@comment -*-texinfo-*-
@comment this file contains the cone/fan definitions

@c -------------------------------------------------------------------
@node cone, fan, User defined types, Data types
@section cone
@cindex cone

In order to use convex objects in Singular, Singular has to be build from sources
together with gfanlib, a C++ library for convex geometry by Anders N. Jensen. 
Please check the readme file for installation instructions.

This version of @sc{Singular} does not support @code{cone}.
@menu
* coneViaPoints::
* coneViaInequalities::
* cone related functions::
@end menu
@c --------------------------------------------------------------------------------
@node coneViaPoints,coneViaInequalities,,cone
@subsection coneViaPoints
@cindex coneViaPoints

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------------------
@node coneViaInequalities,cone related functions,coneViaPoints,cone
@subsection coneViaInequalities
@cindex coneViaInequalities
Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------------------
@node cone related functions,,coneViaInequalities,cone
@subsection cone related functions
@cindex cone related functions

@menu
* ambientDimension::
* canonicalizeCone::
* codimension::
* coneLink::
* containsAsFace::
* containsInSupport::
* containsPositiveVector::
* containsRelatively::
* convexHull::
* convexIntersection::
* dimension::
* dualCone::
* equations::
* facets::
* generatorsOfLinealitySpace::
* generatorsOfSpan::
* getLinearForms::
* getMultiplicity::
* inequalities::
* isFullSpace::
* isOrigin::
* isSimplicial::
* linealityDimension::
* linealitySpace::
* negatedCone::
* quotientLatticeBasis::
* randomPoint::
* rays::
* relativeInteriorPoint::
* semigroupGenerator::
* setLinearForms::
* setMultiplicity::
* span::
* uniquePoint::
@end menu

@c --------------------------------------
@node ambientDimension,canonicalizeCone,,cone related functions
@subsubsection ambientDimension
@cindex ambientDimension

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node canonicalizeCone,codimension,ambientDimension,cone related functions
@subsubsection canonicalizeCone
@cindex canonicalizeCone

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node codimension,coneLink,canonicalizeCone,cone related functions
@subsubsection codimension
@cindex codimension

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node coneLink,containsAsFace,codimension,cone related functions
@subsubsection coneLink
@cindex coneLink

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node containsAsFace,containsInSupport,coneLink,cone related functions
@subsubsection containsAsFace
@cindex containsAsFace

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node containsInSupport,containsPositiveVector,containsAsFace,cone related functions
@subsubsection containsInSupport
@cindex containsInSupport

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node containsPositiveVector,containsRelatively,containsInSupport,cone related functions
@subsubsection containsPositiveVector
@cindex containsPositiveVector

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node containsRelatively,convexHull,containsPositiveVector,cone related functions
@subsubsection containsRelatively
@cindex containsRelatively

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node convexHull,convexIntersection,containsRelatively,cone related functions
@subsubsection convexHull
@cindex convexHull

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node convexIntersection,dimension,convexHull,cone related functions
@subsubsection convexIntersection
@cindex convexIntersection

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node dimension,dualCone,convexIntersection,cone related functions
@subsubsection dimension
@cindex dimension

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node dualCone,equations,dimension,cone related functions
@subsubsection dualCone
@cindex dualCone

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node equations,facets,dualCone,cone related functions
@subsubsection equations
@cindex equations

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node facets,generatorsOfLinealitySpace,equations,cone related functions
@subsubsection facets
@cindex facets

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node generatorsOfLinealitySpace,generatorsOfSpan,facets,cone related functions
@subsubsection generatorsOfLinealitySpace
@cindex generatorsOfLinealitySpace

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node generatorsOfSpan,getLinearForms,generatorsOfLinealitySpace,cone related functions
@subsubsection generatorsOfSpan
@cindex generatorsOfSpan

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node getLinearForms,getMultiplicity,generatorsOfSpan,cone related functions
@subsubsection getLinearForms
@cindex getLinearForms

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node getMultiplicity,inequalities,getLinearForms,cone related functions
@subsubsection getMultiplicity
@cindex getMultiplicity

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node inequalities,isFullSpace,getMultiplicity,cone related functions
@subsubsection inequalities
@cindex inequalities

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node isFullSpace,isOrigin,inequalities,cone related functions
@subsubsection isFullSpace
@cindex isFullSpace

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node isOrigin,isSimplicial,isFullSpace,cone related functions
@subsubsection isOrigin
@cindex isOrigin

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node isSimplicial,linealityDimension,isOrigin,cone related functions
@subsubsection isSimplicial
@cindex isSimplicial

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node linealityDimension,linealitySpace,isSimplicial,cone related functions
@subsubsection linealityDimension
@cindex linealityDimension

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node linealitySpace,negatedCone,linealityDimension,cone related functions
@subsubsection linealitySpace
@cindex linealitySpace

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node negatedCone,quotientLatticeBasis,linealitySpace,cone related functions
@subsubsection negatedCone
@cindex negatedCone

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node quotientLatticeBasis,randomPoint,negatedCone,cone related functions
@subsubsection quotientLatticeBasis
@cindex quotientLatticeBasis

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node randomPoint,rays,quotientLatticeBasis,cone related functions
@subsubsection randomPoint
@cindex randomPoint

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node rays,relativeInteriorPoint,randomPoint,cone related functions
@subsubsection rays
@cindex rays

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node relativeInteriorPoint,semigroupGenerator,rays,cone related functions
@subsubsection relativeInteriorPoint
@cindex relativeInteriorPoint

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node semigroupGenerator,setLinearForms,relativeInteriorPoint,cone related functions
@subsubsection semigroupGenerator
@cindex semigroupGenerator

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node setLinearForms,setMultiplicity,semigroupGenerator,cone related functions
@subsubsection setLinearForms
@cindex setLinearForms

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node setMultiplicity,span,setLinearForms,cone related functions
@subsubsection setMultiplicity
@cindex setMultiplicity

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node span,uniquePoint,setMultiplicity,cone related functions
@subsubsection span
@cindex span

Not supported in this version of @sc{Singular}
@c --------------------------------------
@node uniquePoint,,span,cone related functions
@subsubsection uniquePoint
@cindex uniquePoint

Not supported in this version of @sc{Singular}
@c ---------------------------------------
@node fan, polytope, cone, Data types
@section fan
@cindex fan

Not supported in this version of @sc{Singular}
@menu
* fan related functions::
@end menu
@c --------------------------------------------------------------------
@node fan related functions,,,fan
@subsection fan related functions
@cindex fan related functions

See also @ref{ambientDimension},
@ref{codimension},
@ref{linealityDimension},
@ref{isSimplicial}.

@menu
* containsInCollection::
* emptyFan::
* fanViaCones::
* fullFan::
* fVector::
* getCone::
* insertCone::
* isCompatible::
@c * isComplete::
* isPure::
* nmaxcones::
* ncones::
* numberOfConesOfDimension::
* removeCone::
@end menu

@c --------------------------------------------------------------------
@node containsInCollection,emptyFan,,fan related functions
@subsubsection containsInCollection
@cindex containsInCollection

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node emptyFan,fanViaCones,containsInCollection,fan related functions
@subsubsection emptyFan
@cindex emptyFan

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node fanViaCones,fullFan,emptyFan,fan related functions
@subsubsection fanViaCones
@cindex fanViaCones

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node fullFan,fVector,fanViaCones,fan related functions
@subsubsection fullFan
@cindex fullFan

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node fVector,getCone,fullFan,fan related functions
@subsubsection fullFan
@cindex fVector

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node getCone,insertCone,fVector,fan related functions
@subsubsection getCone
@cindex getCone

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node insertCone,isCompatible,getCone,fan related functions
@subsubsection insertCone
@cindex insertCone

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node isCompatible,isPure,insertCone,fan related functions
@c @node isCompatible,isComplete,insertCone,fan related functions
@subsubsection isCompatible
@cindex isCompatible

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@c @node isComplete,isPure,isCompatible,fan related functions
@c @subsubsection isComplete
@c @cindex isComplete

@c Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node isPure,nmaxcones,isCompatible,fan related functions
@c @node isPure,nmaxcones,isComplete,fan related functions
@subsubsection isPure
@cindex isPure

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node nmaxcones,ncones,isPure,fan related functions
@subsubsection nmaxcones
@cindex nmaxcones

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node ncones,numberOfConesOfDimension,nmaxcones,fan related functions
@subsubsection ncones
@cindex ncones

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node numberOfConesOfDimension,removeCone,ncones,fan related functions
@subsubsection numberOfConesOfDimension
@cindex numberOfConesOfDimension

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node removeCone,,numberOfConesOfDimension,fan related functions
@subsubsection removeCone
@cindex removeCone

Not supported in this version of @sc{Singular}
@c ---------------------------------------
@node polytope, pyobject, fan, Data types
@section polytope
@cindex polytope

Not supported in this version of @sc{Singular}

@menu
* polytopeViaPoints::
* polytopeViaInequalities::
* polytope related functions::
@end menu
@c --------------------------------------------------------------------------------
@node polytopeViaPoints,polytopeViaInequalities,,polytope
@subsection polytopeViaPoints
@cindex polytopeViaPoints
Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------------------
@node polytopeViaInequalities,polytope related functions,polytopeViaPoints,polytope
@subsection polytopeViaInequalities
@cindex polytopeViaInequalities
Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node polytope related functions,,polytopeViaInequalities,polytope
@subsection polytope related functions
@cindex polytope related functions

Not supported in this version of @sc{Singular}
@menu
* dualPolytope::
* newtonPolytope::
* vertices::
@end menu

@c --------------------------------------------------------------------
@node dualPolytope,newtonPolytope,,polytope related functions
@subsubsection dualPolytope
@cindex dualPolytope

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node newtonPolytope,vertices,dualPolytope,polytope related functions
@subsubsection newtonPolytope
@cindex newtonPolytope

Not supported in this version of @sc{Singular}
@c --------------------------------------------------------------------
@node vertices,,newtonPolytope,polytope related functions
@subsubsection vertices
@cindex vertices

Not supported in this version of @sc{Singular}