For installation instructions, see the HowTo pages.

Starting up `polymake`

on the command line gives:

Welcome to polymake version 3.1 Copyright (c) 1997-2017 Ewgenij Gawrilow, Michael Joswig (TU Berlin) http://www.polymake.org This is free software licensed under GPL; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Press F1 or enter 'help;' for basic instructions. Application polytope currently uses following third-party software packages: cdd, jreality, libnormaliz, lrs, nauty, permlib, povray, ppl, sketch, sympol, threejs, tikz, tosimplex For more details: show_credits;

You will face an input prompt which indicates the start up application (usually `polytope >`

). After the prompt you can enter (an enriched form of) perl code. See this introduction and the advanced polymake/perl tutorial for more info.

`polymake`

s namespace is subdivided into so-called “applications”. They group functions and objects that belong together mathematically (see this article for more). For example, the default application `polytope`

deals with polyhedra, while `topaz`

provides tools for topology and `tropical`

for tropical geometry.

To switch to another application, do this:

application 'topaz';

There are introductory tutorials for all applications. Also check out the documentation.

Apart from the tutorials and HowTos, you can often find out what to do to reach your goal by using the built-in help features of the `polymake`

shell.

The polymake help system provides extensive usage information. In the shell, type

polytope > help;

to get started. Invoking

polytope > help 'help';

will explain thy syntax of the help system.

If you type part of an expresison in the shell, you can hit `TAB`

to display possible ways of completing it. For example, to see what methods you can invoke on the graph of the 3-cube, enter the following and hit `TAB`

:

polytope > cube(3)->GRAPH-> # hit TAB! add disable_rules MAX_CLIQUES set_as_default ADJACENCY dont_save name set_as_default_now apply_rule EDGE_DIRECTIONS N_CONNECTED_COMPONENTS SIGNATURE attach EDGES N_EDGES SIGNED_INCIDENCE_MATRIX AVERAGE_DEGREE EIGENVALUES_LAPLACIAN N_NODES SQUARED_EDGE_LENGTHS BICONNECTED_COMPONENTS get_attachment NODE_DEGREES STRONG_COMPONENTS BIPARTITE get_schedule NODE_IN_DEGREES STRONGLY_CONNECTED CHARACTERISTIC_POLYNOMIAL give NODE_LABELS take CONNECTED LATTICE_ACCUMULATED_EDGE_LENGTHS NODE_OUT_DEGREES TRIANGLE_FREE CONNECTED_COMPONENTS LATTICE_EDGE_LENGTHS properties type CONNECTIVITY list_attachments provide VISUAL DEGREE_SEQUENCE list_names remove WEAKLY_CONNECTED description list_properties remove_attachment WEAKLY_CONNECTED_COMPONENTS DIAMETER

You can conveniently access the `polymake`

documentation in the shell. Place the cursor above a thing you want to know about and hit `F1`

. Hitting it once will display brief info on types or function signatures. Hitting it a second time will show you the complete documentation, sometimes even small usage examples:

polytope > simplex( # hit F1 twice! functions/Producing a polytope from scratch/simplex: simplex(d; scale, Options) -> Polytope Produce the standard d-simplex. Combinatorially equivalent to a regular polytope corresponding to the Coxeter group of type A<sub>d-1</sub>. Optionally, the simplex can be scaled by the parameter scale. Arguments: Int d the dimension Scalar scale default value: 1 Options: group => Bool Returns Polytope Examples: *) To print the vertices (in homogeneous coordinates) of the standard 2-simplex, i.e. a right-angled isoceles triangle, type this: > print simplex(2)->VERTICES; (3) (0 1) 1 1 0 1 0 1 The first row vector is sparse and encodes the origin. *) To create a 3-simplex and also calculate its symmetry group, type this: > simplex(3, group=>1);

If you have any questions, feel free to ask in the forum.

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