On Fri, 03 Nov 2006 09:54:14 -0800, Robert Bradshaw
<[EMAIL PROTECTED]> wrote:
> I think the problem here is that it _assumes_ that x and y commute,
> which is not the only option.
>
> I am still looking for a convincing reason that
>
> sage: (1/2) * Matrix(ZZ, 2, 2, [1,2,3,4])
>
> should not give
>
> [1/2 1]
> [3/2 2]
>
> in MatrixSpace(QQ, 2, 2). Maybe it's just the cleanliness/
> implementation of the coercion rules.
In this case there could be a clean coercion rule. E.g.,
Try standard rules. If they fail, then:
(1) Check if the base ring of the parent of the left hand
side coerces to the parent of the right hand side.
(2) Check if the base ring of the right hand side coerces
to the parent of the left hand side.
If exactly one of (1) and (2) succeeds, say (2), then:
(a) Compute the base extension of the right hand side
to the parent of the parent of the left hand side.
(b) Do the algebra multiply.
If both succeed, it's ambiguous -- throw an error.
With your
(1/2) * Matrix(ZZ, 2, 2, [1,2,3,4])
example this gives what you want.
With your
(1/2) * (x^2 + 1)
with x in ZZ['x'] this also gives what you want.
With
x * y
with x in ZZ['x'] and y in ZZ['y'] this gives *ambiguous*
and throws an error.
What do you think?
-- William
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