Singular Manual: gfan_lib

> | ### D.13.1 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.13.1.1 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

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