{
    "info": {
        "author": "Permuta Triangle",
        "author_email": "permutatriangle@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Intended Audience :: Education",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: BSD License",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.5",
            "Programming Language :: Python :: 3.6",
            "Programming Language :: Python :: 3.7",
            "Programming Language :: Python :: Implementation :: CPython",
            "Programming Language :: Python :: Implementation :: PyPy",
            "Topic :: Education",
            "Topic :: Scientific/Engineering :: Mathematics"
        ],
        "description": "Tilings\n=======\n\n.. image:: https://travis-ci.org/PermutaTriangle/Tilings.svg?branch=master\n    :alt: Travis\n    :target: https://travis-ci.org/PermutaTriangle/Tilings\n.. image:: https://coveralls.io/repos/github/PermutaTriangle/Tilings/badge.svg?branch=master\n    :alt: Coveralls\n    :target: https://coveralls.io/github/PermutaTriangle/Tilings?branch=master\n.. image:: https://img.shields.io/pypi/v/Tilings.svg\n    :alt: PyPI\n    :target: https://pypi.python.org/pypi/Tilings\n.. image:: https://img.shields.io/pypi/l/Tilings.svg\n    :target: https://pypi.python.org/pypi/Tilings\n.. image:: https://img.shields.io/pypi/pyversions/Tilings.svg\n    :target: https://pypi.python.org/pypi/Tilings\n.. image:: https://requires.io/github/PermutaTriangle/Tilings/requirements.svg?branch=master\n     :target: https://requires.io/github/PermutaTriangle/Tilings/requirements/?branch=master\n     :alt: Requirements Status\n\n\n``tilings`` is a Python library for working with gridded permutation and\ntilings.\n\nInstalling\n----------\n\nTo install ``tilings`` on your system, run:\n\n.. code:: bash\n\n       pip install tilings\n\nIt is also possible to install ``tilings`` in development mode to work\non the source code, in which case you run the following after cloning\nthe repository:\n\n.. code:: bash\n\n       ./setup.py develop\n\nTo run the unit tests:\n\n.. code:: bash\n\n       ./setup.py test\n\nWhat are gridded permutations and tilings?\n------------------------------------------\n\nWe will be brief in our definitions here, for more details see\n`Christian Bean\u2019s PhD thesis <https://skemman.is/handle/1946/31663>`__.\n\nA ``gridded permutation`` is a pair ``(\u03c0, P)`` where ``\u03c0`` is a\npermutation and ``P`` is a tuple of cells, called the positions, that\ndenote the cells in which the points of ``\u03c0`` are drawn on a grid. Let\n``G`` denote the set of all gridded permutations. Containment of gridded\npermutations is defined the same as containment of permutations, except\nincluding the preservation of the cells.\n\nA ``tiling`` is a triple ``T = ((n, m), O, R)``, where ``n`` and ``m``\nare positive integers, ``O`` is a set of gridded permutations called\n``obstructions``, and ``R`` is a set of sets of gridded permutations\ncalled ``requirements``.\n\nWe say a gridded permutations avoids a set of gridded permutations if it\navoids all of the permutations in the set, otherwise it contains the\nset. To contain a set, therefore, means contains at least one in the\nset. The set of gridded permutations on a tiling ``Grid(T)`` is the set\nof all gridded permutations in the ``n x m`` grid that avoids ``O`` and\ncontains each set ``r`` in ``R``.\n\nUsing tilings\n-------------\n\nOnce you\u2019ve installed ``tilings``, it can be imported by a Python script\nor an interactive Python session, just like any other Python library:\n\n.. code:: python\n\n       >>> from tilings import *\n\nImporting ``*`` from it supplies you with the \u2018GriddedPerm\u2019,\n\u2018Obstruction\u2019, \u2018Requirement\u2019, and \u2018Tiling\u2019 classes.\n\nAs above, a gridded permutation is a pair ``(\u03c0, P)`` where ``\u03c0`` is a\npermutation and ``P`` is a tuple of cells. The permutation is assumed to\nbe a ``Perm`` from the ``permuta`` Python library. Not every tuple of\ncells is a valid position for a given permutation. This can be checked\nusing the ``contradictory`` method.\n\n.. code:: python\n\n       >>> from permuta import Perm\n       >>> gp = GriddedPerm(Perm((0, 2, 1)), ((0, 0), (0, 0), (1, 0)))\n       >>> gp.contradictory()\n       False\n       >>> gp = GriddedPerm(Perm((0, 1, 2)), ((0, 0), (0, 1), (0, 0)))\n       >>> gp.contradictory()\n       True\n\nA ``Tiling`` is created with an iterable of ``Obstruction`` and an\niterable of ``Requirement`` lists. It is assumed that all cells not\nmentioned in some obstruction or requirement is empty. You can print the\ntiling to get an overview of the tiling created. In this example, we\nhave a tiling that corresponds to non-empty permutation avoiding\n``123``.\n\n.. code:: python\n\n       >>> obstructions = [Obstruction.single_cell(Perm((0, 1)), (1, 1)),\n       ...                 Obstruction.single_cell(Perm((1, 0)), (1, 1)),\n       ...                 Obstruction.single_cell(Perm((0, 1)), (0, 0)),\n       ...                 Obstruction.single_cell(Perm((0, 1, 2)), (2, 0)),\n       ...                 Obstruction(Perm((0, 1, 2)), ((0, 0), (2, 0), (2, 0)))]\n       >>> requirements = [[Requirement.single_cell(Perm((0,)), (1, 1))]]\n       >>> til = Tiling(obstructions, requirements)\n       >>> print(til)\n       +-+-+-+\n       | |\u25cf| |\n       +-+-+-+\n       |\\| |1|\n       +-+-+-+\n       1: Av(012)\n       \\: Av(01)\n       \u25cf: point\n       Crossing obstructions:\n       012: (0, 0), (2, 0), (2, 0)\n       Requirement 0:\n       0: (1, 1)\n       >>> til.dimensions\n       (3, 2)\n       >>> sorted(til.active_cells)\n       [(0, 0), (1, 1), (2, 0)]\n       >>> til.point_cells\n       frozenset({(1, 1)})\n       >>> sorted(til.possibly_empty)\n       [(0, 0), (2, 0)]\n       >>> til.positive_cells\n       frozenset({(1, 1)})\n\nThere are a number of methods available on the tiling. You can generate\nthe gridded permutations satisfying the obtructions and requirements\nusing the ``gridded_perms_of_length`` method.\n\n.. code:: python\n\n       >>> for i in range(4):\n       ...     for gp in til.gridded_perms_of_length(i):\n       ...         print(gp)\n       0: (1, 1)\n       10: (1, 1), (2, 0)\n       01: (0, 0), (1, 1)\n       210: (1, 1), (2, 0), (2, 0)\n       201: (1, 1), (2, 0), (2, 0)\n       120: (0, 0), (1, 1), (2, 0)\n       021: (0, 0), (1, 1), (2, 0)\n       102: (0, 0), (0, 0), (1, 1)\n\nThere are numerous other methods and properties. Many of these specific\nto the ``tilescope`` algorithm, discussed in `Christian Bean\u2019s PhD\nthesis <https://skemman.is/handle/1946/31663>`__.",
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