### D.13.1 polymake_lib

Library:
  polymake.lib
Purpose:
  Computations with polytopes and fans, interface to polymake and TOPCOM
Author:
  Thomas Markwig, email: keilen@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
  - polymake by Ewgenij Gawrilow, TU Berlin and Michael Joswig, TU Darmstadt
  (see http://www.math.tu-berlin.de/polymake/),
  respectively (only in the procedure triangulations) by the program
  - topcom by Joerg Rambau, Universitaet Bayreuth (see
  http://www.uni-bayreuth.de/departments/wirtschaftsmathematik/rambau/TOPCOM);
  this library should rather be seen as an interface which allows to use a (very limited) number of options which polymake respectively 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 polymake or topcom, if the options offered here are sufficient for his purposes.
  Note, though, that the procedures concerned with planar polygons are independent of both, polymake and topcom.

Procedures using polymake:

> D.13.1.1 polymakePolytope |  | computes the vertices of a polytope using polymake
> D.13.1.2 newtonPolytopeP |  | computes the Newton polytope of a polynomial
> D.13.1.3 newtonPolytopeLP |  | computes the lattice points of the Newton polytope
> D.13.1.4 normalFanL |  | computes the normal fan of a polytope
> D.13.1.5 groebnerFanP |  | computes the Groebner fan of a polynomial

Procedures using topcom:

> D.13.1.6 triangulations |  | computes all triangulations of a marked polytope
> D.13.1.7 secondaryPolytope |  | computes the secondary polytope of a marked polytope

Procedures using polymake and topcom:

> D.13.1.8 secondaryFan |  | computes the secondary fan of a marked polytope

Procedures conerned with planar polygons:

> D.13.1.9 cycleLength |  | computes the cycleLength of cycle
> D.13.1.10 splitPolygon |  | splits a marked polygon into vertices, facets, interior points
> D.13.1.11 eta |  | computes the eta-vector of a triangulation
> D.13.1.12 findOrientedBoundary |  | computes the boundary of a convex hull
> D.13.1.13 cyclePoints |  | computes lattice points connected to some lattice point
> D.13.1.14 latticeArea |  | computes the lattice area of a polygon
> D.13.1.15 picksFormula |  | computes the ingrediants of Pick's formula for a polygon
> D.13.1.16 ellipticNF |  | computes the normal form of an elliptic polygon
> D.13.1.17 ellipticNFDB |  | displays the 16 normal forms of elliptic polygons

User manual for Singular version 4-0-3, 2016, generated by texi2html.