Singular

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
D.13.2.33 polytopeViaPoints
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