# SymPy Docstrings Style Guide¶

## General Guidelines¶

A documentation string (docstring) is a string literal that occurs as the first statement in a module, function, class, or method definition. Such a docstring becomes the __doc__ special attribute of that object.

Example

Here is a basic docstring:

def fdiff(self, argindex=1):
"""
Returns the first derivative of a Heaviside Function.

Examples
========

>>> from sympy import Heaviside, diff
>>> from sympy.abc import x

>>> Heaviside(x).fdiff()
DiracDelta(x)

>>> Heaviside(x**2 - 1).fdiff()
DiracDelta(x**2 - 1)

>>> diff(Heaviside(x)).fdiff()
DiracDelta(x, 1)

"""


Every public function, class, method, and module should have a docstring that describes what it does. Documentation that is specific to a function or class in the module should be in the docstring of that function or class. The module level docstring should discuss the purpose and scope of the module, and give a high-level example of how to use the functions or classes in the module. A module docstring is the docstring at the very top of the file, for example, the docstring for solvers.ode.

A public function is one that is intended to be used by the end- user, or the public. Documentation is important for public functions because they will be seen and used by many people.

A private function, on the other hand, is one that is only intended to be used in the code in SymPy itself. Although it is less important to document private functions, it also helps to have docstrings on private functions to help other SymPy developers understand how to use the function.

It may not always be clear what is a public function and what is a private function. If a function begins with an underscore, it is private, and if a function is included in __init__.py it is public, but the converse is not always true, so sometimes you have to decide based on context. In general, if you are unsure, having documentation on a function is better than not having documentation, regardless if it is public or private.

Docstrings should contain information aimed at users of the function. Comments specific to the code or other notes that would only distract users should go in comments in the code, not in docstrings.

Every docstring should have examples that show how the function works. Examples are the most important part of a docstring. A single example showing input and output to a function can be more helpful than a paragraph of descriptive text.

Remember that the primary consumers of docstrings are other human beings, not machines, so it is important to describe what the function does in plain English. Likewise, examples of how to use the function should be designed for human readers, not just for the doctest machinery.

Keep in mind that while Sphinx is the primary way users consume docstrings, and therefore the first platform to keep in mind while writing docstrings (especially for public functions), it is not the only way users consume docstrings. You can also view docstrings using help() or ? in IPython. When using help(), for instance, it will show you all of the docstrings on private methods. Additionally, anyone reading the source code directly will see every docstring.

All public functions, classes, and methods and their corresponding docstrings should be imported into the Sphinx docs, instructions on which can be found at the end of this guide.

## Formatting¶

Docstrings are are written in reStructuredText format extended by Sphinx. Here is a concise guide to Quick reStructuredText. More in-depth information about using reStructuredText can be found in the Sphinx Documentation.

In order for Sphinx to render docstrings nicely in the HTML documentation, some formatting guidelines should be followed when writing docstrings:

• Always use “””triple double quotes””” around docstrings. Use r”””raw triple double quotes””” if you use any backslashes in your docstrings.

• Include a blank line before the docstring’s closing quotes.

• Lines should not be longer than 80 characters.

• Always write class-level docstrings under the class definition line, as that is better to read in the source code.

• The various methods on the class can be mentioned in the docstring or examples if they are important, but details on them should go in the docstring for the method itself.

• Be aware that :: creates code blocks, which are rarely used in the docstrings. Any code example with example Python should be put in a doctest. Always check that the final version as rendered by Sphinx looks correct in the HTML.

• In order to make section underlining work nicely in docstrings, numpydoc Sphinx extension is used.

• Always double check that you have formatted your docstring correctly:

1. Make sure that your docstring is imported into Sphinx.

2. Build the Sphinx docs (cd doc; make html).

3. Make sure that Sphinx doesn’t output any errors.

4. Open the page in _build/html and make sure that it is formatted correctly.

## Sections¶

In SymPy’s docstrings, it is preferred that function, class, and method docstrings consist of the following sections in this order:

1. Single-Sentence Summary

2. Explanation

3. Examples

4. Parameters

6. References

The Single-Sentence Summary and Examples sections are required for every docstring. Docstrings will not pass review if these sections are not included.

Do not change the names of these supported sections, for example, the heading “Examples” as a plural should be used even if there is only one example.

SymPy will continue to support all of the section headings listed in the NumPy Docstring Guide.

Headings should be underlined with the same length in equals signs.

If a section is not required and that information for the function in question is unnecessary, do not use it. Unnecessary sections and cluttered docstrings can make a function harder to understand. Aim for the minimal amount of information required to understand the function.

### 1. Single-Sentence Summary¶

This section is required for every docstring. A docstring will not pass review if it is not included. No heading is necessary for this section.

This section consists of a one-line sentence ending in a period that describes the function, class, or method’s effect.

Deprecation warnings should go directly after the Single-Sentence Summary, so as to notify users right away. Deprecation warnings should be written as a deprecated in the Sphinx directive:

.. deprecated:: 1.1

The simplify_this function is deprecated. Use :func:simplify


See Documenting a deprecation for more details.

### 2. Explanation Section¶

This section is encouraged. If you choose to include an Explanation section in your docstring, it should be labeled with the heading “Explanation” underlined with the same length in equals signs.

Explanation
===========


This section consists of a more elaborate description of what the function, class, or method does when the concise Single-Sentence Summary will not suffice. This section should be used to clarify functionality in several sentences or paragraphs.

### 3. Examples Section¶

This section is required for every docstring. A docstring will not pass review if it is not included. It should be labeled with the heading “Examples” (even if there is only one example) underlined with the same length in equals signs.

Examples
========


This section consists of examples that show how the function works, called doctests. Doctests should be complicated enough that they fully demonstrate the API and functionality of the function, but simple enough that a user can understand them without too much thought. The perfect doctest tells the user exactly what they need to know about the function without reading any other part of the docstring.

There should always be a blank line before the doctest. When multiple examples are provided, they should be separated by blank lines. Comments explaining the examples should have blank lines both above and below them.

Do not think of doctests as tests. Think of them as examples that happen to be tested. They should demonstrate the API of the function to the user (i.e., what the input parameters look like, what the output looks like, and what it does). If you only want to test something, add a test to the relevant test_*.py file.

You can use the ./bin/coverage_doctest.py script to test the doctest coverage of a file or module. Run the doctests with ./bin/doctest.

You should only skip the testing of an example if it is impossible to test it. If necessary, testing of an example can be skipped by adding a special comment.

Example

>>> import random
>>> random.random()
0.6868680200532414


If an example is longer than 80 characters, it should be line wrapped. Examples should be line wrapped so that they are still valid Python code, using ... continuation as in a Python prompt. For example, from the ODE module documentation:

Example

>>> from sympy import Function, dsolve, cos, sin
>>> from sympy.abc import x
>>> f = Function('f')
>>> dsolve(cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x),
... f(x), hint='1st_exact')
Eq(x*cos(f(x)) + f(x)**3/3, C1)


Here dsolve(cos(f(x)) - (x*sin(f(x)) - f(x)**2)*f(x).diff(x), f(x), hint='1st_exact') is too long, so we line break it after a comma so that it is readable, and put ... on the continuation lines. If this is not done correctly, the doctests will fail.

The output of a command can also be line wrapped. No ... should be used in this case. The doctester automatically accepts output that is line wrapped.

Example

>>> list(range(30))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29]


In a doctest, write imports like sympy import ... instead of import sympy or from sympy import *. To define symbols, use from sympy.abc import x, unless the name is not in sympy.abc (for instance, if it has assumptions), in which case use symbols like x, y = symbols('x y').

In general, you should run ./bin/doctest to make sure your examples run correctly, and fix them if they do not.

### 4. Parameters Section¶

This section is encouraged. If you choose to include a Parameters section in your docstring, it should be labeled with the heading “Parameters” underlined with the same length in equals signs.

Parameters
==========


If you have parameters listed in parentheses after a function, class, or method name, you must include a parameters section.

This section consists of descriptions of the function arguments, keywords, and their respective types.

Enclose variables in double backticks. The colon must be preceded by a space, or omitted if the type is absent. For the parameter types, be as precise as possible. If it is not necessary to specify a keyword argument, use optional. Optional keyword parameters have default values, which are displayed as part of the function signature. They can also be detailed in the description.

When a parameter can only assume one of a fixed set of values, those values can be listed in braces, with the default appearing first. When two or more input parameters have exactly the same type, shape, and description, they can be combined.

If the Parameters section is not formatted correctly, the documentation build will render incorrectly.

If you wish to include a Returns section, write it as its own section with its own heading.

Example

Here is an example of a correctly formatted Parameters section:

def opt_cse(exprs, order='canonical'):
"""
Find optimization opportunities in Adds, Muls, Pows and negative
coefficient Muls.

Parameters
==========

exprs : list of sympy expressions
The expressions to optimize.
order : string, 'none' or 'canonical'
The order by which Mul and Add arguments are processed. For large
expressions where speed is a concern, use the setting order='none'.

"""


See Also
========


This section consists of a listing of related functions, classes, and methods. The related items can be described with a concise fragment (not a full sentence) if desired, but this is not required. If the description spans more than one line, subsequent lines must be indented.

The See Also section should only be used to reference other SymPy objects. Anything that is a link should be embedded as a hyperlink in the text of the docstring instead; see the References section for details.

Do not reference classes with class:Classname, class:Classname, or :class:Classname, but rather only by their class name.

Examples

class erf(Function):
r"""
The Gauss error function.

========

erfc: Complementary error function.
erfi: Imaginary error function.
erf2: Two-argument error function.
erfinv: Inverse error function.
erfcinv: Inverse Complementary error function.
erf2inv: Inverse two-argument error function.

"""


Here is a correctly formatted See Also section with just a list of names:

class besselj(BesselBase):
r"""
Bessel function of the first kind.

========

bessely, besseli, besselk

"""


### 6. References Section¶

This section is encouraged. If you choose to include a References section in your docstring, it should be labeled with the heading “References” underlined with the same length in equals signs.

References
==========


This section consists of a list of references cited anywhere in the previous sections. Any reference to other SymPy objects should go in the See Also section instead.

The References section should include online resources, paper citations, and/or any other printed resource giving general information about the function. References are meant to augment the docstring, but should not be required to understand it. References are numbered, starting from one, in the order in which they are cited.

For online resources, only link to freely accessible and stable online resources such as Wikipedia, Wolfram MathWorld, and the NIST Digital Library of Mathematical Functions (DLMF), which are unlikely to suffer from hyperlink rot.

References for papers should include, in this order: reference citation, author name, title of work, journal or publication, year published, page number.

If there is a DOI (Digital Object Identifier), include it in the citation and make sure it is a clickable hyperlink.

Examples

Here is a References section that cites a printed resource:

References
==========

.. [1] [Kozen89] D. Kozen, S. Landau, Polynomial Decomposition Algorithms,
Journal of Symbolic Computation 7 (1989), pp. 445-456


Here is a References section that cites printed and online resources:

References
==========

.. [1] Abramowitz, Milton; Stegun, Irene A., "Chapter 9," Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical
Tables, eds. (1965)
.. [2] Luke, Y. L., The Special Functions and Their Approximations,
Volume 1, (1969)
.. [3] https://en.wikipedia.org/wiki/Bessel_function
.. [4] http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/


## Sample Docstring¶

Here is an example of a correctly formatted docstring:

class gamma(Function):
r"""
The gamma function

.. math::
\Gamma(x) := \int^{\infty}_{0} t^{x-1} e^{-t} \mathrm{d}t.

Explanation
===========

The gamma function implements the function which passes through the
values of the factorial function (i.e., $\Gamma(n) = (n - 1)!$), when n
is an integer. More generally, $\Gamma(z)$ is defined in the whole
complex plane except at the negative integers where there are simple
poles.

Examples
========

>>> from sympy import S, I, pi, oo, gamma
>>> from sympy.abc import x

Several special values are known:

>>> gamma(1)
1
>>> gamma(4)
6
>>> gamma(S(3)/2)
sqrt(pi)/2

The gamma function obeys the mirror symmetry:

>>> from sympy import conjugate
>>> conjugate(gamma(x))
gamma(conjugate(x))

Differentiation with respect to $x$ is supported:

>>> from sympy import diff
>>> diff(gamma(x), x)
gamma(x)*polygamma(0, x)

Series expansion is also supported:

>>> from sympy import series
>>> series(gamma(x), x, 0, 3)
1/x - EulerGamma + x*(EulerGamma**2/2 + pi**2/12) + x**2*(-EulerGamma*pi**2/12 +
polygamma(2, 1)/6 - EulerGamma**3/6) + O(x**3)

We can numerically evaluate the gamma function to arbitrary
precision on the whole complex plane:

>>> gamma(pi).evalf(40)
2.288037795340032417959588909060233922890
>>> gamma(1+I).evalf(20)
0.49801566811835604271 - 0.15494982830181068512*I

========

lowergamma: Lower incomplete gamma function.
uppergamma: Upper incomplete gamma function.
polygamma: Polygamma function.
loggamma: Log Gamma function.
digamma: Digamma function.
trigamma: Trigamma function.
beta: Euler Beta function.

References
==========

.. [1] https://en.wikipedia.org/wiki/Gamma_function
.. [2] http://dlmf.nist.gov/5
.. [3] http://mathworld.wolfram.com/GammaFunction.html
.. [4] http://functions.wolfram.com/GammaBetaErf/Gamma/

"""


## Docstrings for Classes that are Mathematical Functions¶

SymPy is unusual in that it also has classes that are mathematical functions. The docstrings for classes that are mathematical functions should include details specific to this kind of class, as noted below:

• The Explanation section should include a mathematical definition of the function. This should use LaTeX math. Use  for inline math and .. math:: for display math, which should be used for the main definition. The variable names in the formulas should match the names of the parameters, and the LaTeX formatting should match the LaTeX pretty printing used by SymPy. As relevant, the mathematical definitions should mention their domain of definition, especially if the domain is different from the complex numbers.

• If there are multiple conventions in the literature for a function, make sure to clearly specify which convention SymPy uses.

• The Explanation section may also include some important mathematical facts about the function. These can alternately be demonstrated in the Examples section. Mathematical discussions should not be too long, as users can check the references for more details.

• The docstring does not need to discuss every implementation detail such as at which operations are defined on the function or at which points it evaluates in the “eval” method. Important or illuminating instances of these can be shown in the Examples section.

• The docstring should go on the class level (right under the line that has “class”). The “eval” method should not have a docstring.

• Private methods on the class, that is, any method that starts with an underscore, do not need to be documented. They can still be documented if you like, but note that these docstrings are not pulled into the Sphinx documentation, so they will only be seen by developers who are reading the code, so if there is anything very important that you want to mention here, it should go in the class-level docstring as well.

## Best Practices for Writing Docstrings¶

When writing docstrings, please follow all of the same formatting, style, and tone preferences as when writing narrative documentation. For guidelines, see Best Practices for Writing Documentation, Formatting, Style, and Tone.

## Importing Docstrings into the Sphinx Documentation¶

Here are excerpts from the doc/src/modules/geometry directory that imports the relevant docstrings from geometry module into documentation:

Utils
=====

.. module:: sympy.geometry.util

.. autofunction:: intersection

.. autofunction:: convex_hull

.. autofunction:: are_similar

Points
======

.. module:: sympy.geometry.point

.. autoclass:: Point
:members:

Lines
=====

.. module:: sympy.geometry.line

.. autoclass:: LinearEntity
:members:

.. autoclass:: Line
:members:

.. autoclass:: Ray
:members:

.. autoclass:: Segment
:members:

Curves
======

.. module:: sympy.geometry.curve

.. autoclass:: Curve
:members:

Ellipses
========

.. module:: sympy.geometry.ellipse

.. autoclass:: Ellipse
:members:

.. autoclass:: Circle
:members:

Polygons
========

.. module:: sympy.geometry.polygon

.. autoclass:: Polygon
:members:

.. autoclass:: RegularPolygon
:members:

.. autoclass:: Triangle
:members:


First namespace is set to particular submodule (file) with .. module:: directive, then docstrings are imported with .. autoclass:: or .. autofunction:: relative to that submodule (file). Other methods are either cumbersome to use (using full paths for all objects) or break something (importing relative to main module using .. module:: sympy.geometry breaks viewcode Sphinx extension). All files in doc/src/modules/ should use this format.

## Cross-Referencing¶

Any text that references another SymPy function should be formatted so that a cross-reference link to that function’s documentation is created automatically. This is done using the RST cross-reference syntax. There are two different kinds of objects that have conventions here:

1. Objects that are included in from sympy import *, for example, sympy.acos.

For these, use :obj:~.acos(). The ~ makes it so that the text in the rendered HTML only shows acos. Without it, it would use the fully qualified name sympy.functions.elementary.trigonometric.acos. However, for names that are part of the global sympy namespace, we do not want to encourage accessing them from their specific submodule, as this is an implementation detail that could change. The . makes it so that the function name is found automatically. Sometimes, Sphinx will give a warning that there are multiple names found. If that happens, replace the . with the full name. For example, :obj:~sympy.solvers.solvers.solve(). For functions, methods, and classes, it is a convention to add () after the name to indicate such.

You may also use a more specific type indicator instead of obj (see https://www.sphinx-doc.org/en/master/usage/restructuredtext/domains.html#cross-referencing-python-objects). However, obj will always work, and sometimes SymPy names are not the type you might expect them to be. For example, mathematical function objects such as sin are not actually a Python function, rather they are a Python class, therefore :func:~.sin will not work.

2. Objects that are not included in from sympy import *, for example, sympy.physics.vector.dynamicsymbols.

This can be public API objects from submodules that are not included in the main sympy/__init__.py, such as the physics submodule, or private API objects that are not necessarily intended to be used by end-users (but should still be documented). In this case, you must show the fully qualified name, so do not use the ~. syntax. For example, :obj:sympy.physics.vector.dynamicsymbols().

You may also write custom text that links to the documentation for something using the following syntax :obj:custom text<object>. For example, :obj:the sine function <.sin> produces the text “the sine function” that links to the documentation for sin. Note that the ~ character should not be used here.

Note that references in the See Also section of the docstrings do not require the :obj: syntax.

If the resulting cross reference is written incorrectly, Sphinx will error when building the docs with an error like:

WARNING: py:obj reference target not found: expand


Here are some troubleshooting tips to fix the errors:

• Make sure you have used the correct syntax, as described above.

• Make sure you spelled the function name correctly.

• Check if the function you are trying to cross-reference is actually included in the Sphinx documentation. If it is not, Sphinx will not be able to create a reference for it. In that case, you should add it to the appropriate RST file as described in the Docstring Guidelines.

• If the function or object is not included in from sympy import *, you will need to use the fully qualified name, like sympy.submodule.submodule.function instead of just function.

• A fully qualified name must include the full submodule for a function all the way down to the file. For example, sympy.physics.vector.ReferenceFrame will not work (even though you can access it that way in code). It has to be sympy.physics.vector.frame.ReferenceFrame.

• If the thing you are referring to does not actually have somewhere to link to, do not use the :obj: syntax. Instead, mark it as code using double backticks. Examples of things that cannot be linked to are Python built in functions like int or NotImplementedError, functions from other modules outside of SymPy like matplotlib.plot, and variable or parameter names that are specific to the text at hand. In general, if the object cannot be accessed as sympy.something.something.object, it cannot be cross- referenced and you should not use the :obj: syntax.

• If you are using are using one of the type specific identifiers like :func:, be sure that the type for it is correct. :func: only refers to Python functions. For classes, you need to use :class:, and for methods on a class you need to use :method:. In general, it is recommended to use :obj:, as this will work for any type of object.

• If you cannot get the cross-referencing syntax to work, go ahead and submit the pull request as is and ask the reviewers for help.

You may also see errors like:

WARNING: more than one target found for cross-reference 'subs()':
sympy.core.basic.Basic.subs, sympy.matrices.common.MatrixCommon.subs,
sympy.physics.vector.vector.Vector.subs,

for instance, from using :obj:~.subs. This means that the . is not sufficient to find the function, because there are multiple names in SymPy named subs. In this case, you need to use the fully qualified name. You can still use ~ to make it shortened in the final text, like :obj:~sympy.core.basic.Basic.subs.