On 19 December 2012 03:16, P Purkayastha <[email protected]> wrote:
>
> It is consistent with whatever A.ambient_vector_space() is doing. There is
> even a doctest:
>
> sage: M = ZZ^3;
> sage: V = M.ambient_vector_space(); V
> Vector space of dimension 3 over Rational Field
>
> Since the "ambient vector space" is the Rational field, A.coordinates
> returns the rational numbers. I don't know what is meant by the term
> "ambient vector space" in this context.
It is defined in the docstring:
def ambient_vector_space(self):
"""
Returns the ambient vector space, which is this free module
tensored with its fraction field.
EXAMPLES::
sage: M = ZZ^3;
sage: V = M.ambient_vector_space(); V
Vector space of dimension 3 over Rational Field
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