-----------------------------------
AutoTherm Wolfram package reference
-----------------------------------

We refer to the :doc:`example notebook<../examples/wlpackage>` for some examples.

.. _AllMasses:

``AllMasses``
-------------

Simple function to compute the thermal masses of all particles in equilibrium

.. _AUTDecrypt:

``AUTDecrypt``
--------------

This function returns a list containing in parameters order:

 - The model path as needed by FeynArts 
 - The list of all gauge couplings 
 - The list of all parameters (that aren't external or don't have indices)

.. _AUThast:

``AUThast``
-----------

Label T and U denominators

.. _AUTIndexDelta:

``AUTIndexDelta``
-----------------

dummy delta function

.. _AUTstatspart:

``AUTstatspart``
----------------

Label statistics

.. _AUTSUNSimplify:

``AUTSUNSimplify``
------------------

Function to simplify the SU(N) algebra that might arise in the amplitudes.
The parameters are (in order):

 - The expression to simplify 
 - The symbol for the generator of the algebra. Assumed to be of the form ``gen[a,i,j]`` where a is an adjoint index and i,j are fundamental indices
 - The symbol for the structure constant of the algebra. Assumed to be of the form ``struct[a,b,c]`` where a,b,c are adjoint indices
 - The dimension of the algebra
 - The generation index

.. _ComputeMatrixElement:

``ComputeMatrixElement``
------------------------

This function computes the matrix element squared for the given 2->2 process. It sums over all degeneracies for all
external states

.. _ComputeTheAmp:

``ComputeTheAmp``
-----------------

Compute one of the amplitudes used in the thermal mass.
The first parameter is the particle whose thermal mass we want, the second parameter is any other particle in the thermal bath. The two parameters can thus be equal.

.. _ConfigParse:

``ConfigParse``
---------------

Parse the configuration and initialize the model.

.. _Cyclic:

``Cyclic``
----------

Helper function for SU(2), returns {:math:`a_n,a_1\ldots a_{n-1}`} from {:math:`a_1\ldots a_{n-1},a_n`}

.. _DoSameIndices:

``DoSameIndices``
-----------------

Function that takes the first part of the amplitude and returns the list of rules to put the indices equal to each other between particles 2 and 4.
The input is something like {...,...}->{...,...}

.. _DoThePolarization:

``DoThePolarization``
---------------------

Compute the polarization list for ``ToComponents``, see the ``VecSet`` documentation in the `FormCalc documentation`_.

.. _FormCalc documentation: https://feynarts.de/formcalc/FC9Guide.pdf

.. _DoTheProcesses:

``DoTheProcesses``
------------------

Compute all 2->2 matrix element squared for ``X[1] X[2] -> X[3] Y``, with ``Y`` the off-equilibrium particle and ``X[i]`` equilibrium ones.


.. _DoTheYukawa:

``DoTheYukawa``
---------------

This function handles the Yukawa sum.
It has 3 parameters (in order): 

 - The expression to simplify 
 - The symbol used for :math:`\epsilon_{ij}` 
 - The name used for the generation index

.. _FindExchanged:

``FindExchanged``
-----------------

This is a function to find the exchanged particle in a t or u channel diagram.
It takes the object created by ``InsertFields`` as an input

.. _FindPartLabel:

``FindPartLabel``
-----------------

Given a particle like :math:`\pm` ``X[n]``, ``FindPartLabel`` finds its label and adapts it if it's an anti-particle.
Returns a string

.. _FindStats:

``FindStats``
-------------

Given the list of particles, returns `AUTstatspart`_ [s1,s2,t1]

.. _ProcessResult:

``ProcessResult``
-----------------

Function to process the sum of the matrix elements squared. It also gets the list of intermediate particles for which we need to compute the thermal masses
if they mediate infrared-divergent exchanges.
Returns a ``json`` file to be read by :func:`analytical.controller.do_the_dict`.


.. _SUAlgebra:

``SUAlgebra``
-------------

Do the SU(N) and generation algebra analytically.
This function expects ``Taf[a,i,j]`` for a fundamental generator, ``sunf[a,b,c]`` for a structure function, ``id[a,b]``
for a Kronecker delta and ``eps[i,j]`` for an SU(2) antisymmetric fundamental tensor. 
In this way we avoid any possible conflict with FeynArts/FormCalc definitions.
``Extrarules`` is an optional argument, useful when dealing with non-SU(N) algebra elements such as Yukawa matrices

.. _Ta:

``Ta``
------

SU(2) fundamental generator

.. _TensorSum:

``TensorSum``
-------------

Function for the tensor polarisation sum, using the method of Eqs. (2.41) and (2.42) in `2004.11392`_.
For the moment defined to sum over one single leg.

.. _2004.11392: https://arxiv.org/abs/2004.11392

.. _TheFilter:

``TheFilter``
-------------

For a list of particles, return the list without the anti-particles IF the associated particle is present.

.. _ThermalMass:

``ThermalMass``
---------------

Compute the thermal mass of a given particle

.. _ToExclude:

``ToExclude``
-------------

Given the value of ``M$ClassesDescription``, find the list of particles to exclude from the self-energies

.. _ToStrWrapped:

``ToStrWrapped``
----------------

Wrapper around the ``ToString`` function from Mathematica to detect Mathematica functions like ``Abs[]`` or ``Conjugate[]``