On 24.05.2013 16:41, Simon King wrote:
Hi Johannes,
On 2013-05-22, Johannes <dajo.m...@web.de> wrote:
is it implemented to create submodules of QQ['x,y,z'] as module over
itself?
I know it works for QQ['x'] or ZZ.
Perhaps you could show us what you do to make things work for QQ['x']
or ZZ, because I do *not* think that it works in this case. Then one
can try to think what features are missing to make it work in the
multivariate case as well.
Ok, I see the problem, I just checked to documentation and the examples
of the submodule being the whole module.
The following works:
sage: R.<x> = QQ[]
sage: FreeModule(R,1)
Ambient free module of rank 1 over the principal ideal domain Univariate
Polynomial Ring in x over Rational Field
sage: FreeModule(ZZ,1)
Ambient free module of rank 1 over the principal ideal domain Integer Ring
but you are right, even in this case considering submodules fails:
I = [x] * R
sage: FreeModule(I * R ,1)
AttributeError: 'Ideal_1poly_field' object has no attribute 'is_field'
otherwise:
sage: g = M.gens()[0]
sage: M.submodule( [x * g] )
Free module of degree 1 and rank 1 over Univariate Polynomial Ring in x
over Rational Field
Echelon basis matrix:
[x]
I do agree that such a feature should be available (it would become
available, or at least easier to make it available, by letting ideals
inherit from sage.structure.parent.Parent).
Best regards,
Simon
bg,
Johannes
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