.. _chapter-conventions:

==============================
Conventions for Coding in Sage
==============================

To meet the goal of making Sage easy to read, maintain, and improve,
all Python/Cython code that is included with Sage should adhere to the
style conventions discussed in this chapter.


Python coding conventions
=========================

Follow the standard Python formatting rules when writing code for
Sage, as explained at the following URLs:

* http://www.python.org/dev/peps/pep-0008
* http://www.python.org/dev/peps/pep-0257

In particular,

- Use 4 spaces for indentation levels. Do not use tabs as they can
  result in indentation confusion. Most editors have a feature that
  will insert 4 spaces when the tab key is hit. Also, many editors
  will automatically search/replace leading tabs with 4 spaces.

- Use all lowercase function names with words separated by
  underscores. For example, you are encouraged to write Python
  functions using the naming convention

  ::

      def set_some_value()

  instead of the CamelCase convention

  ::

      def SetSomeValue()

- Use CamelCase for class names and major functions that create
  objects, e.g. ``PolynomialRing``.

Note, however, that some functions do have uppercase letters where it
makes sense. For instance, the function for lattice reduction by the
LLL algorithm is called ``Matrix_integer_dense.LLL``.


File and directory names
========================

Python Sage library code uses the following conventions. Directory
names may be plural (e.g. ``rings``) and file names are almost always
singular (e.g. ``polynomial_ring.py``). Note that the file
``polynomial_ring.py`` might still contain definitions of several
different types of polynomial rings.

.. You are encouraged
   to include miscellaneous notes, emails, design
   discussions, etc., in your package.  Make these
   plain text files (with extension ``.txt``)
   in a subdirectory called ``notes``.  (For example, see
   ``SAGE_ROOT/devel/sage/sage/ext/notes/``.)


An example is worth a thousand words
====================================

For all of the conventions discussed here, you can find many examples
in the Sage library.  Browsing through the code is helpful, but so is
searching: the functions ``search_src``, ``search_def``, and
``search_doc`` are worth knowing about.  Briefly, from the "sage:"
prompt, ``search_src(string)`` searches Sage library code for the
string ``string``. The command ``search_def(string)`` does a similar
search, but restricted to function definitions, while
``search_doc(string)`` searches the Sage documentation.  See their
docstrings for more information and more options.


Headings of Sage library code files
===================================

The top of each Sage code file should follow this format:

::

    r"""
    <Very short 1-line summary>

    <Paragraph description>
    ...

    AUTHORS:

    - YOUR NAME (2005-01-03): initial version

    - person (date in ISO year-month-day format): short desc

    ...

    - person (date in ISO year-month-day format): short desc

    ...

    Lots and lots of examples.
    """

    #*****************************************************************************
    #       Copyright (C) 2008 YOUR NAME <your email>
    #
    #  Distributed under the terms of the GNU General Public License (GPL)
    #                  http://www.gnu.org/licenses/
    #*****************************************************************************

The following is the top of the file
``SAGE_ROOT/devel/sage/sage/rings/integer.pyx``, which
contains the implementation for :math:`\ZZ`.

::

    """
    Elements of the ring `\ZZ` of integers

    AUTHORS:

    - William Stein (2005): initial version

    - Gonzalo Tornaria (2006-03-02): vastly improved python/GMP
      conversion; hashing

    - Didier Deshommes (2006-03-06): numerous examples
      and docstrings

    - William Stein (2006-03-31): changes to reflect GMP bug fixes

    - William Stein (2006-04-14): added GMP factorial method (since it's
      now very fast).

    - David Harvey (2006-09-15): added nth_root, exact_log

    - David Harvey (2006-09-16): attempt to optimise Integer constructor

    - Rishikesh (2007-02-25): changed quo_rem so that the rem is positive

    - David Harvey, Martin Albrecht, Robert Bradshaw (2007-03-01):
      optimized Integer constructor and pool

    - Pablo De Napoli (2007-04-01): multiplicative_order should return
      +infinity for non zero numbers

    - Robert Bradshaw (2007-04-12): is_perfect_power, Jacobi symbol (with
      Kronecker extension).  Convert some methods to use GMP directly
      rather than pari, Integer(), PY_NEW(Integer)

    - David Roe (2007-03-21): sped up valuation and is_square, added
      val_unit, is_power, is_power_of and divide_knowing_divisible_by

    - Robert Bradshaw (2008-03-26): gamma function, multifactorials

    - Robert Bradshaw (2008-10-02): bounded squarefree part

    EXAMPLES:

    Add 2 integers::

        sage: a = Integer(3) ; b = Integer(4)
        sage: a + b == 7
        True

    Add an integer and a real number::

        sage: a + 4.0
        7.00000000000000

    Add an integer and a rational number::

        sage: a + Rational(2)/5
        17/5

    Add an integer and a complex number::

        sage: b = ComplexField().0 + 1.5
        sage: loads((a+b).dumps()) == a+b
        True

    ::

        sage: z = 32
        sage: -z
        -32
        sage: z = 0; -z
        0
        sage: z = -0; -z
        0
        sage: z = -1; -z
        1

    Multiplication::

        sage: a = Integer(3) ; b = Integer(4)
        sage: a * b == 12
        True
        sage: loads((a * 4.0).dumps()) == a*b
        True
        sage: a * Rational(2)/5
        6/5

    ::

        sage: list([2,3]) * 4
        [2, 3, 2, 3, 2, 3, 2, 3]

    ::

        sage: 'sage'*Integer(3)
        'sagesagesage'

    COERCIONS: Returns version of this integer in the multi-precision
    floating real field R.

    ::

        sage: n = 9390823
        sage: RR = RealField(200)
        sage: RR(n)
        9.3908230000000000000000000000000000000000000000000000000000e6
    """
    #*****************************************************************************
    #       Copyright (C) 2004,2006 William Stein <wstein@gmail.com>
    #       Copyright (C) 2006 Gonzalo Tornaria <tornaria@math.utexas.edu>
    #       Copyright (C) 2006 Didier Deshommes <dfdeshom@gmail.com>
    #       Copyright (C) 2007 David Harvey <dmharvey@math.harvard.edu>
    #       Copyright (C) 2007 Martin Albrecht <malb@informatik.uni-bremen.de>
    #       Copyright (C) 2007,2008 Robert Bradshaw <robertwb@math.washington.edu>
    #       Copyright (C) 2007 David Roe <roed314@gmail.com>
    #
    #  Distributed under the terms of the GNU General Public License (GPL)
    #                  http://www.gnu.org/licenses/
    #*****************************************************************************

All code included with Sage must be licensed under the GPLv2+ or a
less restrictive license (e.g. the BSD license). It is very important
that you include your name in the AUTHORS log so that everybody who
submits code to Sage receives proper credit [2]_. If ever you feel you
are not receiving proper credit for anything you submit to Sage,
please let the development team know!


.. _section-docstrings:

Documentation strings
=====================


Docstring markup with ReST and Sphinx
-------------------------------------

**Every** function must have a docstring that includes the following
information. Source files in the Sage library contain numerous
examples on how to format your documentation, so you could use them as
a guide.

-  A one-sentence description of the function, followed by a blank
   line.

-  An INPUT and an OUTPUT block for input and output arguments (see
   below for format). The type names should be descriptive, but do not
   have to represent the exact Sage/Python types. For example, use
   "integer" for anything that behaves like an integer; you do not have
   to put a precise type name such as ``int``. The INPUT block
   describes the expected input to your function or method, while the
   OUTPUT block describes the expected output of the
   function/method. If appropriate, you need to describe any default
   values for the input arguments. For example::

       INPUT:

       - ``p`` -- (default: 2) a positive prime integer.

       OUTPUT:

       A 5-tuple consisting of integers in this order:

       1. the smallest primitive root modulo p
       2. the smallest prime primitive root modulo p
       3. the largest primitive root modulo p
       4. the largest prime primitive root modulo p
       5. total number of prime primitive roots modulo p

   Some people prefer to format their OUTPUT section as a block by
   using a dash. That is acceptable as well::

       OUTPUT:

       - The plaintext resulting from decrypting the ciphertext ``C``
         using the Blum-Goldwasser decryption algorithm.

-  Instead of INPUT and OUTPUT blocks, you can include descriptions of
   the arguments and output using Sphinx/ReST markup, as described in
   http://sphinx.pocoo.org/markup/desc.html#info-field-lists.  See
   below for an example.

-  An EXAMPLES block for examples. This is not optional. These
   examples are used for automatic testing before each release and new
   functions without these doctests will not be accepted for inclusion
   with Sage.

-  An ALGORITHM block (optional) which indicates what software
   and/or what algorithm is used. For example
   ``ALGORITHM: Uses Pari``. Here's a longer example that describes an
   algorithm used. Note that it also cites the reference where this
   algorithm can be found::

       ALGORITHM:

       The following algorithm is adapted from page 89 of [Nat2000]_.

       Let `p` be an odd (positive) prime and let `g` be a generator
       modulo `p`. Then `g^k` is a generator modulo `p` if and only if
       `\gcd(k, p-1) = 1`. Since `p` is an odd prime and positive, then
       `p - 1` is even so that any even integer between 1 and `p - 1`,
       inclusive, is not relatively prime to `p - 1`. We have now
       narrowed our search to all odd integers `k` between 1 and `p - 1`,
       inclusive.

       So now start with a generator `g` modulo an odd (positive) prime
       `p`. For any odd integer `k` between 1 and `p - 1`, inclusive,
       `g^k` is a generator modulo `p` if and only if `\gcd(k, p-1) = 1`.

       REFERENCES:

       .. [Nat2000] M.B. Nathanson. Elementary Methods in Number Theory.
         Springer, 2000.

   You can also number the steps in your algorithm using the hash-dot
   symbol. This way, the actual numbering of the steps are
   automatically taken care of when you build the documentation::

        ALGORITHM:

        The Blum-Goldwasser decryption algorithm is described in Algorithm
        8.56, page 309 of [MenezesEtAl1996]_. The algorithm works as follows:

        #. Let `C` be the ciphertext `C = (c_1, c_2, \dots, c_t, x_{t+1})`.
           Then `t` is the number of ciphertext sub-blocks and `h` is the
           length of each binary string sub-block `c_i`.
        #. Let `(p, q, a, b)` be the private key whose corresponding
           public key is `n = pq`. Note that `\gcd(p, q) = ap + bq = 1`.
        #. Compute `d_1 = ((p + 1) / 4)^{t+1} \bmod{(p - 1)}`.
        #. Compute `d_2 = ((q + 1) / 4)^{t+1} \bmod{(q - 1)}`.
        #. Let `u = x_{t+1}^{d_1} \bmod p`.
        #. Let `v = x_{t+1}^{d_2} \bmod q`.
        #. Compute `x_0 = vap + ubq \bmod n`.
        #. For `i` from 1 to `t`, do:

           #. Compute `x_i = x_{t-1}^2 \bmod n`.
           #. Let `p_i` be the `h` least significant bits of `x_i`.
           #. Compute `m_i = p_i \oplus c_i`.

        #. The plaintext is `m = m_1 m_2 \cdots m_t`.

-  A NOTES block for special notes (optional). Include information
   such as purpose etc. A NOTES block should start with
   ``.. NOTE::``. You can also use the lower-case version
   ``.. note::``, but do not mix lower-case with upper-case. However,
   you are encouraged to use the upper-case version ``.. NOTE::``. If
   you want to put anything within the NOTES block, you should
   indent it at least 4 spaces (no tabs). Here's an example of a NOTES
   block::

       .. NOTE::

           You should note that this sentence is indented at least 4
           spaces. Avoid tab characters as much as possible when
           writing code or editing the Sage documentation. You should
           follow Python conventions by using spaces only.

- A WARNING block for critical information about your code. For
  example, the WARNING block might include information about when or
  under which conditions your code might break, or information that
  the user should be particularly aware of. A WARNING block should start
  with ``.. WARNING::``. It can also be the lower-case form
  ``.. warning::``. However, you are encouraged to use the upper-case
  form ``.. WARNING::``. Here's an example of a WARNING block::

      .. WARNING::

          Whenever you edit the Sage documentation, make sure that
          the edited version still builds. That is, you need to ensure
          that you can still build the HTML and PDF versions of the
          updated documentation. If the edited documentation fails to
          build, it is very likely that you would be requested to
          change your patch.

- A REFERENCES block to list books or papers (optional). This block serves
  a similar purpose to a list of references in a research paper, or a
  bibliography in a monograph. If your method, function or class uses an
  algorithm that can be found in a standard reference, you should list
  that reference under this block. The Sphinx/ReST markup for
  citations is described at
  http://sphinx.pocoo.org/rest.html#citations. See below for an example.

-  An AUTHORS block (optional, but encouraged for important
   functions, so users can see from the docstring who wrote it and
   therefore whom to contact if they have questions).

Use the following template when documenting functions. Note the
indentation::

    def point(self, x=1, y=2):
        r"""
        This function returns the point `(x^5,y)`.

        INPUT:

         - ``x`` - integer (default: 1) the description of the
	   argument x goes here.  If it contains multiple lines, all
	   the lines after the first need to be indented.

         - ``y`` - integer (default: 2) the ...

        OUTPUT:

        integer -- the ...

        EXAMPLES:

        This example illustrates ...

        ::

            sage: A = ModuliSpace()
            sage: A.point(2,3)
            xxx

        We now ...

        ::

            sage: B = A.point(5,6)
            sage: xxx

        It is an error to ...::

            sage: C = A.point('x',7)
            Traceback (most recent call last):
            ...
            TypeError: unable to convert x (=r) to an integer

        NOTES:

        This function uses the algorithm of [BCDT]_ to determine
        whether an elliptic curve E over Q is modular.

        ...

        REFERENCES:

        .. [BCDT] Breuil, Conrad, Diamond, Taylor, "Modularity ...."

        AUTHORS:

        - William Stein (2005-01-03)

        - First_name Last_name (yyyy-mm-dd)
        """
        <body of the function>

If you used Sphinx/ReST markup for the arguments, the beginning of the
docstring would look like this::

    def point(self, x=1, y=2):
        r"""
        This function returns the point `(x^5,y)`.

        :param x: the description of the argument x goes here.
	   If it contains multiple lines, all the lines after the
	   first need to be indented.

	:type x: integer; default 1

	:param y: the ...

	:type y: integer; default 2

	:returns: the ...

	:rtype: integer, the return type

You are strongly encouraged to:

-  Use nice LaTeX formatting everywhere. If you use backslashes,
   either use double backslashes or place an "r" right before the
   first triple opening quote. For example,

   ::

       def cos(x):
           """
           Returns `\\cos(x)`.
           """

       def sin(x):
           r"""
           Returns `\sin(x)`.
           """

   You can also use the MATH block to format complicated mathematical
   expressions::

       .. MATH::

           \sum_{i=1}^{\infty} (a_1 a_2 \cdots a_i)^{1/i}
           \leq
           e \sum_{i=1}^{\infty} a_i

   .. note::

      In ReST documentation, you use backticks \` to mark LaTeX code
      to be typeset.  In Sage docstrings, unofficially you may use
      dollar signs instead -- "unofficially" means that it ought to
      work, but might be a little buggy.  Thus ```x^2 + y^2 = 1``` and
      ``$x^2 + y^2 = 1$`` should produce identical output, typeset in math
      mode.

      LaTeX style: typeset standard rings and fields like the integers
      and the real numbers using the locally-defined macro ``\\Bold``,
      as in ``\\Bold{Z}`` for the integers. This macro is defined to be
      ordinary bold-face ``\\mathbf`` by default, but users can switch to
      blackboard-bold ``\\mathbb`` and back on-the-fly by using
      ``latex.blackboard_bold(True)`` and
      ``latex.blackboard_bold(False)``.

      The docstring will be available interactively (for the "def
      point..." example above, by typing "point?" at the "sage:"
      prompt) and also in the reference manual. When viewed
      interactively, LaTeX code has the backslashes stripped from it,
      so "\\cos" will appear as "cos".

      Because of the dual role of the docstring, you need to strike a
      balance between readability (for interactive help) and using
      perfect LaTeX code (for the reference manual).  For instance,
      instead of using "\\frac{a}{b}", use "a/b" or maybe "a b^{-1}".
      Also keep in mind that some users of Sage are not familiar with
      LaTeX; this is another reason to avoid complicated LaTeX
      expressions in docstrings, if at all possible: "\\frac{a}{b}"
      will be obscure to someone who doesn't know any LaTeX.

      Finally, a few non-standard LaTeX macros are available to help
      achieve this balance, including "\\ZZ", "\\RR", "\\CC", and
      "\\QQ".  These are names of Sage rings, and they are typeset
      using a single boldface character; they allow the use of "\\ZZ"
      in a docstring, for example, which will appear interactively as
      "ZZ" while being typeset as "\\Bold{Z}" in the reference
      manual.  Other examples are "\\GF" and "\\Zmod", each of which
      takes an argument: "\\GF{q}" is typeset as "\\Bold{F}_{q}" and
      "\\Zmod{n}" is typeset as "\\Bold{Z}/n\\Bold{Z}".  See the
      file ``$SAGE_ROOT/devel/sage/sage/misc/latex_macros.py`` for a
      full list and for details about how to add more macros.

-  Liberally describe what the examples do. Note that there must be
   a blank line after the example code and before the explanatory text
   for the next example (indentation is not enough).

-  Illustrate any exceptions raised by the function with examples,
   as given above. (It is an error to ...; In particular, use ...)

-  Include many examples. These are automatically tested on a regular
   basis, and are crucial for the quality and adaptability of
   Sage. Without such examples, small changes to one part of Sage that
   break something else might not go seen until much later when
   someone uses the system, which is unacceptable. Note that new
   functions without doctests will not be accepted for inclusion in Sage.

.. warning::

   Functions whose names start with an underscore do not currently
   appear in the reference manual, so avoid putting crucial
   documentation in their docstrings. In particular, if you are
   defining a class, you might put a long informative docstring after
   the class definition, not for the ``__init__`` method. For example,
   from the file ``SAGE_ROOT/devel/sage/sage/crypto/classical.py``:

   ::

    class HillCryptosystem(SymmetricKeyCryptosystem):
        """
        Create a Hill cryptosystem defined by the `m` x `m` matrix space
        over `\mathbf{Z} / N \mathbf{Z}`, where `N` is the alphabet size of
        the string monoid ``S``.

        INPUT:

        - ``S`` - a string monoid over some alphabet

        - ``m`` - integer `> 0`; the block length of matrices that specify
          block permutations

        OUTPUT:

        - A Hill cryptosystem of block length ``m`` over the alphabet ``S``.

        EXAMPLES::

            sage: S = AlphabeticStrings()
            sage: E = HillCryptosystem(S,3)
            sage: E
            Hill cryptosystem on Free alphabetic string monoid on A-Z of block length 3
	"""

   and so on, while the ``__init__`` method starts like this::

        def __init__(self, S, m):
            """
            See ``HillCryptosystem`` for full documentation.

	    EXAMPLES::
	    ...
	    """

   Note also that the first docstring is printed if users type
   "HillCryptosystem?" at the "sage:" prompt.

   (Before Sage 3.4, the reference manual used to include methods
   starting with underscores, so you will probably find many examples
   in the code which don't follow this advice...)


Automatic testing
-----------------

The code in the examples should pass automatic testing. This means
that if the above code is in the file ``f.py`` (or ``f.sage``), then
``sage -t f.py`` should not give any error messages. Testing occurs
with full Sage preparsing of input within the standard Sage shell
environment, as described in :ref:`section-preparsing`. **Important:**
The file ``f.py`` is not imported when running tests unless you have
arranged that it be imported into your Sage environment, i.e. unless
its functions are available when you start Sage using the ``sage``
command. For example, the function ``cdd_convert`` in the file
``SAGE_ROOT/devel/sage/sage/geometry/polyhedra.py`` includes
an EXAMPLES block containing the following:

::

        sage: from sage.geometry.polyhedra import cdd_convert
        sage: cdd_convert(' 1 1 0 0')
        [1, 1, 0, 0]

Sage does not know about the function ``cdd_convert`` by default, so
it needs to be imported before it is tested. Hence the first line in
the example.


.. _section-further_conventions:

Further conventions for automated testing of examples
-----------------------------------------------------

The Python script ``SAGE_LOCAL/bin/sage-doctest`` implements
documentation testing in Sage (see :ref:`chapter-testing` for more
details). When writing documentation, keep the following points in
mind:

-  All input is preparsed before being passed to Python, e.g. ``2/3``
   is replaced by ``Integer(2)/Integer(3)``, which evaluates to
   ``2/3`` as a rational instead of the Python int ``0``. For more
   information on preparsing, see :ref:`section-preparsing`.

-  If a test outputs to a file, the file should be in a temporary
   directory.  For example (taken from the file
   ``SAGE_ROOT/devel/sage/sage/plot/plot.py``)::

        sage: fig.savefig(os.path.join(SAGE_TMP, 'test.png'))

   Here ``fig.savefig`` is the function doing the saving, ``SAGE_TMP``
   is a temporary directory---this variable will always be defined
   properly during automated testing---and ``os.path.join`` is the
   preferred way to construct a path from a directory and a file. It
   works more generally than a Unix-flavored construction like
   ``SAGE_TMP + '/test.png'``.  If you want to use ``SAGE_TMP`` in
   Sage code, not just in a doctest, then you need to import
   it. Search the Sage code for examples.

-  If a test line contains the text ``random``, it is executed by
   ``sage-doctest`` but ``sage-doctest`` does not check that the
   output agrees with the output in the documentation string. For
   example, the docstring for the ``__hash__`` method for
   ``CombinatorialObject`` in
   ``SAGE_ROOT/devel/sage/sage/combinat/combinat.py`` includes
   the lines

   .. skip

   ::

           sage: hash(c) #random
           1335416675971793195
           sage: c._hash #random
           1335416675971793195

   However, most functions generating pseudorandom output do not need
   this tag since the doctesting framework guarantees the state of the
   pseudorandom number generators (PRNGs) used in Sage for a given
   doctest. See :ref:`chapter-randomtesting` for details on this
   framework.

-  If a line contains the text ``long time`` then that line is not
   tested unless the ``-long`` option is given, e.g.
   ``sage -t -long f.py``. Use this to include examples that take more
   than about a second to run. These will not be run regularly during
   Sage development, but will get run before major releases. No
   example should take more than about 30 seconds.

   For instance, here is part of the docstring from the ``regulator``
   method for rational elliptic curves, from the file
   ``SAGE_ROOT/devel/sage/sage/schemes/elliptic_curves/ell_rational.py``:

   ::

       sage: E = EllipticCurve([0, 0, 1, -1, 0])
       sage: E.regulator()              # long time (1 second)
       0.0511114082399688

-  If a line contains ``todo: not implemented``, it is never
   tested. It is good to include lines like this to make clear what we
   want Sage to eventually implement:

   ::

           sage: factor(x*y - x*z)    # todo: not implemented

   It is also immediately clear to the user that the indicated example
   does not currently work.

-  If a line contains the text ``optional``, it is not tested unless
   the ``-optional`` flag is passed, e.g.
   ``sage -t -optional f.py``. (Note that ``-optional`` must not be
   the first argument to ``sage``.) Use this to include doctests that
   require optional packages. For example, the docstring for
   ``_magma_init_`` in the class
   ``EllipticCurve_finite_field`` from the file
   ``SAGE_ROOT/devel/sage/sage/schemes/elliptic_curves/ell_finite_field.py``
   contains

   ::

           sage: E = EllipticCurve(GF(41),[2,5])
           sage: E._magma_init_() # optional - requires Magma
           'EllipticCurve([...|GF(41)!0,GF(41)!0,GF(41)!0,GF(41)!2,GF(41)!5])'

-  If the entire documentation string contains all three words
   ``optional``, ``package``, and ``installed``, then the entire
   documentation string is not executed unless the ``-optional`` flag
   is passed to ``sage -t``. This is useful for a long sequence of
   examples that all require that an optional package be installed.

Using ``search_src`` from the Sage prompt (or ``grep``), one can
easily find the aforementioned keywords. In the case of
``todo: not implemented``, one can use the results of such a search to
direct further development on Sage.


.. _chapter-testing:

Automated testing
=================

This section describes Sage's automated testing of test files of the
following types: ``.py``, ``.pyx``, ``.sage``, ``.rst``. Briefly, use
``sage -t <file>`` to test that the examples in ``<file>`` behave
exactly as claimed. See the following subsections for more
details. See also :ref:`section-docstrings` for a discussion on how to
include examples in documentation strings and what conventions to
follow. The chapter :ref:`chapter-doctesting` contains a tutorial on
doctesting modules in the Sage library.


.. _section-testpython:

Testing .py, .pyx and .sage files
---------------------------------

Run ``sage -t <filename.py>`` to test all code examples in
``filename.py``. Similar remarks apply to ``.sage`` and ``.pyx``
files.

::

      sage -t [--verbose] [--optional]  [files and directories ... ]

When you run ``sage -t <filename.py>``, Sage makes a copy of
``<filename.py>`` with all the ``sage`` prompts replaced by ``>>>``,
then uses the standard Python doctest framework to test the
documentation. More precisely, the Python script
``SAGE_LOCAL/bin/sage-doctest`` implements documentation testing. It
does the following when asked to test a file ``foo.py`` or
``foo.sage``.

#. Creates the directory ``.doctest`` if it does not exist and the
   file ``.doctest/foo.py``.

#. The file ``.doctest_foo.py`` contains functions for each docstring
   in ``foo.py``, but with all Sage preparsing applied and with
   ``from sage.all import *`` at the top. The function documentation
   is thus standard Python with ``>>>`` prompts.

#. The script ``SAGE_LOCAL/bin/sage-doctest`` then runs Sage's Python
   interpreter on ``.doctest_foo.py``.

Your file passes these tests if the code in it will run when entered
at the ``sage:`` prompt with no special imports. Thus users are
guaranteed to be able to exactly copy code out of the examples you
write for the documentation and have them work.


Testing ReST documentation
--------------------------

Run ``sage -t <filename.rst>`` to test the examples in verbatim
environments in ReST documentation.  Sage creates a file
``.doctest_filename.py`` and tests it just as for ``.py``, ``.pyx``
and ``.sage`` files.

Of course in ReST files, one often inserts explanatory texts between
different verbatim environments. To link together verbatim
environments, use the ``.. link::`` comment. For example::

    ::

            sage: a = 1


    Next we add 1 to ``a``.

    .. link::

    ::

            sage: 1 + a
            2

You can also put ``.. skip::`` right before a verbatim environment to
have that example skipped when testing the file.  This goes right in
the same place as the ``.. link::`` in the previous example.

See the files in ``SAGE_ROOT/devel/sage/doc/en/tutorial/`` for many
examples of how to include automated testing in ReST documentation
for Sage.


.. _chapter-randomtesting:

Randomized testing
==================

In addition to all the examples in your docstrings, which serve as
both demonstrations and tests of your code, you should consider
creating a test suite. Think of this as a program that will run for a
while and "tries" to crash your code using randomly generated
input. Your test code should define a class ``Test`` with a
``random()`` method that runs random tests. These are all assembled
together later, and each test is run for a certain amount of time on a
regular basis.

For example, see the file
``SAGE_ROOT/devel/sage/sage/modular/modsym/tests.py``.


.. [2]  See http://www.sagemath.org/development-map.html