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.
• Another, very old and long intro tutorial...
• and another introductory demo!
• Using Perl within polymake.
• A bit of polymake lingo: What is an “application”? What is a “big”/“small” object? …
• The polymake interactive shell
• Objects and Properties

• Construct and analyze polytopes

• Short introduction to the application on fans (in preparation)

• Short introduction to the application on matroids

• Dealing with Graphs

• Groups and their actions on polymake objects

• Introduction to the application topaz

• Introduction to the application tropical. Also see Hampe & Joswig, Tropical Computations in polymake, arXiv version

• Short introduction to the application on toric varieties (in preparation)

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

• polymake and Optimization
• Integer Linear Programming tutorials:
  • ILP and Hilbert bases
  • Matching polytopes
  • A Counter-example to an integer analogue to Caratheodory's Theorem
  • Branch & Bound by Michael Schmitt
  • Gomory Cuts by Michael Schmitt
  • 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)

• If you have not used polymake in a long time
• Save and load data in polymake
• Save and load an array of polytopes
• Measure execution time
• Using the polyDB Database
  • Introduction to polyDB explains basic database access functionality
  • Writing to the database explains write and update functionality

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

Learn how to extend polymake.

• Scripting for “power users”
• Writing C++ clients
• Dealing with matrices and vectors
• Using Callable Library (from release 2.10 on)
• Writing rule files
• Writing and using extensions

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