Two separate people today (one a colleague who works in geometric
topology and group theory, the other a number theorist known to many
on these lists) have said to me "Sage is still ridiculously slow on
number field calculations" (quoting one of them).

I also know that when William wanted to do some large-scale
computations over Q(sqrt(5)) he found it necessary to implement
arithmetic in that specific field directly in order to get good
performance;  and a student of mine is finding similar slow
performance for imaginary quadratic fields.

I am only talking about basic field arithmetic here, nothing fancy.

Does anyone know the real cause of this, or have any ideas on how to
improve the situation?  Surely the pari C library is not so slow?  Is
it the interface?

I am CC-ing Bill Hart since I know that he is working on a new
extension to FLINT which would do this.

John

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