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Computational Verification of the Cone Conjecture v1.0

Written and tested in Ubuntu 16.04.4 LTS (xenial), using the development branch of SAGE also.

This is a computational experiment, implementing the Top Down and Bottom Up algorithms found in "The Poset of Rational Cones" (

Getting Started


SAGE - Make sure to compile SAGE from source so that custom packages can be used! Download the developer branch from git.

Similarly, make Normaliz and PyNormaliz. Need to document the installation process for getting the development branch pyNormaliz2

Check ticket #25090 Once closed.

  1. Update sage by navigating to the sage folder, then do the following four commands:
1)	git checkout develop
2)	make
3)	sage -i normaliz
4)	sage -i pynormaliz

Check when a ticket is merged in which version:!forum/sage-release


Install dependencies, save the .py files listed below to the same directory. Then run from terminal in that directory:

chmod +x

And have fun~

The data will be outputted into the folder "DATA/{}d/experiment_name" where {} is the dimension of the experiment, and experiment_name is what you choose in the UI.

Main .json file will be named the same as the experiment name. Data Summary.text - read the title. Graphs : "SIZE" - the number of hilbert basis elements. "LENGTH" - the euclidean norm of the longest element of the hilbert basis element.


Main UI for interfacing with ConeChain objects, and allows user to create, load, generate and save data.

Data structure to store the possible poset chains and the algorithms top_down and bottom_up.

Data structure to hold a polyhedral cone (sage.all.Polyhedra) and holds the hilbert basis of said cone, so that the calculation needs to only be done once.

Holds functions that are used in the top_down and bottom_up algorithms

Holds I/O functions that simplify coding work for cone_conjecture_tester, such as custom menus and user input functions.


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