Why lexicographically? How about the following:
(1) there is a canonical coercion map from K to L
(2) the variables of R are a subset of the variables of S, and
(3) The map from variables of R to variables of S is order
preserving.
Also, I defined base_extend for multivariable polynomial rings, which
means that now
sage: R.<x,y> = ZZ[]
sage: f = (x + y) / 3
sage: f.parent()
Polynomial Ring in x, y over Rational Field
Rather than
sage: f.parent()
Fraction Field of Polynomial Ring in x, y over Integer Ring
Is this a problem?
On Mar 29, 10:12 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On 3/29/07, David Roe <[EMAIL PROTECTED]> wrote:
>
> > I sent this a little while ago but it didn't seem to go through...
> > sorry if it appears twice.
>
> > What do people think of having a canonical map between multivariate
> > polynomial rings when one's variables are a subset of the other's?
> > What about a subset in the same order? What about an initial subset
> > in the same order?
>
> Suppose R and S are multivariate polynomial rings over base rings K and L.
> I think a reasonable convention would be to have a canonical coercion map
> R --> S if the following conditions hold:
> (1) there is a canonical coercion map from K to L
> (2) the variables of R are a subset of the variables of S, and
> (3) if the variables of R equal the variables of S, then when
> ordered lexicographically the variables of R are <=
> the variables of S.
>
> William
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