Opened 6 years ago

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

Reported by: dkrenn major asymptotic expansions cheuberg, behackl N/A

### Description

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.

### comment:1 in reply to:  description Changed 6 years ago by 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.