.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/06_sunset_rmt.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_06_sunset_rmt.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_06_sunset_rmt.py:


A graph-generated multivariate RMT series
==================================================

Exact bracket algebra, analytic pole resolution, and convergent summation.
This example uses no numerical integration backend.

.. GENERATED FROM PYTHON SOURCE LINES 8-30




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

 .. code-block:: none

    Bracket matrix: Matrix([[1, 1, 0, 0, 1, 1, 0], [1, 0, 1, 0, 1, 0, 1], [1, 0, 0, 1, 0, 1, 1], [1, 0, 0, 0, 1, 1, 1]])
    Gamma families: 8
    Chart: momentum
    Integral: 0.629016707590614149590827253884
    Tail bound: 2.0592e-32
    Unequal-mass vacuum: 0.185949303854726222708126019022
    Equal-mass vacuum correctly refused: no certified RMT chart: require p_E > m1+m2+m3, or M > m_a+m_b+p_E; boundaries and equal-mass vacuum are not covered. Received squared masses=(1, 1, 1), p_E^2=0, chart='auto'. For equal masses use integrate_sunset_taylor; otherwise consider integrate_graph with the multiloop extra as a numerical reference






|

.. code-block:: Python

    import mpmath as mp
    from ramanujan_qft import ScalarEdge, ScalarGraph, compile_sunset_rmt, RMTDomainError

    graph = ScalarGraph([ScalarEdge(0, 1, 1) for _ in range(3)],
                        external_momenta={0: [10], 1: [-10]})
    series = compile_sunset_rmt(graph)
    print("Bracket matrix:", series.bracket_system.matrix)
    print("Gamma families:", len(series.families))
    result = series.evaluate(dps=30)
    print("Chart:", result.chart)
    print("Integral:", mp.nstr(result.value, 30))
    print("Tail bound:", mp.nstr(result.truncation_bound, 5))

    vacuum = ScalarGraph([ScalarEdge(0, 1, m2) for m2 in (1, 4, 100)])
    result = compile_sunset_rmt(vacuum).evaluate(dps=30)
    print("Unequal-mass vacuum:", mp.nstr(result.value, 30))

    # This finite integral needs another series chart, not a forced summation.
    try:
        compile_sunset_rmt(ScalarGraph([ScalarEdge(0, 1, 1) for _ in range(3)]))
    except RMTDomainError as error:
        print("Equal-mass vacuum correctly refused:", error)


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

   **Total running time of the script:** (0 minutes 0.706 seconds)


.. _sphx_glr_download_auto_examples_06_sunset_rmt.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 06_sunset_rmt.ipynb <06_sunset_rmt.ipynb>`

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

      :download:`Download Python source code: 06_sunset_rmt.py <06_sunset_rmt.py>`

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

      :download:`Download zipped: 06_sunset_rmt.zip <06_sunset_rmt.zip>`


.. only:: html

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

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