### Linear Combination for Resultant

Let

```
R.<a, b, X> = ZZ[]
f = 1 - a*X^2
g = 1 - b*X^3
```

I need to compute polynomials `u`

and `v`

such that `u f + v g = r`

where `r = f.resultant(g, X)`

.

Pari has a function `polresultantext`

for that purpose, so one solution for my problem is

```
(u, v, r) = (R(p) for p in f._pari_().polresultantext(g._pari_(), 'X'))
```

Nevertheless, I have a few questions:

- Is there a method in Sage which directly does this?
- Is the detour via Pari the recommended solution? Or is there an alternative, e.g., in singular?
- If there is currently no method in Sage for doing this directly, what name would you recommend?
`resultant_ext`

?