On 2018-06-13 01:33, Simon King wrote:
It is, if the absence of a direct coercion triggers the construction of
a pushout that uses a more efficient implementation than the two rings
under consideration.
What do you have against R[x][y]? There are certainly cases where that's
a much more natura
On 2018-06-12 17:39, Nils Bruin wrote:
Possibly a nice test for
seeing if the list of coercions and conversions present is sufficient is
to see if all those maps can be defined by giving a list of images of
generators.
No, that won't be sufficient because you need to give a map from the
base r
On 2018-06-12, Jeroen Demeyer wrote:
>> However,
>> these iterated polynomial ring constructions are quite inefficient.
>
> True, but I don't see that as an argument to have no coercion.
It is, if the absence of a direct coercion triggers the construction of
a pushout that uses a more efficient i
On Tuesday, June 12, 2018 at 2:09:53 PM UTC-7, Simon King wrote:
>
>
> Problem:
> It is currently possible to create the polynomial ring R[x][x]
> (hence, x occurs twice). If "x" has two different meanings in the
> same ring, the notion "name preserving map" makes no sense. I believe
> it shoul
On 2018-06-12 23:07, Simon King wrote:
And now think about quotients of polynomial rings. Let A,B have the same
variable names in the same positions, but let the monomial orderings be
different. Let I be an ideal in A and J the corresponding ideal in B.
So, if we say that there is a name and posi
Hi!
We are talking about rings that mathematically are multivariate
polynomial rings over a commutative ring R. So, R[x,y], R[y,x], R[x][y],
R[y][x], PolynomialRing(R,['x','y'],'lex'), PolynomialRing(R,['x','y'],
'degrevlex'),...
About conversions: They can basically be anything. But:
i) There
On Tuesday, June 12, 2018 at 7:24:45 AM UTC-7, Jeroen Demeyer wrote:
>
> I'd like to say that the following should be coercions:
> R -> R[x,y]
> R[x] -> R[x,y]
> R[y] -> R[x,y]
> R[x][y] -> R[x,y]
>
> But not the following:
> R[x,y] -> R[x][y]
> R[x,y] -> R[y,x]
> R[x,y][z] -> R[x][y,z]
>
