.13.1.43 containsInCollection  f contains c?
D.13.1.44 emptyFan  empty fan in ambient dimension n
D.13.1.45 fanViaCones  fan generated by the cones in L
D.13.1.46 fullFan  full fan in ambient dimension n
D.13.1.47 fVector  the f-Vector of f
D.13.1.48 getCone  the i-th cone of dimension d in f
D.13.1.49 insertCone  inserts the cone c into f
D.13.1.50 isCompatible  f and c live in the same ambient space
D.13.1.51 isPure  all maximal cones of f are of the same dimension
D.13.1.52 nmaxcones  number of maximal cones in f
D.13.1.53 ncones  number of cones in f
D.13.1.54 numberOfConesOfDimension  the number of cones in dimension d
D.13.1.55 removeCone  removes the cone c
D.13.1.56 dualPolytope  the dual of p
D.13.1.57 newtonPolytope  convex hull of all exponent vectors of f
D.13.1.58 vertices  vertices of p
D.13.1.59 onesVector  intvec of length n with all entries 1