polymake Lingo

This page wants to explain common terminology which is used throughout the documentation.


An application is a bunch of things which belong together mathematically. Within the polymake project applications form the highest level in the overall hierarchy of things. Each application comes with its own set of big objects.

The prompt in the polymake shell lists the currently active application. Switch via “application 'that_application';” or use the -A flag on the command line.

Within the source code an application is visible as the top level subdirectory “apps/this_application”. This directory always contains the file “rules/main.rules” which defines the big objects and the rules among them.

Each application defines a namespace, both in the Perl and the C++ realms. Applications can import types and functions from other applications' namespaces.

Examples are polytope, fan, matroid, fan, fulton, or tropical.

There is a special application “common” which takes care of much of the polymake magic ;-)


An extension is a bunch of things which do not belong to the polymake core.

An extension may define new applications and/or new big objects to existing applications and/or new rules for existing big objects.

Some extensions are “bundled”, that is, they are shipped with polymake. Bundled extensions allow for more flexible configuration. They primarily exist for legal or technical reasons.

Big Object

A big object is an instance of a data type which represents a mathematical concept with clear semantics.

Big objects are defined in a rule file which is included from apps/this_application/rules/main.rules. Big objects have properties which come with a type, which is either built-in or a small object type or a big object type. Big objects are immutable in the following sense: while, during the computation, properties may be added the actual instance of the mathematical concept does not change.

Big object types may have template parameters.

Examples are polytope::Polytope or topaz::SimplicialComplex.

In the rulefiles, big object types are simply referred to as objects.

Here is an svg file to describe the version 3.2 big object hierarchy.

Small Object

A small object is an instance of one of the many data types commonly used in computer science.

Small object types are implemented in C++ and may or may not be accessible from the Perl side of polymake. The magic files for gluing the C++ world and the Perl world mostly reside in apps/common/rules.

Small object types may have template parameters.

Examples are Array, Set or Map.

In the rulefiles, small object types are referred to as property types, because they are used, first of all, for definition of atomic properties of big objects.

howto/lingo.txt · Last modified: 2018/02/13 13:24 by benmuell
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