Conditional Independence Net

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# NAME

CInet::Polyhedral - Building blocks for polyhedral geometry

# SYNOPSIS

# Imports all related modules
use CInet::Polyhedral;

## VERSION

This document describes CInet::Polyhedral v0.1.0.

# DESCRIPTION

This module provides access to software for polyhedral geometry,
in particular to a linear programming solver. Linear programming is known
to apply to conditional independence through concepts such as polymatroids
and structural semigraphoids.

The main object of this module is a [CInet::Imset](/doc/CInet%3A%3AImset). An _imset_ is an
**i**nteger-valued **m**ulti**set**. It associates to each subset of a given
set `N` an integer number. Studený uses imsets in the theory of conditional
independence structures to describe information inequalities, that is linear
inequalities with integer coefficients on the cone on multiinformation
functions, the faces of which correspond to CI structures. The work of
Matúš studies dually integer polymatroids, which are abstractions of
entropies or multiinformation functions, which can also be written as
imsets. Each imset requires a [CInet::Cube](/doc/CInet%3A%3ACube) domain over which (that
is over whose vertices) it is defined.

In the future, syntactic sugar similar to [CInet::Propositional](/doc/CInet%3A%3APropositional) will
be provided to write down linear programs for CI purposes clearly and
quickly. Based on this, objects and methods will be added which expose
the link between polyhedral geometry and CI implication but also blend
in with the interface of [CInet::Base](/doc/CInet%3A%3ABase).

# AUTHOR

Tobias Boege <tobs@taboege.de>

# COPYRIGHT AND LICENSE

This is free software; you can redistribute it and/or
modify it under the terms of the Artistic License 2.0.