# First steps with polymake

### Installation

To get your copy of polymake, visit the downloads page. For installation instructions, see the installation instructions.

### Getting started

Once you have polymake installed, fire it up by entering `polymake`

on the command line. You should be presented with a greeting, followed by an input prompt which looks like this:

polytope >

After the prompt you can enter an enriched form of perl code. You will probably want to look at some of the various code examples performing tasks of different complexity that can be found in the tutorials. Also see the polymake-perl introduction for more info.

To get helpful tips on things you can do in the shell, visit the interactive shell wiki page.

### Applications

An application is a collection of object types, functions and other stuff all related to some distinct mathematical subject. Currently polymake consists of the following applications:

- 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

The prompt in the polymake shell indicates the currently active application. You can switch by typing

application 'topaz';

The only difference between the current application and the rest is that you can call the functions and object constructors of the former without having to qualify them with the application name as a prefix. To use things from other applications, you need to do this:

topaz > $c = polytope::cube(3);

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

### Getting help

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

Apart from reading the user guide, 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 > $c = cube(3); polytope > $c->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);

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