#15215: Non-square matrices should inherit from ModuleElement, not RingElement
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Reporter: pbruin | Owner:
Type: task | Status: new
Priority: minor | Milestone: sage-5.12
Component: categories | Keywords: inheritance
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Matrices inherit from `RingElement` even if they are not square. Their
parents do behave correctly.
{{{
sage: A = Matrix([[1, 2], [3, 4]])
sage: A.parent() in Rings()
True
sage: A.parent() in Modules(ZZ)
True
sage: isinstance(A, RingElement)
True
sage: B = Matrix([[1, 2, 3], [4, 5, 6]])
sage: B.parent() in Rings()
False
sage: A.parent() in Modules(ZZ)
True
sage: isinstance(B, RingElement)
True
}}}
The same happens with `Algebras(ZZ)` and `AlgebraElement`.
Square matrices over a ring `R` should be made to inherit dynamically from
`AlgebraElement`; non-square matrices should only inherit from
`ModuleElement`.
''Motivation:'' Multiplication of matrices over a commutative ring ''R''
is in general only a bilinear map between ''R''-modules (in general three
different ones). Only if the matrices are square of the same size ''n''
can this be described as the multiplication map on an ''R''-algebra,
namely Mat,,''n'',,(''R'').
--
Ticket URL: <http://trac.sagemath.org/ticket/15215>
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