.. _spkg_sagemath_latte_4ti2:

====================================================================================================
sagemath_latte_4ti2: Lattice points in polyhedra with LattE integrale and 4ti2
====================================================================================================


This pip-installable source distribution ``passagemath-latte-4ti2`` provides an interface
to `LattE integrale <https://www.math.ucdavis.edu/~latte/>`_
(for the problems of counting lattice points in and integration over convex polytopes)
and `4ti2 <https://github.com/4ti2/4ti2>`_
(for algebraic, geometric and combinatorial problems on linear spaces).


What is included
----------------

- `Python interface to LattE integrale programs <https://passagemath.org/docs/latest/html/en/reference/interfaces/sage/interfaces/latte.html#module-sage.interfaces.latte>`_

- `Python interface to 4ti2 programs <https://passagemath.org/docs/latest/html/en/reference/interfaces/sage/interfaces/four_ti_2.html>`_

- Raw access to all executables from Python using `sage.features.latte <https://passagemath.org/docs/latest/html/en/reference/spkg/sage/features/latte.html>`_ and `sage.features.four_ti_2 <https://passagemath.org/docs/latest/html/en/reference/spkg/sage/features/four_ti_2.html>`_

- The binary wheels published on PyPI include a prebuilt copy of
  LattE integrale and 4ti2.


Examples
--------

Using LattE integrale and 4ti2 programs on the command line::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-latte-4ti2" sage -sh -c 'ppi 5'
    ...
    ### This makes 47 PPI up to sign
    ### Writing data file ppi5.gra and matrix file ppi5.mat done.

Finding the installation location of a LattE integrale or 4ti2 program in Python::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-latte-4ti2[test]" ipython

    In [1]: from sage.features.latte import Latte_count

    In [2]: Latte_count().absolute_filename()
    Out[2]: '/Users/mkoeppe/.local/pipx/.cache/2dc147a5e4863b4/lib/python3.11/site-packages/sage_wheels/bin/count'

    In [3]: from sage.features.four_ti_2 import FourTi2Executable

    In [4]: FourTi2Executable('ppi').absolute_filename()
    Out[2]: '/Users/mkoeppe/.local/pipx/.cache/2dc147a5e4863b4/lib/python3.11/site-packages/sage_wheels/bin/ppi'

Using the low-level Python interfaces::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-latte-4ti2[test]" ipython

    In [1]: from sage.interfaces.latte import count

    In [2]: cdd_Hrep = 'H-representation\nbegin\n 6 4 rational\n 2 -1 0 0\n 2 0 -1 0\n 2 0 0 -1\n 2 1 0 0\n 2 0 0 1\n 2 0 1 0\nend\n'

    In [3]: count(cdd_Hrep, cdd=True)
    Out[3]: 125

Use with sage.geometry.polyhedron::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-latte-4ti2[test]" ipython

    In [1]: from sage.all__sagemath_polyhedra import *

    In [2]: P = Polyhedron(vertices=[[1,0,0], [0,0,1], [-1,1,1], [-1,2,0]])

    In [3]: P.volume(measure='induced_lattice', engine='latte')
    Out[3]: 3


Type
----

optional


Dependencies
------------

- $(PYTHON)
- $(PYTHON_TOOLCHAIN)
- :ref:`spkg_4ti2`
- :ref:`spkg_cysignals`
- :ref:`spkg_cython`
- :ref:`spkg_gmp`
- :ref:`spkg_latte_int`
- :ref:`spkg_mpc`
- :ref:`spkg_mpfr`
- :ref:`spkg_pkgconf`
- :ref:`spkg_pkgconfig`
- :ref:`spkg_sage_conf`
- :ref:`spkg_sage_setup`
- :ref:`spkg_sagemath_categories`
- :ref:`spkg_sagemath_cddlib`
- :ref:`spkg_sagemath_environment`
- :ref:`spkg_sagemath_objects`
- :ref:`spkg_setuptools`

Version Information
-------------------

package-version.txt::

    10.6.13

version_requirements.txt::

    passagemath-latte-4ti2 ~= 10.6.13.0

Equivalent System Packages
--------------------------

(none known)
