polymake User Guide

Welcome to the user guide! Here you will find tutorials for various computation tasks as well as technical information about polymake's inner workings.

• Introduction Tutorial: Please read this first.
• Further general information about how polymake works
  • Using Perl within polymake
  • The polymake interactive shell
  • Objects and Properties
• If you plan on writing an polymake extension, you can find a user guide here.

These are introductory tutorials for the applications on the different mathematical topics you can use polymake for.

• fan for fans
• fulton for toric varieties
• graph for graphs
• group for groups and their actions on polymake objects
• matroid for matroids
• polytope for polyhedra
• topaz for topology
• tropical for tropical geometry

• Coordinates for Polyhedra
• Polytope Semantics
• Polytopes and Linear Maps

• polymake and Optimization by Sebastian Pokutta and Marc E. Pfetsch
• Integer Linear Programming tutorials:
  • ILP and Hilbert bases
  • Matching polytopes
  • A Counter-example to an integer analogue to Caratheodory's Theorem
  • Convex hulls and Lattice Points

• Basic visualization tutorial
• Embed interactive visualizations in PDF files

• Regular Subdivisions
• Lattice polytopes in polymake
• Face Lattices (of Polytopes)
• Polyhedral complexes
• Voronoi diagrams
• Random constructions
• Computing with polynomials
• Automorphisms of graphs
• General chain complexes and their homology
• Persistent Homology
• 1-flowing matroids (pdf) by Gordon F. Royle
• Wronski Polynomial Systems with polymake and Singular (Mega2013 submission)
• Patchworking real tropical hypersurfaces

• Save and load data in polymake
• Save and load an array of polytopes
• Measure execution time
• If you have not used polymake in a very long time

• Configuring polymake for a group of users
• Customizing the polymake interactive shell
• Configure interfaces to other software
• Using polymake with jupyter

Learn how to extend polymake.

• Scripting for “power users”
• Writing C++ clients
• Dealing with matrices and vectors
• Using the Callable Library
• Writing rule files
• Writing unit tests
• Writing and using extensions
• Dealing with data model changes

Details on selected topics, also linked from general pages above.

• Production rules
• Formatting help blocks
• Permutations
• Polymorphic functions
• Property type binding to C++ classes

• Guides for developers