Dynamic classes¶
Why dynamic classes?
The short answer:
 Multiple inheritance is a powerful tool for constructing new classes by combining preexisting building blocks.
 There is a combinatorial explosion in the number of potentially useful classes that can be produced this way.
 The implementation of standard mathematical constructions calls for producing such combinations automatically.
 Dynamic classes, i.e. classes created on the fly by the Python interpreter, are a natural mean to achieve this.
The long answer:
Say we want to construct a new class MyPermutation
for
permutations in a given set \(S\) (in Sage, \(S\) will be modelled by a
parent, but we won’t discuss this point here). First, we have to
choose a data structure for the permutations, typically among the
following:
 Stored by cycle type
 Stored by code
 Stored in list notation  C arrays of short ints (for small permutations)  python lists of ints (for huge permutations)  …
 Stored by reduced word
 Stored as a function
 …
Luckily, the Sage library provides (or will provide) classes implementing each of those data structures. Those classes all share a common interface (or possibly a common abstract base class). So we can just derive our class from the chosen one:
class MyPermutation(PermutationCycleType):
...
Then we may want to further choose a specific memory behavior (unique representation, copyonwrite) which (hopefuly) can again be achieved by inheritance:
class MyPermutation(UniqueRepresentation, PermutationCycleType):
...
Finaly, we may want to endow the permutations in \(S\) with further operations coming from the (algebraic) structure of \(S\):
 group operations
 or just monoid operations (for a subset of permutations not stable by inverse)
 poset operations (for left/right/Bruhat order)
 word operations (searching for substrings, patterns, …)
Or any combination thereof. Now, our class typically looks like:
class MyPermutation(UniqueRepresentation, PermutationCycleType, PosetElement, GroupElement):
...
Note the combinatorial explosion in the potential number of classes which can be created this way.
In practice, such classes will be used in mathematical constructions like:
SymmetricGroup(5).subset(... TODO: find a good example in the context above ...)
In such a construction, the structure of the result, and therefore the operations on its elements can only be determined at execution time. Let us take another standard construction:
A = cartesian_product( B, C )
Depending on the structure of \(B\) and \(C\), and possibly on further options passed down by the user, \(A\) may be:
 an enumerated set
 a group
 an algebra
 a poset
 …
Or any combination thereof.
Hardcoding classes for all potential combinations would be at best tedious. Furthermore, this would require a cumbersome mechanism to lookup the appropriate class depending on the desired combination.
Instead, one may use the ability of Python to create new classes dynamically:
type("class name", tuple of base classes, dictionary of methods)
This paradigm is powerful, but there are some technicalities to address. The purpose of this library is to standardize its use within Sage, and in particular to ensure that the constructed classes are reused whenever possible (unique representation), and can be pickled.
Combining dynamic classes and Cython classes
Cython classes cannot inherit from a dynamic class (there might be
some partial support for this in the future). On the other hand, such
an inheritance can be partially emulated using __getattr__()
. See
sage.categories.examples.semigroups_cython
for an example.

class
sage.structure.dynamic_class.
DynamicClasscallMetaclass
¶ Bases:
sage.structure.dynamic_class.DynamicMetaclass
,sage.misc.classcall_metaclass.ClasscallMetaclass

class
sage.structure.dynamic_class.
DynamicInheritComparisonClasscallMetaclass
¶ Bases:
sage.structure.dynamic_class.DynamicMetaclass
,sage.misc.inherit_comparison.InheritComparisonClasscallMetaclass

class
sage.structure.dynamic_class.
DynamicInheritComparisonMetaclass
¶ Bases:
sage.structure.dynamic_class.DynamicMetaclass
,sage.misc.inherit_comparison.InheritComparisonMetaclass

class
sage.structure.dynamic_class.
DynamicMetaclass
¶ Bases:
type
A metaclass implementing an appropriate reducebyconstruction method

sage.structure.dynamic_class.
M
¶ alias of
sage.structure.dynamic_class.DynamicInheritComparisonClasscallMetaclass

class
sage.structure.dynamic_class.
TestClass
¶ Bases:
object
A class used for checking that introspection works

bla
()¶ bla …


sage.structure.dynamic_class.
dynamic_class
(name, bases, cls=None, reduction=None, doccls=None, prepend_cls_bases=True, cache=True)¶ INPUT:
name
– a stringbases
– a tuple of classescls
– a class orNone
reduction
– a tuple orNone
doccls
– a class orNone
prepend_cls_bases
– a boolean (default:True
)cache
– a boolean or"ignore_reduction"
(default:True
)
Constructs dynamically a new class
C
with namename
, and basesbases
. Ifcls
is provided, then its methods will be inserted intoC
, and its bases will be prepended tobases
(unlessprepend_cls_bases
isFalse
).The module, documentation and source instrospection is taken from
doccls
, orcls
ifdoccls
isNone
, orbases[0]
if both areNone
(thereforebases
should be non empty ifcls` is ``None
).The constructed class can safely be pickled (assuming the arguments themselves can).
Unless
cache
isFalse
, the result is cached, ensuring unique representation of dynamic classes.See
sage.structure.dynamic_class
for a discussion of the dynamic classes paradigm, and its relevance to Sage.EXAMPLES:
To setup the stage, we create a class Foo with some methods, cached methods, and lazy attributes, and a class Bar:
sage: from sage.misc.lazy_attribute import lazy_attribute sage: from sage.misc.cachefunc import cached_function sage: from sage.structure.dynamic_class import dynamic_class sage: class Foo(object): ....: "The Foo class" ....: def __init__(self, x): ....: self._x = x ....: @cached_method ....: def f(self): ....: return self._x^2 ....: def g(self): ....: return self._x^2 ....: @lazy_attribute ....: def x(self): ....: return self._x sage: class Bar: ....: def bar(self): ....: return self._x^2
We now create a class FooBar which is a copy of Foo, except that it also inherits from Bar:
sage: FooBar = dynamic_class("FooBar", (Bar,), Foo) sage: x = FooBar(3) sage: x.f() 9 sage: x.f() is x.f() True sage: x.x 3 sage: x.bar() 9 sage: FooBar.__name__ 'FooBar' sage: FooBar.__module__ '__main__' sage: Foo.__bases__ (<type 'object'>,) sage: FooBar.__bases__ # py2 (<type 'object'>, <class __main__.Bar at ...>) sage: FooBar.__bases__ # py3 (<class '__main__.Bar'>,) sage: Foo.mro() [<class '__main__.Foo'>, <type 'object'>] sage: FooBar.mro() # py2 [<class '__main__.FooBar'>, <type 'object'>, <class __main__.Bar at ...>] sage: FooBar.mro() # py3 [<class '__main__.FooBar'>, <class '__main__.Bar'>, <class 'object'>]
If all the base classes have a zero
__dictoffset__
, the dynamic class also has a zero__dictoffset__
. This means that the instances of the class don’t have a__dict__
(see trac ticket #23435):sage: dyn = dynamic_class("dyn", (Integer,)) sage: dyn.__dictoffset__ 0
Pickling
Dynamic classes are pickled by construction. Namely, upon unpickling, the class will be reconstructed by recalling dynamic_class with the same arguments:
sage: type(FooBar).__reduce__(FooBar) # py2 (<function dynamic_class at ...>, ('FooBar', (<class __main__.Bar at ...>,), <class '__main__.Foo'>, None, None)) sage: type(FooBar).__reduce__(FooBar) # py3 (<function dynamic_class at ...>, ('FooBar', (<class '__main__.Bar'>,), <class '__main__.Foo'>, None, None))
Technically, this is achieved by using a metaclass, since the Python pickling protocol for classes is to pickle by name:
sage: type(FooBar) <class 'sage.structure.dynamic_class.DynamicMetaclass'>
The following (meaningless) example illustrates how to customize the result of the reduction:
sage: BarFoo = dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,))) sage: type(BarFoo).__reduce__(BarFoo) (<type 'str'>, (3,)) sage: loads(dumps(BarFoo)) '3'
Caching
By default, the built class is cached:
sage: dynamic_class("FooBar", (Bar,), Foo) is FooBar True sage: dynamic_class("FooBar", (Bar,), Foo, cache=True) is FooBar True
and the result depends on the reduction:
sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,))) is BarFoo True sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,))) is BarFoo False
With
cache=False
, a new class is created each time:sage: FooBar1 = dynamic_class("FooBar", (Bar,), Foo, cache=False); FooBar1 <class '__main__.FooBar'> sage: FooBar2 = dynamic_class("FooBar", (Bar,), Foo, cache=False); FooBar2 <class '__main__.FooBar'> sage: FooBar1 is FooBar False sage: FooBar2 is FooBar1 False
With
cache="ignore_reduction"
, the class does not depend on the reduction:sage: BarFoo = dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,)), cache="ignore_reduction") sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,)), cache="ignore_reduction") is BarFoo True
In particular, the reduction used is that provided upon creating the first class:
sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,)), cache="ignore_reduction")._reduction (<type 'str'>, (3,))
Warning
The behaviour upon creating several dynamic classes from the same data but with different values for
cache
option is currently left unspecified. In other words, for a given application, it is recommended to consistently use the same value for that option.

sage.structure.dynamic_class.
dynamic_class_internal
(name, bases, cls=None, reduction=None, doccls=None, prepend_cls_bases=True)¶ See sage.structure.dynamic_class.dynamic_class? for indirect doctests.