ordering of (O-)terms: absolute values, real parts, etc.

[dkrenn]

The following (although correct) is not ideal:

sage: A.<n> = AsymptoticRing('ZZ^n * n^ZZ', ZZ)
sage: (-1)^n/n + O((-1)^n/n^2) + n + O(1/n^3) + O(1/n^(2+I))
(-1)^n*n^(-1) + O((-1)^n*n^(-2)) + n + O(n^(-I - 2))

The O-Terms could/should be combined. The O-Term O((-1)^n*n^(-2)) should be O(n^-2) and O(n^(-I - 2)) should be O(n^-2).

The ordering is also not what one would expect, e.g.

sage: (-1)^n/n + O((-1)^n/n^2) + n^2 + O(1/n^3) + O(1/n^(2+I))
(-1)^n*n^(-1) + O((-1)^n*n^(-2)) + n^2 + O(n^(-I - 2))

and we would like to see the n^2 at the front.

[dkrenn]

Replying to dkrenn:

The ordering is also not what one would expect, e.g.

sage: (-1)^n/n + O((-1)^n/n^2) + n^2 + O(1/n^3) + O(1/n^(2+I))
(-1)^n*n^(-1) + O((-1)^n*n^(-2)) + n^2 + O(n^(-I - 2))

and we would like to see the n^2 at the front.

Here I am not sure, if this is the same problem as above; if not, then we can either forget about it or open a new ticket for it.

[dkrenn]

Moreover, I am not sure, how to deal with these issues.