Tutorial: Objects and Classes in Python and Sage

<span id="tutorial-objects-and-classes"></span>


</pre><p>This tutorial is an introduction to object oriented programming in Python and
Sage. It requires basic knowledges on imperative/procedural programming (the
most common programming style) that is conditional instructions, loops,
functions (see <a href="#id1"><span class="problematic" id="id2">:ref:`tutorial-programming-python`</span></a>), but now further knowledge
about objects and classes is assumed. It is designed as an alternating
sequence of formal introduction and exercises. <a href="#id3"><span class="problematic" id="id4">:ref:`solutions`</span></a> are given at
the end.</p>

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<h1>Object oriented programming paradigm</h1>
<p>The object oriented programming paradigm relies on the two following
fundamental rules:</p>
<ol class="arabic simple">
<li>Any thing of the real (or mathematical) world which needs to be manipulated
by the computer is modeled by an <strong>object</strong>.</li>
<li>Each object is an <strong>instance</strong> of some <strong>class</strong>.</li>
</ol>
<p>At this point, those two rules are a little meaningless, so let's give some
more or less precise definition of the terms:</p>
<hr class="docutils">
<dl class="docutils">
<dt><strong>object</strong></dt>
<dd>a <strong>portion of memory</strong> which contains the information needed to model
the real world thing.</dd>
<dt><strong>class</strong></dt>
<dd>defines the <strong>data structure</strong> used to store the objects which are instance
of the class together with their <strong>behavior</strong>.</dd>
</dl>
<hr class="docutils">
<p>Let's start with some examples: We consider the vector space over $QQ$ whose
basis is indexed by permutations, and a particular element in it:</p>

{{{id=0|
F = CombinatorialFreeModule(QQ, Permutations())
el = 3*F([1,3,2])+ F([1,2,3])
el
///
B[[1, 2, 3]] + 3*B[[1, 3, 2]]
}}}

<p>In python, everything is an object so there isn't any difference between types
and classes. On can get the class of the object <tt class="docutils literal"><span class="pre">el</span></tt> by:</p>
<!-- link -->

{{{id=1|
type(el)
///
<class 'sage.combinat.free_module.CombinatorialFreeModule_with_category.element_class'>
}}}

<p>As such, this is not very informative. We'll go back to it later. The data
associated to objects are stored in so called <strong>attributes</strong>. They are
accessed through the syntax <tt class="docutils literal"><span class="pre">obj.attributes_name</span></tt>:</p>
<!-- link -->

{{{id=2|
el._monomial_coefficients
///
{[1, 2, 3]: 1, [1, 3, 2]: 3}
}}}

<p>Modifying the attribute modifies the objects:</p>
<!-- link -->

{{{id=3|
el._monomial_coefficients[Permutation([3,2,1])] = 1/2
el
///
B[[1, 2, 3]] + 3*B[[1, 3, 2]] + 1/2*B[[3, 2, 1]]
}}}

<p class="first admonition-title">Warning</p>
<p>as a user, you are <em>not</em> supposed to do that by yourself (see
note on <a href="#id5"><span class="problematic" id="id6">:ref:`private attributes &lt;private_attributes&gt;`</span></a> below).</p>

<p class="system-message-title">System Message: ERROR/3 (<tt class="docutils">tutorial-objects-and-classes.rst</tt>, line 84); <em><a href="#id6">backlink</a></em></p>
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<p>As an element of a vector space <tt class="docutils literal"><span class="pre">el</span></tt> has a particular behavior:</p>
<!-- link -->

{{{id=4|
2*el
///
2*B[[1, 2, 3]] + 6*B[[1, 3, 2]] + B[[3, 2, 1]]
}}}

{{{id=5|
el.support()
///
[[1, 2, 3], [1, 3, 2], [3, 2, 1]]
}}}

{{{id=6|
el.coefficient([1, 2, 3])
///
1
}}}

<p>The behavior is defined through <strong>methods</strong> (<tt class="docutils literal"><span class="pre">support,</span> <span class="pre">coefficient</span></tt>). Note
that this is true, even for equality, printing or mathematical operations. For
example the call <tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt> actually is translated to the method call
<tt class="docutils literal"><span class="pre">a.__eq__(b)</span></tt>. The names of those special methods which are usually called
through operators are fixed by the Python language and are of the form
<tt class="docutils literal"><span class="pre">__name__</span></tt>. Example include <tt class="docutils literal"><span class="pre">__eq__</span></tt>, <tt class="docutils literal"><span class="pre">__le__</span></tt> for operators <tt class="docutils literal"><span class="pre">==</span></tt> and
<tt class="docutils literal"><span class="pre">&lt;=</span></tt>, <tt class="docutils literal"><span class="pre">__repr__</span></tt> (see <a href="#id7"><span class="problematic" id="id8">:ref:`sage_specifics`</span></a>) for printing, <tt class="docutils literal"><span class="pre">__add__</span></tt> and
<tt class="docutils literal"><span class="pre">__mult__</span></tt> for operators <tt class="docutils literal"><span class="pre">+</span></tt> and <tt class="docutils literal"><span class="pre">*</span></tt> (see
<a class="reference external" href="http://docs.python.org/library/">http://docs.python.org/library/</a>) for a complete list:</p>

<p class="system-message-title">System Message: ERROR/3 (<tt class="docutils">tutorial-objects-and-classes.rst</tt>, line 100); <em><a href="#id8">backlink</a></em></p>
Unknown interpreted text role &quot;ref&quot;.
<!-- link -->

{{{id=7|
el.__eq__(F([1,3,2]))
///
False
}}}

{{{id=8|
el.__repr__()
///
'B[[1, 2, 3]] + 3*B[[1, 3, 2]] + 1/2*B[[3, 2, 1]]'
}}}

{{{id=9|
el.__mul__(2)
///
2*B[[1, 2, 3]] + 6*B[[1, 3, 2]] + B[[3, 2, 1]]
}}}

<p>Some particular actions allows to modify the data structure of <tt class="docutils literal"><span class="pre">el</span></tt>:</p>
<!-- link -->

{{{id=10|
el.rename(&quot;bla&quot;)
el
///
bla
}}}

<p class="first admonition-title">Note</p>
<p>The class is stored in a particular attribute called <tt class="docutils literal"><span class="pre">__class__</span></tt> the
normal attribute are stored in a dictionary called <tt class="docutils literal"><span class="pre">__dict__</span></tt>:</p>
<!-- link -->

{{{id=11|
F = CombinatorialFreeModule(QQ, Permutations())
el = 3*F([1,3,2])+ F([1,2,3])
el.rename(&quot;foo&quot;)
el.__class__
///
 <class 'sage.combinat.free_module.CombinatorialFreeModule_with_category.element_class'>
}}}

{{{id=12|
el.__dict__
///
{'_monomial_coefficients': {[1, 2, 3]: 1, [1, 3, 2]: 3}, '__custom_name': 'foo'}
}}}

<p>Lots of sage objects are not Python objects but compiled Cython
objects. Python sees them as builtin objects and you don't have access to
the data structure. Examples include integers and permutation group
elements:</p>
<!-- link -->
<pre class="last literal-block">
sage: e = Integer(9)
sage: type(e)
&lt;type 'sage.rings.integer.Integer'&gt;
sage: e.__dict__
&lt;dictproxy object at 0x...&gt;
sage: e.__dict__.keys()
['__module__', '_reduction', '__doc__', '_sage_src_lines_']

sage: id4 = SymmetricGroup(4).one()
sage: type(id4)
&lt;type 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement'&gt;
sage: id4.__dict__
&lt;dictproxy object at 0x...&gt;
</pre>


<p class="first admonition-title">Note</p>
<p>Each objects corresponds to a portion of memory called its <strong>identity</strong> in
python. You can get the identity using <tt class="docutils literal"><span class="pre">id</span></tt>:</p>
<!-- link -->

{{{id=13|
el = Integer(9)
id(el)  # random
///
139813642977744
}}}

{{{id=14|
el1 = el; id(el1) == id(el)
///
True
}}}

{{{id=15|
el1 is el
///
True
}}}

<p>This is different from mathematical identity:</p>
<!-- link -->
<pre class="last literal-block">
sage: el2 = Integer(9)
sage: el2 == el1
True
sage: el2 is el1
False
sage: id(el2) == id(el)
False
</pre>


<h2>Summary</h2>
<p>To define some object, you first have to write a <strong>class</strong>. The class will
defines the methods and the attributes of the object.</p>
<dl class="docutils">
<dt><strong>method</strong></dt>
<dd>particular kind of function associated with an object used to get
information about the object or to manipulate it.</dd>
<dt><strong>attribute</strong></dt>
<dd>variables where the info about the object are stored;</dd>
</dl>


<h2>An example: glass of beverage in a restaurant</h2>
<p>Let's write a small class about glasses in a restaurant:</p>

{{{id=16|
class Glass(object):
       def __init__(self, size):
           assert size &gt; 0
           self._size = float(size)
           self._content = float(0.0)
       def __repr__(self):
           if self._content == 0.0:
               return &quot;An empty glass of size %s&quot;%(self._size)
           else:
               return &quot;A glass of size %s cl containing %s cl of water&quot;%(
                       self._size, self._content)
       def fill(self):
           self._content = self._size
       def empty(self):
           self._content = float(0.0)
///
}}}

<p>Let's create a small glass:</p>
<!-- link -->

{{{id=17|
myGlass = Glass(10); myGlass
///
An empty glass of size 10.0
}}}

{{{id=18|
myGlass.fill(); myGlass
///
A glass of size 10.0 cl containing 10.0 cl of water
}}}

{{{id=19|
myGlass.empty(); myGlass
///
An empty glass of size 10.0
}}}

<p>Some comments:</p>
<ol class="arabic simple">
<li>The method <tt class="docutils literal"><span class="pre">__init__</span></tt> is used to initialize the object, it is used by the
so called <strong>constructor</strong> of the class that is executed when calling <tt class="docutils literal"><span class="pre">Glass(10)</span></tt>.</li>
<li>The method <tt class="docutils literal"><span class="pre">__repr__</span></tt> is supposed to return a string which is used to
print the object.</li>
</ol>

<p class="first admonition-title">Note</p>
<p><strong>Private Attributes</strong></p>
<ul class="last simple" id="private-attributes">
<li>most of the time, the user should not change directly the
attribute of an object. Those attributes are called <strong>private</strong>. Since
there is no mechanism to ensure privacy in python, the usage is to prefix
the name by an underscore.</li>
<li>as a consequence attribute access is only made through methods.</li>
<li>methods which are only for internal use are also prefixed with an
underscore.</li>
</ul>



<h2>Exercises</h2>
<ol class="arabic simple">
<li>add a method <tt class="docutils literal"><span class="pre">is_empty</span></tt> which returns true if a glass is empty.</li>
<li>define a method <tt class="docutils literal"><span class="pre">drink</span></tt> with a parameter <tt class="docutils literal"><span class="pre">amount</span></tt> which allows to
partially drink the water in the glass. Raise an error if one asks to
drink more water than there is in the glass or a negative amount of
water.</li>
<li>Allows the glass to be filled with wine, beer or other beverage. The method
<tt class="docutils literal"><span class="pre">fill</span></tt> should accept a parameter <tt class="docutils literal"><span class="pre">beverage</span></tt>. The beverage is stored in
an attribute <tt class="docutils literal"><span class="pre">_beverage</span></tt>. Update the method <tt class="docutils literal"><span class="pre">__repr__</span></tt> accordingly.</li>
<li>Add an attribute <tt class="docutils literal"><span class="pre">_clean</span></tt> and methods <tt class="docutils literal"><span class="pre">is_clean</span></tt> and <tt class="docutils literal"><span class="pre">wash</span></tt>. At the
creation a glass is clean, as soon as it's filled it becomes dirty, and must
be washed to become clean again.</li>
<li>Test everything.</li>
<li>Make sure that everything is tested.</li>
<li>Test everything again.</li>
</ol>



<h1>Inheritance</h1>
<p>The problem: object of <strong>different</strong> classes may share a <strong>common behavior</strong>.</p>
<p>For example, if one wants to deal now with different dishes (forks, spoons
...) then there is common behavior (becoming dirty and being washed). So the
different classes associated to the different kinds of dishes should have the
same <tt class="docutils literal"><span class="pre">clean</span></tt>, <tt class="docutils literal"><span class="pre">is_clean</span></tt> and <tt class="docutils literal"><span class="pre">wash</span></tt> methods. But copying and pasting
code is bad and evil ! This is done by having a base class which factorizes
the common behavior:</p>

{{{id=20|
class AbstractDish(object):
       def __init__(self):
           self._clean = True
       def is_clean(self):
           return self._clean
       def state(self):
           return &quot;clean&quot; if self.is_clean() else &quot;dirty&quot;
       def __repr__(self):
           return &quot;An unspecified %s dish&quot;%self.state()
       def _make_dirty(self):
           self._clean = False
       def wash(self):
           self._clean = True
///
}}}

<p>Now one can reuse this behavior within a class <tt class="docutils literal"><span class="pre">Spoon</span></tt>:</p>
<!-- link -->

{{{id=21|
class Spoon(AbstractDish):
       def __repr__(self):
           return &quot;A %s spoon&quot;%self.state()
       def eat_with(self):
           self._make_dirty()
///
}}}

<p>Let's tests it:</p>
<!-- link -->

{{{id=22|
s = Spoon(); s
///
A clean spoon
}}}

{{{id=23|
s.is_clean()
///
True
}}}

{{{id=24|
s.eat_with(); s
///
A dirty spoon
}}}

{{{id=25|
s.is_clean()
///
False
}}}

{{{id=26|
s.wash(); s
///
A clean spoon
}}}

<h2>Summary</h2>
<ol class="arabic">
<li><p class="first">Any class can reuse the behavior of another class. One says that the
subclass <strong>inherits</strong> from the superclass or that it <strong>derives</strong> from it.</p>
</li>
<li><p class="first">Any instance of the subclass is also an instance its superclass:</p>
<!-- link -->

{{{id=27|
type(s)
///
<class '__main__.Spoon'>
}}}

{{{id=28|
isinstance(s, Spoon)
///
True
}}}

{{{id=29|
isinstance(s, AbstractDish)
///
True
}}}

</li>
<li><p class="first">If a subclass redefines a method, then it replaces the former one. One says
that the subclass <strong>overloads</strong> the method. One can nevertheless explicitly
call the hidden superclass method.</p>
<!-- link -->

{{{id=30|
s.__repr__()
///
'A clean spoon'
}}}

{{{id=31|
Spoon.__repr__(s)
///
'A clean spoon'
}}}

{{{id=32|
AbstractDish.__repr__(s)
///
'An unspecified clean dish'
}}}

</li>
</ol>

<p class="first admonition-title">Note</p>
<p><strong>Advanced superclass method call</strong></p>
<p>Sometimes one wants to call an overloaded method without knowing in which
class it is defined. On use the <tt class="docutils literal"><span class="pre">super</span></tt> operator</p>
<!-- link -->

{{{id=33|
super(Spoon, s).__repr__()
///
'An unspecified clean dish'
}}}

<p>A very common usage of this construct is to call the __init__ method of the
super classes:</p>
<!-- link -->
<pre class="last literal-block">
sage: class Spoon(AbstractDish):
...       def __init__(self):
...           print &quot;Building a spoon&quot;
...           super(Spoon, self).__init__()
...       def __repr__(self):
...           return &quot;A %s spoon&quot;%self.state()
...       def eat_with(self):
...           self.make_dirty()
sage: s = Spoon()
Building a spoon
sage: s
A clean spoon
</pre>



<h2>Exercises</h2>
<ol class="arabic simple">
<li>Modify the class <tt class="docutils literal"><span class="pre">Glasses</span></tt> so that it inherits from <tt class="docutils literal"><span class="pre">Dish</span></tt>.</li>
<li>Write a class <tt class="docutils literal"><span class="pre">Plate</span></tt> whose instance can contain any meals together with
a class <tt class="docutils literal"><span class="pre">Fork</span></tt>. Avoid at much as possible code duplication (hint:
you can write a factorized class <tt class="docutils literal"><span class="pre">ContainerDish</span></tt>).</li>
<li>Test everything.</li>
</ol>



<span id="sage-specifics"></span><h1>Sage specifics about classes</h1>
<p>Compared to Python, Sage has its particular way to handles objects:</p>
<ul class="simple">
<li>Any classes for mathematical objects in Sage should inherits from
<tt class="docutils literal"><span class="pre">SageObject</span></tt> rather than from <tt class="docutils literal"><span class="pre">object</span></tt>.</li>
<li>Printing should be done through <tt class="docutils literal"><span class="pre">_repr_</span></tt> instead of <tt class="docutils literal"><span class="pre">__repr__</span></tt> to allows
for renaming.</li>
<li>More generally, Sage specific special methods are usually named <tt class="docutils literal"><span class="pre">_meth_</span></tt>
rather than <tt class="docutils literal"><span class="pre">__meth__</span></tt>. For example, lots of classes implement <tt class="docutils literal"><span class="pre">_hash_</span></tt>
which is used and cached by <tt class="docutils literal"><span class="pre">__hash__</span></tt>.</li>
</ul>


<span id="solutions"></span><h1>Solutions to the exercises</h1>
<ol class="arabic">
<li><p class="first">Here is a solution to the first exercise:</p>

{{{id=34|
class Glass(object):
       def __init__(self, size):
           assert size &gt; 0
           self._size = float(size)
           self.wash()
       def __repr__(self):
           if self._content == 0.0:
               return &quot;An empty glass of size %s&quot;%(self._size)
           else:
               return &quot;A glass of size %s cl containing %s cl of %s&quot;%(
                       self._size, self._content, self._beverage)
       def content(self):
           return self._content
       def beverage(self):
           return self._beverage
       def fill(self, beverage = &quot;water&quot;):
           if not self.is_clean():
               raise ValueError, &quot;Don't want to fill a dirty glass&quot;
           self._clean = False
           self._content = self._size
           self._beverage = beverage
       def empty(self):
           self._content = float(0.0)
       def is_empty(self):
           return self._content == 0.0
       def drink(self, amount):
           if amount &lt;= 0.0:
               raise ValueError, &quot;amount must be positive&quot;
           elif amount &gt; self._content:
               raise ValueError, &quot;not enough beverage in the glass&quot;
           else:
               self._content -= float(amount)
       def is_clean(self):
           return self._clean
       def wash(self):
           self._content = float(0.0)
           self._beverage = None
           self._clean = True
///
}}}

</li>
<li><p class="first">Let's check that everything is working as expected:</p>
<!-- link -->

{{{id=35|
G = Glass(10.0)
G
///
An empty glass of size 10.0
}}}

{{{id=36|
G.is_empty()
///
True
}}}

{{{id=37|
G.drink(2)
///
Traceback (most recent call last):
ValueError: not enough beverage in the glass
}}}

{{{id=38|
G.fill(&quot;beer&quot;)
G
///
A glass of size 10.0 cl containing 10.0 cl of beer
}}}

{{{id=39|
G.is_empty()
///
False
}}}

{{{id=40|
G.is_clean()
///
False
}}}

{{{id=41|
G.drink(5.0)
G
///
A glass of size 10.0 cl containing 5.0 cl of beer
}}}

{{{id=42|
G.is_empty()
///
False
}}}

{{{id=43|
G.is_clean()
///
False
}}}

{{{id=44|
G.drink(5)
G
///
An empty glass of size 10.0
}}}

{{{id=45|
G.is_clean()
///
False
}}}

{{{id=46|
G.fill(&quot;orange juice&quot;)
///
Traceback (most recent call last):
ValueError: Don't want to fill a dirty glass
}}}

{{{id=47|
G.wash()
G
///
An empty glass of size 10.0
}}}

{{{id=48|
G.fill(&quot;orange juice&quot;)
G
///
A glass of size 10.0 cl containing 10.0 cl of orange juice
}}}

</li>
</ol>
<p>Here is the solution to the second exercice:</p>
<p>TODO !!!!</p>
<p>That all folks !</p>