Hi Luis!
On 25 Nov., 10:34, luisfe <lftab...@yahoo.es> wrote:
> Suppose the following:
>
> sage: K.<r4> = NumberField(x^4-2)
> sage: L1.<r2_1> = NumberField(x^2-2, embedding = r4**2)
> sage: L2.<r2_2> = NumberField(x^2-2, embedding = -r4**2)
> sage: K.has_coerce_map_from(L1)
> True
> sage: K.has_coerce_map_from(L2)
> True
> sage: L3.<a> = NumberField(x^2-2)
>
> If there where coercions from non-embedded fields to embedding field,
> there would be an embedding from L3 to L1 and L3 to L2. So, the
> coercion model would discover two possible coercions from L3 to K. How
> can we make them compatible?
Excellent argument!
I was not aware that there already is a coercion from L1 and L2 to K.
Then, indeed, it is not possible to extend everything consistently in
a structure preserving way, and I have to withdraw the answer that I
just gave to John.
> By the way, is there a problem with coercions?
> With the first set of fields I encounter the following error:
>
> sage: r4+r2_1
> r4^2 + r4
> sage: r4+r2_2
> -r4^2 + r4
> sage: r2_1+r2_2
> ERROR: An unexpected error occurred while tokenizing input
> The following traceback may be corrupted or invalid
> The error message is: ('EOF in multi-line statement', (1077, 0))
That seems fine to me. You can add r4 with r2_1 or r2_2, because there
is coercion from L1 or L2 to K. But I guess there is no way to
construct a canonical parent into which both L1 and L2 coerce (K is
certainly not canonical, or is it?). So, the coercion system would not
find a parent structure in which to perform the sum of r2_1 and r2_2.
Cheers,
Simon
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