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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 software is copyright (C) 2020 by Tobias Boege. This is free software; you can redistribute it and/or modify it under the terms of the Artistic License 2.0.