.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/combinatorics/pascals_triangle/plot_01_triangle_and_binomials.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_combinatorics_pascals_triangle_plot_01_triangle_and_binomials.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_combinatorics_pascals_triangle_plot_01_triangle_and_binomials.py:


Pascal's triangle vs. scipy-computed binomial coefficients
==================================================================

Builds Pascal's triangle by hand via the addition recurrence and
confirms every entry matches ``scipy.special.comb``.

.. GENERATED FROM PYTHON SOURCE LINES 10-13

.. code-block:: Python

    from mathematicskit.combinatorics import combinations_count, pascals_triangle
    from mathematicskit.combinatorics.visualizers.plots import plot_pascals_triangle








.. GENERATED FROM PYTHON SOURCE LINES 14-16

Build and cross-check
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 16-24

.. code-block:: Python


    triangle = pascals_triangle(10)
    for n, row in enumerate(triangle):
        print(f"n={n}: {row}")
        for k, value in enumerate(row):
            assert value == combinations_count(n, k)
    print("\nevery entry matches scipy.special.comb")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    n=0: [1]
    n=1: [1, 1]
    n=2: [1, 2, 1]
    n=3: [1, 3, 3, 1]
    n=4: [1, 4, 6, 4, 1]
    n=5: [1, 5, 10, 10, 5, 1]
    n=6: [1, 6, 15, 20, 15, 6, 1]
    n=7: [1, 7, 21, 35, 35, 21, 7, 1]
    n=8: [1, 8, 28, 56, 70, 56, 28, 8, 1]
    n=9: [1, 9, 36, 84, 126, 126, 84, 36, 9, 1]

    every entry matches scipy.special.comb




.. GENERATED FROM PYTHON SOURCE LINES 25-27

Visualize
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-29

.. code-block:: Python


    plot_pascals_triangle(triangle)



.. image-sg:: /api/gallery/combinatorics/pascals_triangle/images/sphx_glr_plot_01_triangle_and_binomials_001.png
   :alt: Pascal's triangle
   :srcset: /api/gallery/combinatorics/pascals_triangle/images/sphx_glr_plot_01_triangle_and_binomials_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Axes: title={'center': "Pascal's triangle"}, xlabel='k', ylabel='n'>




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.016 seconds)


.. _sphx_glr_download_api_gallery_combinatorics_pascals_triangle_plot_01_triangle_and_binomials.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_triangle_and_binomials.ipynb <plot_01_triangle_and_binomials.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_triangle_and_binomials.py <plot_01_triangle_and_binomials.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_triangle_and_binomials.zip <plot_01_triangle_and_binomials.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_