Translated documentation with latex changes

docs/source/_ext/pygments_mad_lexer.py

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+# -- Custom Lexer ------------------------------------------------------------
+from pygments.lexers.scripting import LuaLexer 
+from pygments.token import Comment, Operator
+
+
+class MadLexer(LuaLexer):
+    """
+    Exactly the same as the Lua Lexer, except for the following changes:
+    New name, aliases, filenames and url (also removed mimetypes)
+    The comment can also be !
+    The character "\\" is now an accepted operator.
+    """
+
+    name = 'MAD'
+    url = "https://mad.web.cern.ch/mad/"
+    aliases = ['mad']
+    filenames = ['*.mad']
+    mimetypes = []
+
+    tokens = {
+        **LuaLexer.tokens,
+        'ws': [
+            (r'(?:!.*$)', Comment.Single),
+            *LuaLexer.tokens["ws"],
+        ],
+        'base': [
+            (r'\\', Operator),
+            *LuaLexer.tokens["base"],
+        ],
+    }

docs/source/alignments.rst

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+.. _ch.phy.align:
+
+Misalignments
+=============
+

docs/source/aperture.rst

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+.. _ch.phy.aper:
+
+Aperture
+========

docs/source/beam.rst

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+Beams
+=====
+.. _ch.gen.beam:
+
+The ``beam`` object is the *root object* of beams that store information relative to particles and particle beams. It also provides a simple interface to the particles and nuclei database.
+
+The ``beam`` module extends the :doc:`typeid <types>` module with the ``is_beam`` *function*, which returns ``true`` if its argument is a ``beam`` object, ``false`` otherwise.
+
+Attributes
+----------
+
+The ``beam`` *object* provides the following attributes:
+
+**particle**
+	 A *string* specifying the name of the particle. (default: ``"positron"``).
+
+**mass**
+	 A *number* specifying the energy-mass of the particle [GeV]. (default: ``emass``).
+
+**charge**
+	 A *number* specifying the charge of the particle in [q] unit of ``qelect``. [#f1]_ (default: ``1``).
+
+**spin**
+	 A *number* specifying the spin of the particle. (default: ``0``).
+
+**emrad**
+	 A *lambda* returning the electromagnetic radius of the particle [m], 
+
+	 :math:`\mathrm{emrad} = \mathrm{krad\_GeV}\times\mathrm{charge}^2/\mathrm{mass}` where :math:`\mathrm{krad\_GeV} = 10^{-9} (4 \pi\varepsilon_0)^{-1} q`.
+
+**aphot**
+	 A *lambda* returning the average number of photon emitted per bending unit, 
+
+	 :math:`\mathrm{aphot} = \mathrm{kpht\_GeV}\times\mathrm{charge}^2*\mathrm{betgam}` where :math:`\mathrm{kpht\_GeV}` :math:`= \frac{5}{2\sqrt{3}}`.
+
+**energy**
+	 A *number* specifying the particle energy [GeV]. (default: ``1``).
+
+**pc**
+	 A *lambda* returning the particle momentum times the speed of light [GeV],
+
+	 :math:`\mathrm{pc} = (\mathrm{energy}^2 - \mathrm{mass}^2)^{\frac{1}{2}}`.
+
+**beta**
+	 A *lambda* returning the particle relativistic :math:`\beta=\frac{v}{c}`,
+
+	 :math:`\mathrm{beta} = (1 - (\mathrm{mass}/\mathrm{energy})^2)^{\frac{1}{2}}`.
+
+**gamma**
+	 A *lambda* returning the particle Lorentz factor :math:`\gamma=(1-\beta^2)^{-\frac{1}{2}}`,
+
+	 :math:`\mathrm{gamma} = \mathrm{energy}/\mathrm{mass}`.
+
+**betgam**
+	 A *lambda* returning the product :math:`\beta\gamma`,
+
+	 :math:`\mathrm{betgam} = (\mathrm{gamma}^2 - 1)^\frac{1}{2}`.
+
+**pc2**
+	 A *lambda* returning :math:`\mathrm{pc}^2`, avoiding the square root.
+
+**beta2**
+	 A *lambda* returning :math:`\mathrm{beta}^2`, avoiding the square root.
+
+**betgam2**
+	 A *lambda* returning :math:`\mathrm{betgam}^2`, avoiding the square root.
+
+**brho**
+	 A *lambda* returning the magnetic rigidity [T.m], 
+
+	 :literal:`brho = GeV_c * pc/|charge|` where ``GeV_c`` = :math:`10^{9}/c`
+
+**ex**
+	 A *number* specifying the horizontal emittance :math:`\epsilon_x` [m]. (default: ``1``).
+
+**ey**
+	 A *number* specifying the vertical emittance :math:`\epsilon_y` [m]. (default: ``1``).
+
+**et**
+	 A *number* specifying the longitudinal emittance :math:`\epsilon_t` [m]. (default: :literal:`1e-3`).
+
+**exn**
+	 A *lambda* returning the normalized horizontal emittance [m], 
+
+	 :literal:`exn = ex * betgam`.
+
+**eyn**
+	 A *lambda* returning the normalized vertical emittance [m], 
+
+	 :literal:`eyn = ey * betgam`.
+
+**etn**
+	 A *lambda* returning the normalized longitudinal emittance [m], 
+
+	 :literal:`etn = et * betgam`.
+
+**nbunch**
+	 A *number* specifying the number of particle bunches in the machine. (default: ``0``).
+
+**npart**
+	 A *number* specifying the number of particles per bunch. (default: ``0``).
+
+**sigt**
+	 A *number* specifying the bunch length in :math:`c \sigma_t`. (default: ``1``).
+
+**sige**
+	 A *number* specifying the relative energy spread in :math:`\sigma_E/E` [GeV]. (default: :literal:`1e-3`).
+
+
+The ``beam`` *object* also implements a special protect-and-update mechanism for its attributes to ensure consistency and precedence between the physical quantities stored internally:
+
+#.	 The following attributes are *read-only*, i.e. writing to them triggers an error:
+		``mass, charge, spin, emrad, aphot``
+
+#.	 The following attributes are *read-write*, i.e. hold values, with their accepted numerical ranges:
+		``particle, energy`` :math:`>` ``mass``,
+		``ex`` :math:`>0`, ``ey`` :math:`>0`, ``et`` :math:`>0`,
+		``nbunch`` :math:`>0`, ``npart`` :math:`>0`, ``sigt`` :math:`>0`, ``sige`` :math:`>0`.
+
+#.	 The following attributes are *read-update*, i.e. setting these attributes update the ``energy``, with their accepted numerical ranges:
+		``pc`` :math:`>0`, :math:`0.9>` ``beta`` :math:`>0`, ``gamma`` :math:`>1`, ``betgam`` :math:`>0.1`, ``brho`` :math:`>0`,
+		``pc2``, ``beta2``, ``betgam2``.
+#.	 The following attributes are *read-update*, i.e. setting these attributes update the emittances ``ex``, ``ey``, and ``et`` repectively, with their accepted numerical ranges:
+		``exn`` :math:`>0`, ``eyn`` :math:`>0`, ``etn`` :math:`>0`.
+
+
+Methods
+-------
+
+The ``beam`` object provides the following methods:
+
+**new_particle**
+	 A *method*	``(particle, mass, charge, [spin])`` creating new particles or nuclei and store them in the particles database. The arguments specify in order the new ``particle``'s name, energy-``mass`` [GeV], ``charge`` [q], and ``spin`` (default: ``0``). These arguments can also be grouped into a *table* with same attribute names as the argument names and passed as the solely argument.
+
+**set_variables**
+	 A *method*	``(set)`` returning ``self`` with the attributes set to the pairs (*key*, *value*) contained in ``set``. This method overrides the original one to implement the special protect-and-update mechanism, but the order of the updates is undefined. It also creates new particle on-the-fly if the ``mass`` and the ``charge`` are defined, and then select it. Shortcut ``setvar``.
+
+**showdb**
+	 A *method*	``([file])`` displaying the content of the particles database to ``file`` (default: ``io.stdout``).
+
+
+Metamethods
+-----------
+
+The ``beam`` object provides the following metamethods:
+
+**__init**
+	 A *metamethod*	``()`` returning ``self`` after having processed the attributes with the special protect-and-update mechanism, where the order of the updates is undefined. It also creates new particle on-the-fly if the ``mass`` and the ``charge`` are defined, and then select it.
+
+**__newindex**
+	 A *metamethod*	``(key, val)`` called by the assignment operator ``[key]=val`` to create new attributes for the pairs (*key*, *value*) or to update the underlying physical quantity of the ``beam`` objects.
+
+
+The following attribute is stored with metamethods in the metatable, but has different purpose:
+
+
+**__beam**
+	 A unique private *reference* that characterizes beams.
+
+
+Particles database
+------------------
+
+The ``beam`` *object* manages the particles database, which is shared by all ``beam`` instances. The default set of supported particles is:
+		electron, positron, proton, antiproton, neutron, antineutron, ion, muon, 
+		antimuon, deuteron, antideuteron, negmuon (=muon), posmuon (=antimuon).
+
+New particles can be added to the database, either explicitly using the ``new_particle`` method, or by creating or updating a beam *object* and specifying all the attributes of a particle, i.e. ``particle``'s name, ``charge``, ``mass``, and (optional) ``spin``:
+
+.. code-block:: lua
+
+	local beam in MAD
+	local nmass, pmass, mumass in MAD.constant
+
+	-- create a new particle
+	beam:new_particle{ particle='mymuon', mass=mumass, charge=-1, spin=1/2 }
+
+	-- create a new beam and a new nucleus
+	local pbbeam = beam { particle='pb208', mass=82*pmass+126*nmass, charge=82 }
+
+The particles database can be displayed with the ``showdb`` method at any time from any beam:
+
+.. code-block:: lua
+
+	beam:showdb()  -- check that both, mymuon and pb208 are in the database.
+
+
+Particle charges
+----------------
+
+The physics of \MAD is aware of particle charges. To enable the compatibility with codes like MAD-X that ignores the particle charges, the global option ``nocharge`` can be used to control the behavior of created beams as shown by the following example:
+
+.. code-block:: lua
+
+	local beam, option in MAD
+	local beam1 = beam { particle="electron" } -- beam with negative charge
+	print(beam1.charge, option.nocharge)       -- display: -1  false
+
+	option.nocharge = true                     -- disable particle charges
+	local beam2 = beam { particle="electron" } -- beam with negative charge
+	print(beam2.charge, option.nocharge)       -- display:  1  true
+
+	-- beam1 was created before nocharge activation...
+	print(beam1.charge, option.nocharge)       -- display: -1  true
+
+This approach ensures consistency of beams behavior during their entire lifetime. [#f2]_ 
+
+Examples
+--------
+
+
+
+.. code-block:: lua
+
+	local beam in MAD
+	local lhcb1, lhcb2 in MADX
+	local nmass, pmass, amass in MAD.constant
+	local pbmass = 82*pmass+126*nmass
+
+	-- attach a new beam with a new particle to lhcb1 and lhcb2.
+	lhc1.beam = beam 'Pb208' { particle='pb208', mass=pbmass, charge=82 }
+	lhc2.beam = lhc1.beam -- let sequences share the same beam...
+
+	-- print Pb208 nuclei energy-mass in GeV and unified atomic mass.
+	print(lhcb1.beam.mass, lhcb1.beam.mass/amass)
+
+
+.. rubric:: Footnotes
+
+.. [#f1] The ``qelect`` value is defined in the :doc:`constants` module.``
+.. [#f2] The option ``rbarc`` in MAD-X is too volatile and does not ensure such consistency...

docs/source/beta0.rst

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+Beta0 Blocks
+============
+.. _ch.gen.beta0:
+
+
+
+The ``beta0`` object is the *root object* of beta0 blocks that store information relative to the phase space at given positions, e.g. initial conditions, Poincaré section.
+
+The ``beta0`` module extends the :doc:`typeid <types>` module with the ``is_beta0`` *function*, which returns ``true`` if its argument is a ``beta0`` object, ``false`` otherwise.
+
+Attributes
+----------
+
+The ``beta0`` *object* provides the following attributes:
+
+**particle**
+	 A *string* specifying the name of the particle. (default: ``"positron"``).
+
+
+Methods
+-------
+
+The ``beta0`` object provides the following methods:
+
+**showdb**
+	 A *method*	``([file])`` displaying the content of the particles database to ``file`` (default: ``io.stdout``).
+
+
+Metamethods
+-----------
+
+The ``beta0`` object provides the following metamethods:
+
+**__init**
+	 A *metamethod*	``()`` returning \SLF after having processed the attributes with the special protect-and-update mechanism, where the order of the updates is undefined. It also creates new particle on-the-fly if the ``mass`` and the ``charge`` are defined, and then select it.
+
+
+
+
+**__beta0**
+	 A unique private *reference* that characterizes beta0 blocks.
+
+
+Examples
+--------
+
+.. rubric:: Footnotes
+

docs/source/cffi.rst

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+.. _ch.prg.cffi:
+
+Using C FFI
+===========