On 2016-01-19 22:50, Volker Braun wrote:
Presumably nobody has a problem with
sage: R.<x> = QQ[]
sage: (3*x^2+1) // (2*x)
3/2*x
and it would be rather strange if the binary operations on the scalars
behave different in QQ vs degree-0-part(QQ[x]).
Well, you cannot have a fully consistent floor division in any case:
Either you make floor division on QQ consistent with ZZ or with QQ[x]
but you cannot have both. Personally, I would prefer making it
consistent with ZZ.
If E is any Euclidean domain, then you can extend // naturally to the
fraction field of E. I think this is the most useful definition. This
would also be consistent with gcd() where we already treat QQ and QQ[x]
differently:
sage: R.<x> = QQ[]
sage: gcd(QQ(2), QQ(2))
2
sage: gcd(R(2), R(2))
1
Of course we could just always answer "1" in both cases which would be
mathematically correct but rather useless.
Jeroen.
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