#14249: There should be no need to have _an_element_ implement to multiply
elements
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Reporter: SimonKing | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-5.9
Component: coercion | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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We currently have
{{{
sage: from sage.structure.element import ModuleElement
sage: class MyElement(ModuleElement):
....: def __init__(self, x, y, parent=None):
....: ModuleElement.__init__(self, parent)
....: def _mul_(self, other):
....: return self
....: def _rmul_(self, other):
....: return self
....: def _lmul_(self, other):
....: return self
....:
sage: class MyParent(Parent):
....: Element = MyElement
....:
sage: P = MyParent(category=Rings())
sage: P(1,2)
Generic element of a structure
sage: a = _
sage: a*2
Traceback (most recent call last):
...
NotImplementedError: please implement _an_element_ for <class
'__main__.MyParent_with_category'>
}}}
I find this very annoying.
The background is that the coercion model tries to get a multiplication
action, namely `RightModuleAction`. During initialisation of the module
action, some sanity tests are performed. In particular, an element of the
acting parent and the acted-upon set are taken and the action called on
these two elements.
Problem: Where to get the two elements from? Currently, they are gotten
from the method `an_element()`, which in turn relies on `_an_element_()`
being implemented if the default implementation is not good enough (which
is the case in the example above).
But normally, we do not want to have the `RightModuleAction` just out of
the blue: Typically (in the example above, at least), we want to create it
during the first multiplication. And in that moment we ''do'' have two
elements.
So, I propose to make it possible to pass the two elements being
multiplied to the constructor of `Left/RightModuleAction`, and let
`an_element()` be called ''only'' if no element is passed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14249>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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