> | ### D.13.4 polymake_lib Library: polymake.lib Purpose: Computations with polytopes and fans, interface to TOPCOM Author: Thomas Markwig, email: keilen@mathematik.uni-kl.de Yue Ren, email: ren@mathematik.uni-kl.de Warning: Most procedures will not work unless polymake or topcom is installed and if so, they will only work with the operating system LINUX! For more detailed information see IMPORTANT NOTE respectively consult the help string of the procedures. The conventions used in this library for polytopes and fans, e.g. the length and labeling of their vertices resp. rays, differs from the conventions used in polymake and thus from the conventions used in the polymake extension polymake.so of Singular. We recommend to use the newer polymake.so whenever possible. Important note: Even though this is a Singular library for computing polytopes and fans such as the Newton polytope or the Groebner fan of a polynomial, most of the hard computations are NOT done by Singular but by the program - TOPCOM by Joerg Rambau, Universitaet Bayreuth (see http://www.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/); this library should rather be seen as an interface which allows to use a (very limited) number of options which topcom offers to compute with polytopes and fans and to make the results available in Singular for further computations; moreover, the user familiar with Singular does not have to learn the syntax of topcom, if the options offered here are sufficient for his purposes. Note, though, that the procedures concerned with planar polygons are independent of topcom. Procedures using topcom:
> D.13.4.1 triangulations |  | computes all triangulations of a marked polytope
> D.13.4.2 secondaryPolytope |  | computes the secondary polytope of a marked polytope
> Procedures concerned with planar polygons:
> D.13.4.3 cycleLength |  | computes the cycleLength of cycle
> D.13.4.4 splitPolygon |  | splits a marked polygon into vertices, facets, interior points
> D.13.4.5 eta |  | computes the eta-vector of a triangulation
> D.13.4.6 findOrientedBoundary |  | computes the boundary of a convex hull
> D.13.4.7 cyclePoints |  | computes lattice points connected to some lattice point
> D.13.4.8 latticeArea |  | computes the lattice area of a polygon
> D.13.4.9 picksFormula |  | computes the ingrediants of Pick's formula for a polygon
> D.13.4.10 ellipticNF |  | computes the normal form of an elliptic polygon

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