On Wednesday, January 1, 2014 4:17:28 PM UTC-8, Peter Bruin wrote:
>
> I would like to add that in my opinion the first line of this example,
>
> sage: f = GF(11).convert_map_from(GF(7))
>
> should not be assumed to work at all, and it would be preferable to raise 
> an error rather than returning something that is mathematically completely 
> arbitrary.
>
I think the fact that it is defined is a corollary of the fact that 
GF(11)(input) accepts as input anything that can be turned into an integer, 
and elements of GF(7) can be turned into an integer. I agree that it's 
probably preferable to not have this conversion, but its existence may be a 
natural consequence of the implementation and ensuring that it does not 
exist may require introducing special cases. You'll have to see if that can 
be done at acceptable cost. 

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