Element Wrapper

Wrapping Sage or Python objects as Sage elements.

AUTHORS:

• Nicolas Thiery (2008-2010): Initial version

• Travis Scrimshaw (2013-05-04): Cythonized version

class sage.structure.element_wrapper.DummyParent(name)

Bases: UniqueRepresentation, Parent

A class for creating dummy parents for testing ElementWrapper

class sage.structure.element_wrapper.ElementWrapper

Bases: Element

A class for wrapping Sage or Python objects as Sage elements.

EXAMPLES:

Sage

sage: from sage.structure.element_wrapper import DummyParent
sage: parent = DummyParent("A parent")
sage: o = ElementWrapper(parent, "bla"); o
'bla'
sage: isinstance(o, sage.structure.element.Element)
True
sage: o.parent()
A parent
sage: o.value
'bla'

Python

>>> from sage.all import *
>>> from sage.structure.element_wrapper import DummyParent
>>> parent = DummyParent("A parent")
>>> o = ElementWrapper(parent, "bla"); o
'bla'
>>> isinstance(o, sage.structure.element.Element)
True
>>> o.parent()
A parent
>>> o.value
'bla'

Note that o is not an instance of str, but rather contains a str. Therefore, o does not inherit the string methods. On the other hand, it is provided with reasonable default implementations for equality testing, hashing, etc.

The typical use case of ElementWrapper is for trivially constructing new element classes from pre-existing Sage or Python classes, with a containment relation. Here we construct the tropical monoid of integers endowed with min as multiplication. There, it is desirable not to inherit the factor method from Integer:

Sage

sage: class MinMonoid(Parent):
....:     def _repr_(self):
....:         return "The min monoid"
....:
sage: M = MinMonoid()
sage: class MinMonoidElement(ElementWrapper):
....:     wrapped_class = Integer
....:
....:     def __mul__(self, other):
....:         return MinMonoidElement(self.parent(), min(self.value, other.value))
sage: x = MinMonoidElement(M, 5); x
5
sage: x.parent()
The min monoid
sage: x.value
5
sage: y = MinMonoidElement(M, 3)
sage: x * y
3

Python

>>> from sage.all import *
>>> class MinMonoid(Parent):
...     def _repr_(self):
...         return "The min monoid"
....:
>>> M = MinMonoid()
>>> class MinMonoidElement(ElementWrapper):
...     wrapped_class = Integer
....:
>>>     def __mul__(self, other):
...         return MinMonoidElement(self.parent(), min(self.value, other.value))
>>> x = MinMonoidElement(M, Integer(5)); x
5
>>> x.parent()
The min monoid
>>> x.value
5
>>> y = MinMonoidElement(M, Integer(3))
>>> x * y
3

This example was voluntarily kept to a bare minimum. See the examples in the categories (e.g. Semigroups().example()) for several full featured applications.

Warning

Versions before Issue #14519 had parent as the second argument and the value as the first.

value

class sage.structure.element_wrapper.ElementWrapperCheckWrappedClass

Bases: ElementWrapper

An element wrapper such that comparison operations are done against subclasses of wrapped_class.

wrapped_class

alias of object

class sage.structure.element_wrapper.ElementWrapperTester

Bases: ElementWrapper

Test class for the default __copy() method of subclasses of ElementWrapper.

append(x)