passagemath-latte-4ti2

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

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SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

About this pip-installable distribution package

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://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/latte.html#module-sage.interfaces.latte>_

• Python interface to 4ti2 programs <https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/four_ti_2.html>_

• Raw access to all executables from Python using sage.features.latte <https://doc.sagemath.org/html/en/reference/spkg/sage/features/latte.html>_ and sage.features.four_ti_2 <https://doc.sagemath.org/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