This does not look right, does it?

sage: K.<a> = NumberField(x^2-3)
sage: O = K.ring_of_integers()
sage: c = O(2*a + 4)
sage: isinstance(O, Field)
False
sage: isinstance(c, FieldElement)
True

Martin
On Thursday, 12 December 2024 at 23:35:40 UTC+1 Nils Bruin wrote:

> On Thursday, 12 December 2024 at 12:39:46 UTC-8 axio...@yahoo.de wrote:
>
> Great, thank you! This - almost - provides a performance test:
>
>
> Yes, you would need to convince sage that this is indeed a euclidean ring 
> (I think for this one the usual norm actually is a euclidean norm). I don't 
> think that simply being a UFD will do it for you. 
>

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