### D.13.2 gfan_lib

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

Procedures:

> D.13.2.1 fullSpace |  | cone, the ambient space of dimension n
> D.13.2.2 origin |  | cone, the origin in an ambient space of dimension n
> D.13.2.3 positiveOrthant |  | cone, the positive orthant of dimension n
> D.13.2.4 ambientDimension |  | the dimension of the ambient space the input lives in
> D.13.2.5 canonicalizeCone |  | a unique representation of the cone c
> D.13.2.6 codimension |  | the codimension of the input
> D.13.2.7 coneViaPoints |  | define a cone
> D.13.2.8 coneViaInequalities |  | define a cone
> D.13.2.9 coneLink |  | the link of c around w
> D.13.2.10 containsAsFace |  | is d a face of c
> D.13.2.11 containsInSupport |  | is d contained in c
> D.13.2.12 containsPositiveVector |  | contains a vector with only positive entries?
> D.13.2.13 containsRelatively |  | p in c?
> D.13.2.14 convexHull |  | convex hull
> D.13.2.15 convexIntersection |  | convex hull
> D.13.2.16 dimension |  | dimension of c
> D.13.2.17 dualCone |  | the dual of c
> D.13.2.18 equations |  | defining equations of c
> D.13.2.19 faceContaining |  | the face of c containing w in its relative interior
> D.13.2.20 facets |  | the facets of c
> D.13.2.21 generatorsOfLinealitySpace |  | generators of the lineality space of c
> D.13.2.22 generatorsOfSpan |  | generators of the span of c
> D.13.2.23 getLinearForms |  | linear forms previously stored in c
> D.13.2.24 getMultiplicity |  | multiplicity previously stored in c
> D.13.2.25 inequalities |  | inequalities of c
> D.13.2.26 isFullSpace |  | is the entire ambient space?
> D.13.2.27 isOrigin |  | is the origin?
> D.13.2.28 isSimplicial |  | is simplicial?
> D.13.2.29 linealityDimension |  | the dimension of the lineality space of c
> D.13.2.30 linealitySpace |  | the lineality space of c
> D.13.2.31 negatedCone |  | the negative of c
> D.13.2.32 polytopeViaInequalities |  | define a polytope
> D.13.2.33 polytopeViaPoints |  | define a polytope
> D.13.2.34 quotientLatticeBasis |  | basis of Z^n intersected with the span of c modulo Z^n intersected with the lineality space of c
> D.13.2.35 randomPoint |  | a random point in the relative interior of c
> D.13.2.36 rays |  | generators of the rays of c
> D.13.2.37 relativeInteriorPoint |  | point in the relative interior of c
> D.13.2.38 semigroupGenerator |  | generator of Z^n intersected with c modulo Z^n intersected with the lineality space of c
> D.13.2.39 setLinearForms |  | stores linear forms in c
> D.13.2.40 setMultiplicity |  | stores a multiplicity in c
> D.13.2.41 span |  | unique irredundant equations of c
> D.13.2.42 uniquePoint |  | a unique point in c stable under reflections at coordinate hyperplanes
> D.13.2.43 containsInCollection |  | f contains c?
> D.13.2.44 emptyFan |  | empty fan in ambient dimension n
> D.13.2.45 fanViaCones |  | fan generated by the cones in L
> D.13.2.46 fullFan |  | full fan in ambient dimension n
> D.13.2.47 fVector |  | the f-Vector of f
> D.13.2.48 getCone |  | the i-th cone of dimension d in f
> D.13.2.49 insertCone |  | inserts the cone c into f
> D.13.2.50 isCompatible |  | f and c live in the same ambient space
> D.13.2.51 isPure |  | all maximal cones of f are of the same dimension
> D.13.2.52 nmaxcones |  | number of maximal cones in f
> D.13.2.53 ncones |  | number of cones in f
> D.13.2.54 numberOfConesOfDimension |  | the number of cones in dimension d
> D.13.2.55 removeCone |  | removes the cone c
> D.13.2.56 dualPolytope |  | the dual of p
> D.13.2.57 newtonPolytope |  | convex hull of all exponent vectors of f
> D.13.2.58 vertices |  | vertices of p
> D.13.2.59 onesVector |  | intvec of length n with all entries 1

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