.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/05_multiloop_graphs.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_05_multiloop_graphs.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_05_multiloop_graphs.py:


Massive Euclidean multiloop graphs
==================================

Graph construction, RMT scale integration, and numerical Hepp sectors.
Requires ``pip install '.[multiloop]'``. Errors are statistical estimates.

.. GENERATED FROM PYTHON SOURCE LINES 8-29




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

 .. code-block:: none

    Two-loop sunset: 2.3439237883304793 +/- 0.0001121289678955105
    Independent Clausen value: 2.34390723868945889060156228887
    Three-loop banana: 8.414374265374155 +/- 0.0001499799562677391
    Independent exact value: 8.41439832211715999779816713058
    U, F: (x0*x1 + x0*x2 + x1*x2, x0**2*x1 + x0**2*x2 + 4*x0*x1**2 + 19*x0*x1*x2 + 9*x0*x2**2 + 4*x1**2*x2 + 9*x1*x2**2)
    UV margins: {(0, 1): 1, (0, 2): 1, (1, 2): 1, (0, 1, 2): 1}
    Moving sunset: 0.6000549591783353






|

.. code-block:: Python

    import mpmath as mp
    from ramanujan_qft import ScalarEdge, ScalarGraph, integrate_graph

    # A two-loop equal-mass vacuum sunset, in D=2.
    sunset = ScalarGraph([ScalarEdge(0, 1, 1) for _ in range(3)])
    value = integrate_graph(sunset, D=2, epsrel=1e-4)
    print("Two-loop sunset:", value.value, "+/-", value.error_estimate)
    print("Independent Clausen value:", 4/mp.sqrt(3)*mp.im(mp.polylog(2, mp.exp(mp.j*mp.pi/3))))

    # Add a fourth propagator: a genuine three-loop graph, without a topology dispatch.
    banana = ScalarGraph([ScalarEdge(0, 1, 1) for _ in range(4)])
    value = integrate_graph(banana, D=2, epsrel=1e-4)
    print("Three-loop banana:", value.value, "+/-", value.error_estimate)
    print("Independent exact value:", 7*mp.zeta(3))

    # Unequal masses and conserved Euclidean external vectors.
    moving = ScalarGraph([ScalarEdge(0, 1, mass) for mass in (1, 4, 9)],
                         external_momenta={0: [2, 1], 1: [-2, -1]})
    print("U, F:", moving.symanzik()[1:])
    print("UV margins:", moving.uv_margins(D=2))
    print("Moving sunset:", integrate_graph(moving, D=2, epsrel=1e-3).value)


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

   **Total running time of the script:** (0 minutes 0.947 seconds)


.. _sphx_glr_download_auto_examples_05_multiloop_graphs.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 05_multiloop_graphs.ipynb <05_multiloop_graphs.ipynb>`

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

      :download:`Download Python source code: 05_multiloop_graphs.py <05_multiloop_graphs.py>`

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

      :download:`Download zipped: 05_multiloop_graphs.zip <05_multiloop_graphs.zip>`


.. only:: html

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

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