Metadata-Version: 1.1
Name: cn-hyperarr
Version: 0.0.1
Summary: Computation of congruence normality for hyperplane arrangements
Home-page: https://github.com/sophiasage/cn_hyperarr
Author: Sophia Elia
Author-email: sophiae56@zedat.fu-berlin.de
License: GNU General Public License v3
Description: ===================================================
        Congruence Normality for Hyperplane Arrangements
        ===================================================
        .. image:: https://travis-ci.com/sophiasage/cn_hyperarr.svg?branch=master
            :target: https://travis-ci.com/sophiasage/cn_hyperarr
        .. image:: https://travis-ci.org/sophiasage/cn_hyperarr.svg?branch=master
            :target: https://travis-ci.com/sophiasage/cn_hyperarr
        
        This package is a `SageMath <http://www.sagemath.org>`_ package for 
        computing congruence normality of rank-three, simplicial hyperplane arrangements.
        
        This package includes a database of known rank-three simplicial hyperplane
        arrangements. It also includes modules for creating vector configurations and 
        the three infinite families of simplicial rank-three arrangements.
        A vector configuration can be seen as the set of normals to a hyperplane
        arrangement. A simplicial hyperplane arrangement has a lattice of regions 
        associated to each chamber. This lattice is congruence normal if it is 
        obtainable through a sequence of doublings of convex sets. 
        A hyperplane arrangement can be always or sometimes or never congruence normal,
        depending on whether its lattices of regions are congruence normal.
        
        Here are examples of arrangements that are always, sometimes, and never
        congruence normal. 
        First we load the normals of the three arrangements from the database. 
        The entries of the database are labeled in the same way as in [CEL]_::
        
            sage: from cn_hyperarr import *
            sage: always_normals = db_normals_CEL[(6,24,1)] 
            sage: somet_normals = db_normals_CEL[(10,60,3)]
            sage: never_normals = db_normals_CEL[(22,288,1)]
        
            Now we make them into vector configurations::
        
            sage: always_vc = VectorConfiguration([vector(x) for x in always_normals]) 
            sage: somet_vc = VectorConfiguration([vector(x) for x in somet_normals]) 
            sage: never_vc = VectorConfiguration([vector(x) for x in never_normals])
             
            To test congruence normality, use the function `RegionsCongruenceNormal`::
        
            sage: always_check = RegionsCongruenceNormality(always_vc)
            sage: always_vals_list = list(always_check.values())
            sage: [always_vals_list.count(True), always_vals_list.count(False)]
            [24,0]
            sage: somet_check = RegionsCongruenceNormality(somet_vc)
            sage: somet_vals_list = list(somet_check.values())
            sage: [somet_vals_list.count(True), somet_vals_list.count(False)]
            [40,20]
            sage: never_check = RegionsCongruenceNormality(never_vc)
            sage: never_vals_list = list(never_check.values())
            sage: [never_vals_list.count(True), never_vals_list.count(False)]
            [0,288]
        
        The full documentation for the package can be found at https://sophiasage.github.io/cn_hyperarr/doc/html/
        
        Notebooks
        ---------
        
        You can experience this package on a binder notebook (click on the binder image):
        
        .. image:: https://mybinder.org/badge.svg 
           :target: https://mybinder.org/v2/gh/sophiasage/cn_hyperarr/master?filepath=notebooks/examples.ipynb
        
        
        References
        ----------
        
        .. [CEL] Michael Cuntz, Sophia Elia, and Jean-Philippe Labbé. Congruence normality of simplicial hyperplane arrangements via oriented matroids, 2020. arXiv:2009.14152.
        
        .. [Gru] Branko Grunbaum. A catalogue of simplicial arrangements in the real projective plane, 2009. Ars Math. Contemp. 2, no. 1, 1-25.
        
        Installation
        ------------
        
        Local install from source
        ^^^^^^^^^^^^^^^^^^^^^^^^^
        
        Download the source from the git repository::
        
            $ git clone https://github.com/sophiasage/cn_hyperarr.git
        
        Change to the root directory and run::
        
            $ sage -pip install --upgrade --no-index -v .
        
        For convenience this package contains a [makefile](makefile) with this
        and other often used commands. Should you wish too, you can use the
        shorthand::
        
            $ make install
        
Keywords: SageMath packaging
Platform: UNKNOWN
Classifier: 
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Classifier: Programming Language :: Python :: 3.1
Classifier: 
