On Jan 18, 2008 7:58 AM, David R. Kohel <[EMAIL PROTECTED]> wrote:
> Hi William,
>
> Some features/bugs to be traqued:
This sort of discussion should be archived on sage-devel, so
I've cc'd this email there. Also, I don't really agree with your suggestions
below, so I want to see what other people think.
> Let A be a matrix not over ZZ or QQ:
>
> A.adjoint()
> A.inverse()
>
> are not implemented.
I don't think they should be. There are already (at least) 3 ways to do this:
sage: A = random_matrix(ZZ,2)
sage: ~A
[ 1/34 1/17]
[-6/17 5/17]
sage: A.__invert__()
[ 1/34 1/17]
[-6/17 5/17]
sage: A^(-1)
[ 1/34 1/17]
[-6/17 5/17]
> For x a commutative ring element:
>
> x.inverse()
>
> is not implemented even if x^-1 exists.
Same remark as above.
> sage: x = 7
> sage: type(x)
> <type 'sage.rings.integer.Integer'>
> sage: x^-1
> 1/7
> sage: type(x^-1)
> <type 'sage.rings.rational.Rational'>
> sage: x = -1
> sage: type(x^-1)
>
> Should the field of fractions be created?
Hmm, I don't think so, since x has an inverse in ZZ already. Yes, I realize
that in Magma the field of fractions is created:
sage: magma.eval('Parent((-1)^(-1))')
'Rational Field'
And I realize that this is inconsistent with:
sage: parent(1/1)
Rational Field
So I'm a little torn here.
> Certaily x.inverse() should return an error for non-units.
No it shouldn't. It should compute the inverse as an element of a natural
larger structure.
-- William
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