.. _spkg_sagemath_giac:

================================================================================================
sagemath_giac: Symbolic computation with Giac
================================================================================================


`Giac/Xcas <https://www-fourier.ujf-grenoble.fr/~parisse/giac.html>`_
is a general purpose Computer algebra system by Bernard Parisse released under GPLv3.
It has been developed since 2000 and is widely used: Giac/Xcas is the native CAS engine
of the HP Prime calculators; the C++ kernel of the system, Giac, provides the CAS view
of `Geogebra <https://www.geogebra.org/>`_.

This pip-installable source distribution ``passagemath-giac`` makes Giac available
from Python and provides integration with the Sage Mathematical Software System.


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

- `Cython interface to GIAC <https://passagemath.org/docs/latest/html/en/reference/libs/sage/libs/giac.html>`_

  The Cython interface is by Frederic Han and was previously available under the name
  `giacpy-sage <https://gitlab.math.univ-paris-diderot.fr/han/giacpy-sage/>`_.
  It was merged into the Sage library in 2020.

- `Pexpect interface to GIAC <https://passagemath.org/docs/latest/html/en/reference/interfaces/sage/interfaces/giac.html>`_

- see https://github.com/passagemath/passagemath/blob/main/pkgs/sagemath-giac/MANIFEST.in

- The binary wheels on PyPI ship a prebuilt copy of the Giac library.


Examples
--------

A quick way to try it out interactively::

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

    In [1]: from sage.all__sagemath_giac import *

    In [2]: x = libgiac('x')

    In [3]: V = [[x[i]**j for i in range(8)] for j in range(8)]

    In [4]: libgiac(V).dim()
    Out[4]: [8,8]

    In [5]: libgiac.det_minor(V).factor()
    Out[5]: (x[6]-(x[7]))*(x[5]-(x[7]))*(x[5]-(x[6]))*(x[4]-(x[7]))*(x[4]-(x[6]))*(x[4]-(x[5]))*(x[3]-(x[7]))*(x[3]-(x[6]))*(x[3]-(x[5]))*(x[3]-(x[4]))*(x[2]-(x[7]))*(x[2]-(x[6]))*(x[2]-(x[5]))*(x[2]-(x[4]))*(x[2]-(x[3]))*(x[1]-(x[7]))*(x[1]-(x[6]))*(x[1]-(x[5]))*(x[1]-(x[4]))*(x[1]-(x[3]))*(x[1]-(x[2]))*(x[0]-(x[7]))*(x[0]-(x[6]))*(x[0]-(x[5]))*(x[0]-(x[4]))*(x[0]-(x[3]))*(x[0]-(x[2]))*(x[0]-(x[1]))

    In [6]: (x+5)**(1/3)        # note here 1/3 is done in Python before being sent to Giac
    Out[6]: (x+5)^0.333333333333

    In [7]: (x+5)**QQ('1/3')    # using Sage rationals
    Out[7]: (x+5)^(1/3)

    In [8]: from fractions import Fraction  # using Python rationals

    In [9]: (x+5)**Fraction(1,3)
    Out[9]: (x+5)^(1/3)

The last example again, using the Sage REPL::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-giac[test]" sage
    Warning: sage.all is not available; this is a limited REPL.

    sage: from sage.all__sagemath_giac import *

    sage: x = libgiac('x')

    sage: (x+5)^(1/3)           # the Sage preparser translates this to (x+5)**QQ('1/3')
    (x+5)^(1/3)


Type
----

optional


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

- $(PYTHON)
- $(PYTHON_TOOLCHAIN)
- :ref:`spkg_cysignals`
- :ref:`spkg_cython`
- :ref:`spkg_giac`
- :ref:`spkg_gmp`
- :ref:`spkg_gmpy2`
- :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_environment`
- :ref:`spkg_setuptools`

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

package-version.txt::

    10.6.29

version_requirements.txt::

    passagemath-giac ~= 10.6.29.0

Installation commands
---------------------

.. tab:: PyPI:

   .. CODE-BLOCK:: bash

       $ pip install passagemath-giac~=10.6.29.0

.. tab:: Sage distribution:

   .. CODE-BLOCK:: bash

       $ sage -i sagemath_giac


However, these system packages will not be used for building Sage
because ``spkg-configure.m4`` has not been written for this package;
see :issue:`27330` for more information.
