Hi John,
On 2013-01-05, john_perry_usm <john.pe...@usm.edu> wrote:
> thinking of how java interfaces & multiple inheritance work:
> wouldn't it be possible to have an interface orabstract class
> that defines an abstract function abs, along with associated
> functions that require an abs functions, then declare in the
> class header that it implements it, and define the function so?
The category framework offers such functionality. For example, one
could define the following in sage.categories.rings:
from sage.misc.abstract_method import abstract_method
class Rings(Category):
...
class ElementMethods:
@abstract_method(optional=True)
def abs(self):
"""
Return the absolute value. Implement only if that
makes sense in this ring.
"""
pass
and then, for example:
sage: from sage.structure.element import Element
sage: from sage.structure.parent import Parent
sage: class MyRingElement(Element):
....: def _mul_(self, other):
....: return self
....:
sage: class MyRingElementWithAbs(MyRingElement):
....: def abs(self):
....: return self
....:
sage: class MyRing(Parent):
....: def __init__(self, has_abs=None):
....: if has_abs:
....: self.Element = MyRingElementWithAbs
....: else:
....: self.Element = MyRingElement
....: Parent.__init__(self, category=Rings())
....: def _element_constructor_(self, *args, **kwds):
....: return self.element_class(parent=self)
....:
sage: R = MyRing()
sage: RAbs = MyRing(has_abs=True)
sage: a = R()
sage: b = RAbs()
sage: b.abs
<bound method MyRing_with_category.element_class.abs of Generic
element of a structure>
sage: b.abs()
Generic element of a structure
sage: hasattr(a, 'abs') # yes, still available by tab completion
True
sage: a.abs # but that's good:
NotImplemented
sage: a.__class__.abs?
...
Definition: a.__class__.abs(self)
Docstring:
Return the absolute value. Implement only if that makes sense in
this ring.
...
I guess the main problem is that the abs() method of
sage.structure.element.RingElement has been introduced long before the
category framework was created. But we could consider to move abs() from
the base class RingElement to the element class of the category of
rings. The question is how to deal with old code, that tries to
implement abs() by means of __abs__().
Best regards,
Simon
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