On 12 June 2018 at 15:24, Jeroen Demeyer <j.deme...@ugent.be> wrote:

> Sometimes you start working on a ticket thinking "this is just a few hours
> of work" when it turns out to be a huge can of worms...
>
> Coercion for multi-variate polynomials might fall in this category. There
> are several strange things and bugs. The best example so far:
>
> sage: R.<x,y> = QQ[]
> sage: QQ["y,x"](x)
> x
>
> sage: R.<x,y> = QQbar[]
> sage: QQbar["y,x"](x)
> y
>
> So depending on the base ring, you get different maps
> R[x,y] -> R[y,x]. In both cases, Sage considers this map a coercion.
>
> I would like to forget the current situation and simply start from scratch
> thinking which maps should be coercions. I don't have a good idea so far, I
> wonder if somebody else does.
>
> 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]
>

I agree with the above.


>
> But not the following:
> R[x,y] -> R[x][y]
> R[x,y] -> R[y,x]
> R[x,y][z] -> R[x][y,z]


OK, but having an easy way to produce the above maps would be very
helpful.  (I'm not saying they cannot be done now, just making sure they
can be after you have kniited your can of worms together.

John

>
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