There are many ways to contribute to Sage including sharing scripts and Sage worksheets that implement new functionality using Sage, improving to the Sage library, or to working on the many underlying libraries distributed with Sage [1]. This guide focuses on editing the Sage library itself.

Sage is not just about gathering together functionality. It is about providing a clear, systematic and consistent way to access a large number of algorithms, in a coherent framework that makes sense mathematically. In the design of Sage, the semantics of objects, the definitions, etc., are informed by how the corresponding objects are used in everyday mathematics.

[1] | See http://www.sagemath.org/links-components.html for a full list of packages shipped with every copy of 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.

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

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.

Whitespace before and after assignment and binary operator of the lowest priority in the expression:

i = i + 1 c = (a+b) * (a-b)

No whitespace before or after the

`=`sign if it is used for keyword arguments:def complex(real, imag=0.0): return magic(r=real, i=imag)

No whitespace immediately inside parenthesis, brackets, and braces:

spam(ham[1], {eggs: 2}) [i^2 for i in range(3)]

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(): return 1

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`.Use CamelCase for class names:

class SomeValue(object): def __init__(self, x): self._x = 1

and factory functions that mimic object constructors, for example

`PolynomialRing`or:def SomeIdentityValue(x): return SomeValue(1)

Roughly, the Sage directory tree is layout like this. Note that we use
`SAGE_ROOT` in the following as a shortcut for the (arbitrary) name
of the directory containing the Sage sources:

```
SAGE_ROOT/
sage # the Sage launcher
Makefile # top level Makefile
build/ # sage's build system
deps
install
...
pkgs/ # install, patch, and metadata from spkgs
src/
setup.py
module_list.py
...
sage/ # sage library (formerly devel/sage-main/sage)
ext/ # extra sage resources (formerly devel/ext-main)
mac-app/ # would no longer have to awkwardly be in extcode
bin/ # the scripts in local/bin that are tracked
upstream/ # tarballs of upstream sources
local/ # installed binaries
```

Python Sage library code goes into `src/` and 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.

Note

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/src/sage/ext/notes/`.

If you want to create a new directory in the Sage library
`SAGE_ROOT/src/sage` (say, `measure_theory`), that directory
should contain a file `__init__.py` that contains the single line
`import all` in addition to whatever
files you want to add (say, `borel_measure.py` and
`banach_tarski.py`), and also a file `all.py` listing imports from
that directory that are important enough to be in the Sage’s global
namespace at startup.
The file `all.py` might look like this:

```
from borel_measure import BorelMeasure
from banach_tarski import BanachTarskiParadox
```

but it is generally better to use the lazy import framework:

```
from sage.misc.lazy_import import lazy_import
lazy_import('sage.measure_theory.borel_measue', 'BorelMeasure')
lazy_import('sage.measure_theory.banach_tarski', 'BanachTarskiParadox')
```

Then in the file `SAGE_ROOT/src/sage/all.py`, add a line

```
from sage.measure_theory.all import *
```

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.

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
EXAMPLES::
<Lots and lots of examples>
"""
#*****************************************************************************
# Copyright (C) 2013 YOUR NAME <your email>
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# http://www.gnu.org/licenses/
#*****************************************************************************
```

As an example, see `SAGE_ROOT/src/sage/rings/integer.pyx` which
contains the implementation for \(\ZZ\). The `AUTHORS:` section is
redundant, the authoritative log for who wrote what is always the git
repository (see the output of `git blame`). Nevertheless, it is
sometimes useful to have a very rough overview over the history,
especially if a lot of people have been working on that source file.

All code included with Sage must be licensed under the GPLv3+ or a compatible, that is, less restrictive license (e.g. GPLv2+ or the BSD license).

**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 and ending in a period. It prescribes the function or method’s effect as a command (“Do this”, “Return that”), not as a description; e.g. don’t write “Returns the pathname ...”.

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.

An EXAMPLES block for examples. This is not optional. These examples are used both for documentation and for automatic testing before each release so should have good coverage of the functionality in question. New functions without these doctests will not be accepted for inclusion with Sage.

A SEEALSO block (optional) with links to related things in Sage. A SEEALSO block should start with

`.. SEEALSO::`. It can also be the lower-case form`.. seealso::`. However, you are encouraged to use the upper-case form`.. SEEALSO::`. See*Hyperlinks*for details on how to setup link in Sage. Here’s an example of a SEEALSO block:.. SEEALSO:: :ref:`chapter-sage_manuals_links`

An ALGORITHM block (optional) which indicates what algorithm and/or what software 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 NOTE block for special notes (optional). Include information such as purpose etc. A NOTE 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 NOTE 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 TODO block for room for improvements. The TODO block might contains disabled doctests to demonstrate the desired feature. A TODO block should start with

`.. TODO::`. It can also be the lower-case form`.. todo::`. However, you are encouraged to use the upper-case form`.. TODO::`. Here’s an example of a TODO block:.. TODO:: Improve further function ``have_fresh_beers`` using algorithm ``buy_a_better_fridge``:: sage: have_fresh_beers('Bière de l\'Yvette') # todo: not implemented Enjoy !

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. Sage also add specific markup for links to sage trac tickets and Wikipedia. See

*Hyperlinks*. Here’s an example of a REFERENCES block:This docstring is referencing [SC]_. Just remember that references are global, so we can also reference to [Nat2000]_ in the ALGORITHM block, even if it is in a separate file. However we would not include the reference here since it would cause a conflict. REFERENCES: .. [SC] Conventions for coding in sage. http://www.sagemath.org/doc/developer/conventions.html.

A TESTS block (optional), formatted just like EXAMPLES, for additional tests which should be part of the regression suite but are not illustrative enough to merit placement in EXAMPLES.

Use the following template when documenting functions. Note the indentation

```
def point(self, x=1, y=2):
r"""
Return 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 begin at the same indentation
as the backtick.
- ``y`` -- integer (default: 2) the ...
OUTPUT:
The point as a tuple.
.. SEEALSO::
:func:`line`
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
.. NOTE::
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 ...."
"""
<body of the function>
```

You are strongly encouraged to:

- Use nice LaTeX formatting everywhere, see
*LaTeX Typesetting*. - 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.

Functions whose names start with an underscore are considered private. Hence they do not appear in the reference manual, and their docstring should not contain any information that is crucial for Sage users. Having said that, you can explicitly enable their docstrings to be shown as part of the documentation of another method. For example:

```
class Foo(SageObject):
def f(self):
"""
<usual docstring>
.. automethod:: _f
"""
return self._f()
def _f(self):
"""
This would be hidden without the ``.. automethod::``
"""
```

An EXAMPLES or TESTS block is still required for these private functions.

A special case is the constructor `__init__`, which clearly starts
with an underscore. However, due to its special status the
`__init__` docstring is used as the class docstring if there is not
one already. That is, you can do the following:

```
sage: class Foo(SageObject):
....: # no class docstring
....: def __init__(self):
....: """Construct a Foo."""
sage: foo = Foo()
sage: from sage.misc.sageinspect import sage_getdoc
sage: sage_getdoc(foo) # class docstring
'Construct a Foo.\n'
sage: sage_getdoc(foo.__init__) # constructor docstring
'Construct a Foo.\n'
```

In ReST documentation, you use backticks ` to mark LaTeX code to be
typeset. In Sage docstrings, you may also use dollar signs instead.
Thus ``x^2 + y^2 = 1`` and `$x^2 + y^2 = 1$` should produce
identical output. If you use TeX commands containing backslashes in
docstrings, then either use double backslashes or place an “r” right
before the first triple opening quote. For example, both of the
following are valid:

```
def cos(x):
"""
Return `\\cos(x)`.
"""
def sin(x):
r"""
Return $\sin(x)$.
"""
```

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 that the MATH block is automatically wrapped in a latex math
environment (i.e. in `\[ \]` or `$$`, etc.). To use aligned equations,
use the **aligned** environment:

```
.. MATH::
\begin{aligned}
f(x) & = x^2 - 1 \\
g(x) & = x^x - f(x - 2)
\end{aligned}
```

If you wish to explicitly not wrap the MATH block, make the first line of
the indented block `:nowrap:`:

```
.. MATH::
:nowrap:
This is now plain text so I can do things like $x = 5$.
```

Warning

With or without `:nowrap:`, the *html* documentation output
currently will work if you use environments such as **align**
which wrap their contents in math mode. However, `:nowrap:`
is necessary for the *pdf* documentation to build correctly.

The Sage LaTeX style is to 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/src/sage/misc/latex_macros.py` for a
full list and for details about how to add more macros.

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 *Sage 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 `AA()` in the file
`SAGE_ROOT/src/sage/algebras/steenrod/steenrod_algebra.py` includes
an EXAMPLES block containing the following:

```
sage: from sage.algebras.steenrod.steenrod_algebra import AA as A
sage: A()
mod 2 Steenrod algebra, milnor basis
```

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

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*Sage Preparsing*.If a test outputs to a file, the file should be a temporary file. Use

`tmp_filename()`to get a temporary filename, or`tmp_dir()`to get a temporary directory. For example (taken from the file`SAGE_ROOT/src/sage/plot/graphics.py`):sage: plot(x^2 - 5, (x, 0, 5), ymin=0).save(tmp_filename(ext='.png'))

You may write tests that span multiple lines. The best way to do so is to use the line continuation marker

`....:`sage: for n in srange(1,10): ....: if n.is_prime(): ....: print n, 2 3 5 7

If you have a long line of code, you may want to consider adding a backslash to the end of the line, which tells the doctesting framework to join that current line with the next. This syntax is non-standard so may be removed in a future version of Sage, but in the mean time it can be useful for breaking up large integers across multiple lines:

sage: n = 123456789123456789123456789\ ....: 123456789123456789123456789 sage: n.is_prime() False

There are a number of magic comments that you can put into the example code that change how the output is verified by the Sage doctest framework. Here is a comprehensive list:

If a test line contains the comment

`random`, it is executed but it is not checked that the output agrees with the output in the documentation string. For example, the docstring for the`__hash__`method for`CombinatorialObject`in`SAGE_ROOT/src/sage/combinat/combinat.py`includes the lines:sage: c = CombinatorialObject([1,2,3]) 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

*Randomized Testing*for details on this framework. It is preferable to write tests that do not expose this non-determinism, for example rather than checking the value of the hash in a dockets, one could illustrate successfully using it as a key in a dict.If a line contains the comment

`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 comment contains

`tol`or`tolerance`, numerical results are only verified to the given tolerance. This may be prefixed by`abs[olute]`or`rel[ative]`to specify whether to measure absolute or relative error; this defaults to relative error except when the expected value is exactly zero:sage: RDF(pi) # abs tol 1e-5 3.14159 sage: [10^n for n in [0.0 .. 4]] # rel tol 2e-4 [0.9999, 10.001, 100.01, 999.9, 10001]

This can be useful when the exact output is subject to rounding error and/or processor floating point arithmetic variation. Here are some more examples.

A singular value decomposition of a matrix will produce two unitary matrices. Over the reals, this means the inverse of the matrix is equal to its transpose. We test this result by applying the norm to a matrix difference. The result will usually be a “small” number, distinct from zero:

sage: A = matrix(RDF, 8, range(64)) sage: U, S, V = A.SVD() sage: (U.transpose()*U-identity_matrix(8)).norm(p=2) # abs tol 1e-10 0.0

The 8-th cyclotomic field is generated by the complex number \(e^\frac{i\pi}{4}\). Here we compute a numerical approximation:

sage: K.<zeta8> = CyclotomicField(8) sage: N(zeta8) # absolute tolerance 1e-10 0.7071067812 + 0.7071067812*I

A relative tolerance on a root of a polynomial. Notice that the root should normally print as

`1e+16`, or something similar. However, the tolerance testing causes the doctest framework to use the output in a*computation*, so other valid text representations of the predicted value may be used. However, they must fit the pattern defined by the regular expression`float_regex`in`sage.doctest.parsing`:sage: y = polygen(RDF, 'y') sage: p = (y - 10^16)*(y-10^(-13))*(y-2); p y^3 - 1e+16*y^2 + 2e+16*y - 2000.0 sage: p.roots(multiplicities=False)[2] # relative tol 1e-10 10000000000000000

If a comment contains

`not implemented`or`not tested`, 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 one of the first 10 lines of a file starts with

`r""" nodoctest`(or`""" nodoctest`or`# nodoctest`or`% nodoctest`or`.. nodoctest`, or any of these with different spacing), then that file will be skipped. If a directory contains a file`nodoctest.py`, then that whole directory will be skipped. Neither of this applies to files or directories which are explicitly given as command line arguments: those are always tested.If a comment contains

`optional - PKGNAME`, it is not tested unless the`--optional=PKGNAME`flag is passed to`sage -t`. Mark a doctest as`optional`if it requires optional packages. Running`sage -t --optional=all f.py`executes all doctests, including all optional tests. Running`sage -t --optional=sage,sloane_database f.py`runs the normal tests (because of`--optional=sage`), as well as those marked as`# optional - sloane_database`. For example, the file`SAGE_ROOT/src/sage/databases/sloane.py`contains the lines:sage: sloane_sequence(60843) # optional - internet

and:

sage: SloaneEncyclopedia[60843] # optional - sloane_database

The first of these just needs internet access, while the second requires that the “sloane_database” package be installed. Calling

`sage -t --optional=all`on this file runs both of these tests, while calling`sage -t --optional=sage,internet`on it will only run the first test. A test requiring several packages should be marked`# optional - pkg1 pkg2`and executed by`sage -t --optional=sage,pkg1,pkg2 f.py`.Note

Any words after

`# optional`are interpreted as a list of package names, separated by spaces. Any punctuation (periods, commas, hyphens, semicolons, ...) after the first word ends the list of packages. Hyphens or colons between the word`optional`and the first package name are allowed. Therefore, you should not write`optional: needs package CHomP`but simply`optional: CHomP`. Optional tags are case-insensitive, so you could also write`optional: cHoMp`.If you are documenting a known bug in Sage, mark it as

`known bug`or`optional: bug`. For example:The following should yield 4. See :trac:`2`. :: sage: 2+2 # optional: bug 5

Then the doctest will be skipped by default, but could be revealed by running

`sage -t --optional=sage,bug ...`. (A doctest marked as`known bug`gets automatically converted to`optional bug`).Some tests (hashing for example) behave differently on 32-bit and 64-bit platforms. You can mark a line (generally the output) with either

`# 32-bit`or`# 64-bit`and the testing framework will remove any lines that don’t match the current architecture. For example:sage: z = 32 sage: z.powermodm_ui(2^32-1, 14) ... # 32-bit OverflowError: exp (=4294967295) must be <= 4294967294 # 32-bit 8 # 64-bit

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.

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 *Documentation Strings* for a discussion on how to
include examples in documentation strings and what conventions to
follow. The chapter *Doctesting the Sage Library* contains a tutorial on
doctesting modules in the Sage library.

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 ... ]`

The Sage doctesting framework is based on the standard Python doctest
module, but with many additional features (such as parallel testing,
timeouts, optional tests). The Sage doctester recognizes `sage:`
prompts as well as `>>>` prompts. It also preparses the doctests,
just like in interactive Sage sessions.

Your file passes the tests if the code in it will run when entered
at the `sage:` prompt with no extra 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.

For more information, see *Doctesting the Sage Library*.

Run `sage -t <filename.rst>` to test the examples in verbatim
environments in ReST documentation.

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:

```
EXAMPLES::
sage: a = 1
Next we add 1 to ``a``.
.. link::
sage: 1 + a
2
```

If you want to link all the verbatim environments together, you can
put `.. linkall` anywhere in the file, on a line by itself. (For
clarity, it might be best to put it near the top of the file.) Then
`sage -t` will act as if there were a `.. link` before each
verbatim environment. The file
`SAGE_ROOT/devel/sage/doc/en/tutorial/interfaces.rst` contains a
`.. linkall` directive, for example.

You can also put `.. skip` right before a verbatim environment to
have that example skipped when testing the file. This goes 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.

Sage maintains a pickle jar at
`SAGE_ROOT/src/ext/pickle_jar/pickle_jar.tar.bz2` which is a tar
file of “standard” pickles created by `sage`. This pickle jar is
used to ensure that sage maintains backward compatibility by have
having `sage.structure.sage_object.unpickle_all()` check that
`sage` can always unpickle all of the pickles in the pickle jar as
part of the standard doc testing framework.

Most people first become aware of the pickle_jar when their patch breaks the unpickling of one of the “standard” pickles in the pickle jar due to the failure of the doctest:

`sage -t devel/sage-main/sage/structure/sage_object.pyx`

When this happens an error message is printed which contains the following hints for fixing the uneatable pickle:

```
----------------------------------------------------------------------
** This error is probably due to an old pickle failing to unpickle.
** See sage.structure.sage_object.register_unpickle_override for
** how to override the default unpickling methods for (old) pickles.
** NOTE: pickles should never be removed from the pickle_jar!
----------------------------------------------------------------------
```

For more details about how to fix unpickling errors in the pickle jar
see `sage.structure.sage_object.register_unpickle_override()`

Warning

Sage’s pickle jar helps to ensure backward compatibility in sage. Pickles should
**only** be removed from the pickle jar after the corresponding objects
have been properly deprecated. Any proposal to remove pickles from the
pickle jar should first be discussed on sage-devel.

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 an example, see the file
`SAGE_ROOT/src/sage/modular/modsym/tests.py`.

Global options for classes can be defined in Sage using
`GlobalOptions`.