On Monday, 30 October 2023 at 00:26:55 UTC+13 G. M.-S. wrote:

If I understand you correctly, SageMath is a bit loose at the moment about 
its categories.


That's not what I meant also not what is indicated by what I noticed: by 
the looks of it, sage does know about euclidean domains and has quite a bit 
of ED-specific functionality. It's just that no-one has bothered 
specializing the *ideals* of euclidean domains. The definition of a 
Euclidean domain doesn't really mention ideals and indeed the subsequent 
properties of its ideals are established by lemmas and propositions. 
Basically, no-one has bothered making sagemath aware of those theorems (or 
even put the infrastructure in place to teach it about those results). So, 
no evidence of looseness in its categories. Just a little uneducated.


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