Sergey B Kirpichev

@jksuom, it seems for this case `Z[I]` would be really needed. I doubt if they could be added to mpmath (after all, it seems unmaintained), so it may be better...

> It is special but probably useful in some situations. Your `QQ(I)`, probably, also will be little more efficient than the current gaussian rationals implementation. But the GaussianRationalField must be...

On Wed, Feb 19, 2020 at 03:41:09AM -0800, Kalevi Suominen wrote: >  3. Matrix of the regular representation. Again an integer matrix and a > common denominator of all entries....

I think, the 2-nd option does make sense, except that in general there is no power basis (in `theta`). I'm not sure, however, that this representation will work for general...

I'm start thinking that support for tower of extensions was a bad idea, it complicates things. E.g. see above problem with a canonical representation for it's integers. @jksuom, I would...

> An implementation with a single generator will have high degree but it might still be more efficient The problem rather with canonicalization (how to compute gcd, etc - to...

Yes. Currently, we allow generic towers of extensions, i.e. finite extension over any algebraic field `K`. For `K=QQ` it's possible to represent `K` elements as `sum(x_k*t_k/d for k in range(n))`,...

What do you mean? Any integral basis in `O_K` should be fine. By "unique" I mean the unique representation w.r.t to the given basis. The computation of some integral basis...

> Then there is a unique representation. Hmm, I'm not sure (if `K!=QQ`).

BTW, similar error is in the Subs._eval_nseries(), adopted from the @Upabjojr code in the https://github.com/sympy/sympy/pull/11408.