Path: blob/master/doc/en/developer/coding_in_python.rst
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.. _chapter-python:
=========================
Coding in Python for Sage
=========================
This chapter discusses some issues with, and advice for, coding in
Sage.
Design
======
If you are planning to develop some new code for Sage, design is
important. So think about what your program will do and how that fits
into the structure of Sage. In particular, much of Sage is implemented
in the object-oriented language Python, and there is a hierarchy of
classes that organize code and functionality. For example, if you
implement elements of a ring, your class should derive from
``sage.structure.element.RingElement``, rather than starting from
scratch. Try to figure out how your code should fit in with other Sage
code, and design it accordingly.
Special Sage functions
======================
Functions with leading and trailing double underscores ``__XXX__`` are
all predefined by Python. Functions with leading and trailing single
underscores ``_XXX_`` are defined for Sage. Functions with a single
leading underscore are meant to be semi-private, and those with a
double leading underscore are considered really private. Users can
create functions with leading and trailing underscores.
Just as Python has many standard special methods for objects, Sage
also has special methods. They are typically of the form
``_XXX_``. (In a few cases, the trailing underscore is not included,
but this will be changed so that the trailing underscore is always
included.) This section describes these special methods.
All objects in Sage should derive from the Cython extension class
``SageObject``:
::
from sage.ext.sage_object import SageObject
class MyClass(SageObject,...):
...
or from some other already existing Sage class:
::
from sage.rings.ring import Algebra
class MyFavoriteAlgebra(Algebra):
...
You should implement the ``_latex_`` and ``_repr_`` method for every
object. The other methods depend on the nature of the object.
LaTeX representation
--------------------
Every object ``x`` in Sage should support the command ``latex(x)``, so
that any Sage object can be easily and accurately displayed via
LaTeX. Here is how to make a class (and therefore its instances)
support the command ``latex``.
#. Define a method ``_latex_(self)`` that returns a LaTeX
representation of your object. It should be something that can be
typeset correctly within math mode. Do not include opening and
closing $'s.
#. Often objects are built up out of other Sage objects, and these
components should be typeset using the ``latex`` function. For
example, if ``c`` is a coefficient of your object, and you want to
typeset ``c`` using LaTeX, use ``latex(c)`` instead of
``c._latex_()``, since ``c`` might not have a ``_latex_`` method,
and ``latex(c)`` knows how to deal with this.
#. Do not forget to include a docstring and an example that
illustrates LaTeX generation for your object.
#. You can use any macros included in ``amsmath``, ``amssymb``, or
``amsfonts``, or the ones defined in
``SAGE_ROOT/doc/commontex/macros.tex``.
An example template for a ``_latex_`` method follows:
::
class X:
...
def _latex_(self):
r"""
Returns the LaTeX representation of X.
EXAMPLES::
sage: a = X(1,2)
sage: latex(a)
'\\frac{1}{2}'
"""
return '\\frac{%s}{%s}'%(latex(self.numer), latex(self.denom))
As shown in the example, ``latex(a)`` will produce LaTeX code
representing the object ``a``. Calling ``view(a)`` will display the
typeset version of this.
Print representation
--------------------
The standard Python printing method is ``__repr__(self)``. In Sage,
that is for objects that derive from ``SageObject`` (which is
everything in Sage), instead define ``_repr_(self)``. This is
preferable because if you only define ``_repr_(self)`` and not
``__repr__(self)``, then users can rename your object to print however
they like. Also, some objects should print differently depending on
the context.
Here is an example of the ``_latex_`` and ``_repr_`` functions for the
``Pi`` class. It is from the file
``SAGE_ROOT/devel/sage/sage/functions/constants.py``:
::
class Pi(Constant):
"""
The ratio of a circle's circumference to its diameter.
EXAMPLES:
sage: pi
pi
sage: float(pi)
3.1415926535897931
"""
...
def _repr_(self):
return "pi"
def _latex_(self):
return "\\pi"
Matrix or vector from object
----------------------------
Provide a ``_matrix_`` method for an object that can be coerced to a
matrix over a ring `R`. Then the Sage function ``matrix`` will work
for this object.
The following is from
``SAGE_ROOT/devel/sage/sage/graphs/graph.py``:
::
class GenericGraph(SageObject):
...
def _matrix_(self, R=None):
if R is None:
return self.am()
else:
return self.am().change_ring(R)
def adjacency_matrix(self, sparse=None, boundary_first=False):
...
Similarly, provide a ``_vector_`` method for an object that can be
coerced to a vector over a ring `R`. Then the Sage function ``vector``
will work for this object.
.. Provide example from a .py file
The following is from the file
``SAGE_ROOT/sage/sage/modules/free_module_element.pyx``::
cdef class FreeModuleElement(element_Vector): # abstract base class
...
def _vector_(self, R):
return self.change_ring(R)
.. _section-preparsing:
Sage preparsing
===============
The following files are relevant to preparsing in Sage:
#. ``SAGE_ROOT/spkg/bin/sage``
#. ``SAGE_ROOT/local/bin/sage-preparse``
#. ``SAGE_ROOT/devel/sage/sage/misc/preparser.py``
.. Talk about ``SAGE_ROOT/devel/sage/sage/misc/preparser_ipython.py`` file
In particular, the file ``preparser.py`` contains the Sage preparser
code. The following are some notes from it:
- In Sage, methods can be called on integer and real literals. Note
that in pure Python this would be a syntax error. For example:
::
sage: 16.sqrt()
4
sage: 87.factor()
3 * 29
- Raw literals are not preparsed, which can be useful from an
efficiency point of view. Just like Python ints are denoted by an
L, in Sage raw integer and floating literals are followed by an "r"
(or "R") for raw, meaning not preparsed. For example:
::
sage: a = 393939r
sage: a
393939
sage: type(a)
<type 'int'>
sage: b = 393939
sage: type(b)
<type 'sage.rings.integer.Integer'>
sage: a == b
True
- Raw literals can be very useful in certain cases. For instance,
Python integers can be more efficient than Sage integers when they
are very small. Large Sage integers are much more efficient than
Python integers since they are implemented using the GMP C
library.
Consult the file ``preparser.py`` for more details about Sage
preparsing, more examples involving raw literals, etc.
When a file ``foo.sage`` is loaded in a Sage session, a preparsed
version of ``foo.sage`` is created and named ``foo.py``. The beginning
of ``foo.py`` states:
::
This file was *autogenerated* from the file foo.sage.
The Sage coercion model
=======================
The primary goal of coercion is to be able to transparently do
arithmetic, comparisons, etc. between elements of distinct sets. For
example, when one writes `1 + 1/2`, one wants to perform arithmetic on
the operands as rational numbers, despite the left term being an
integer. This makes sense given the obvious and natural inclusion of
the integers into the rational numbers. The goal of the coercion
system is to facilitate this (and more complicated arithmetic) without
having to explicitly map everything over into the same domain, and at
the same time being strict enough to not resolve ambiguity or accept
nonsense.
The coercion model for Sage is described in detail, with examples, in
the Coercion section of the Sage Reference Manual.
Mutability
==========
Parent structures (e.g. rings, fields, matrix spaces, etc.) should be
immutable and globally unique whenever possible. Immutability means,
among other things, that properties like generator labels and default
coercion precision cannot be changed.
Global uniqueness while not wasting memory is best implemented using
the standard Python weakref module, a factory function, and module
scope variable.
.. {Rewrite. Difficult to parse. Make gentler}
.. {Put a tutorial on this here}
Certain objects, e.g. matrices, may start out mutable and become
immutable later. See the file
``SAGE_ROOT/devel/sage/sage/structure/mutability.py``.
The __hash__ special method
============================
Here is the definition of ``__hash__`` from the Python reference
manual.
Called by built-in function ``hash()`` and for operations on members of
hashed collections including set, frozenset, and dict. ``__hash__()``
should return an integer. The only required property is that objects which
compare equal have the same hash value; it is advised to somehow mix
together (e.g. using exclusive or) the hash values for the components of
the object that also play a part in comparison of objects. If a class does
not define a
``__cmp__()`` method it should not define a
``__hash__()`` operation either; if it defines
``__cmp__()`` or ``__eq__()`` but not
``__hash__()``, its instances will not be usable as
dictionary keys. If a class defines mutable objects and implements
a ``__cmp__()`` or ``__eq__()`` method, it
should not implement ``__hash__()``, since the dictionary
implementation requires that a key's hash value is immutable (if
the object's hash value changes, it will be in the wrong hash
bucket).
Notice the phrase, "The only required property is that objects which
compare equal have the same hash value." This is an assumption made by
the Python language, which in Sage we simply cannot make (!), and
violating it has consequences. Fortunately, the consequences are
pretty clearly defined and reasonably easy to understand, so if you
know about them they do not cause you trouble. The following example
illustrates them pretty well:
::
sage: v = [Mod(2,7)]
sage: 9 in v
True
sage: v = set([Mod(2,7)])
sage: 9 in v
False
sage: 2 in v
True
sage: w = {Mod(2,7):'a'}
sage: w[2]
'a'
sage: w[9]
Traceback (most recent call last):
...
KeyError: 9
Here is another example:
::
sage: R = RealField(10000)
sage: a = R(1) + R(10)^-100
sage: a == RDF(1) # because the a gets coerced down to RDF
True
but ``hash(a)`` should not equal ``hash(1)``.
Unfortunately, in Sage we simply cannot require
::
(#) "a == b ==> hash(a) == hash(b)"
because serious mathematics is simply too complicated for this
rule. For example, the equalities ``z == Mod(z, 2)`` and
``z == Mod(z, 3)`` would force ``hash()`` to be constant on the
integers.
The only way we could "fix" this problem for good would be to abandon
using the ``==`` operator for "Sage equality", and implement Sage
equality as a new method attached to each object. Then we could follow
Python rules for ``==`` and our rules for everything else, and all
Sage code would become completely unreadable (and for that matter
unwritable). So we just have to live with it.
So what is done in Sage is to attempt to satisfy ``(#)`` when it is
reasonably easy to do so, but use judgment and not go overboard.
For example,
::
sage: hash(Mod(2,7))
2
The output 2 is better than some random hash that also involves the
moduli, but it is of course not right from the Python point of view,
since ``9 == Mod(2,7)``.
The goal is to make a hash function that is fast, but within reason
respects any obvious natural inclusions and coercions.
Exceptions
==========
Please avoid code like this:
::
try:
some_code()
except: # bad
more_code()
Instead, catch specific exceptions. For example,
::
try:
return self.__coordinate_ring
except (AttributeError, OtherExceptions), msg: # Good
more_code_to_compute_something()
Note that the syntax in ``except`` is to list all the exceptions that
are caught as a tuple, followed by an error message.
If you do not have any exceptions explicitly listed (as a tuple), your
code will catch absolutely anything, including ``ctrl-C``, typos in
the code, and alarms, and this will lead to confusion. Also, this
might catch real errors which should be propagated to the user.
Importing
=========
We mention two issues with importing: circular imports and importing
large third-party modules.
First, you must avoid circular imports. For example, suppose that
the file
``SAGE_ROOT/devel/sage/sage/algebras/steenrod_algebra.py``
started with a line
::
from sage.sage.algebras.steenrod_algebra_bases import *
and that the file
``SAGE_ROOT/devel/sage/sage/algebras/steenrod_algebra_bases.py``
started with a line
::
from sage.sage.algebras.steenrod_algebra import SteenrodAlgebra
This sets up a loop: loading one of these files requires the other,
which then requires the first, etc.
With this set-up, running Sage will produce an error:
::
Exception exceptions.ImportError: 'cannot import name SteenrodAlgebra'
in 'sage.rings.polynomial.polynomial_element.
Polynomial_generic_dense.__normalize' ignored
-------------------------------------------------------------------
ImportError Traceback (most recent call last)
...
ImportError: cannot import name SteenrodAlgebra
Instead, you might replace the ``import *`` line at the top of the
file by more specific imports where they are needed in the code. For
example, the ``basis`` method for the class ``SteenrodAlgebra`` might
look like this (omitting the documentation string):
::
def basis(self, n):
from steenrod_algebra_bases import steenrod_algebra_basis
return steenrod_algebra_basis(n, basis=self._basis_name, p=self.prime)
Second, do not import at the top level of your module a third-party
module that will take a long time to initialize (e.g. matplotlib). As
above, you might instead import specific components of the module when
they are needed, rather than at the top level of your file.
It is important to try to make ``from sage.all import *`` as fast as
possible, since this is what dominates the Sage startup time, and
controlling the top-level imports helps to do this.
Editing existing files
======================
There are several copies of Sage library files, and it can be
confusing for beginners to know which one to modify. In the directory
``SAGE_ROOT/devel/sage``, there is a subdirectory ``build`` which
contains copies of Python files and their byte-compiled versions,
along with compiled version of Cython files. These are the files that
Sage actually uses, but *you* *never* *need* *to* *touch* *these*.
Instead, always work with files in the directory
``SAGE_ROOT/devel/sage/sage``. For example, if you want to add a new
method for simplicial complexes, then edit the file
``SAGE_ROOT/devel/sage/sage/homology/simplicial_complex.py``. Save
your changes, and then type ``sage -b`` to incorporate those changes.
This automatically copies the appropriate files into the appropriate
places under ``SAGE_ROOT/devel/sage/build``.
You should also read :ref:`chapter-mercurial` for information about
how to create a copy of the Sage library and make your changes there,
so that first, it is easy to undo your changes, and second, it is easy
to produce a "patch" file so you can share your changes with other
people.
Creating a new directory
========================
If you want to create a new directory in the Sage library
``SAGE_ROOT/devel/sage/sage`` (say, ``measure_theory``), that directory
should contain an empty file ``__init__.py`` 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. The file ``all.py`` might look like this::
from borel_measure import BorelMeasure
from banach_tarski import BanachTarskiParadox
Then in the file ``SAGE_ROOT/devel/sage/sage/all.py``, add a line ::
from sage.measure_theory.all import *
Finally, add the directory name ("measure_theory") to the ``packages``
list in the Distutils section of the file
``SAGE_ROOT/devel/sage/setup.py``: add a line ::
'sage.measure_theory',
between ::
'sage.matrix',
and ::
'sage.media',
As noted above, you should also read :ref:`chapter-mercurial` for
information about how to do this in a copy of the Sage library and how
to disseminate your changes.
Using optional packages
=======================
If a function requires an optional package, that function should fail
gracefully---perhaps using a ``try``-``except`` block---when the
optional package is not available, and should give a hint about how to
install it. For example, typing ``sage -optional`` gives a list of all
optional packages, so it might suggest to the user that they type
that. The command ``optional_packages()`` from within Sage also
returns this list.