# Monkey-patching PARI calls

I'm currently trying to implement some number field computations on a very particular number field (specifically, $K = \mathbb{Q}(\zeta_{n-1},n^{1/(n-1)})$). The code I've written so far has some bottlenecks that profiling via %prun has identified, namely:

`{method '_nf_rnfeq' of 'sage.libs.cypari2.gen.gen' objects}`

, which seems to compute the minimal polynomial of $K$ (currently I'm defining $K$ via`F.<u> = CyclotomicField(n-1)`

, and then`K.<a> = F.extension(x^(n-1) - n)`

, so $K$ is a relative extension.`_nf_rnfeq`

seems to compute the absolute minimal polynomial of a given relative extension (via PARI).`{method 'discriminant' of 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint' objects}`

, which appears to just be the polynomial discriminant computation.

Assume I've done analysis by hand gives me a much faster computation of the absolute minimal polynomial for this particular number field. I'd then want a version of `_nf_rnfeq`

that:

- Checks if it's being called on my special case, where better algorithms exist. If so, run that.
- Otherwise, run the traditional algorithm.

Of course, I'd prefer to make this modification without modifying the source code, as that seems to be an especially ugly solution.

One way to implement this is to change is by modifying the relevant method at run-time, via a technique known as "Monkey-Patching" (see https://stackoverflow.com/questions/47503061/replacing-specific-function-calls/47503146#47503146 (here)).

The issue I'm having now is that attempting to monkey-patch the PARI call gives me the error:

`TypeError: can't set attributes of built-in/extension type 'sage.libs.cypari2.gen.gen'`

The code I'm using (in the first cell of my IPython notebook) is below:

```
import sage.libs.cypari2.gen
orig_nf_rnfeq = sage.libs.cypari2.gen.gen._nf_rnfeq
def _nf_rnfeq(*args, **kwargs):
print("Rnfeq works!")
return orig_nf_rnfeq(*args, **kwargs)
sage.libs.cypari2.gen.gen._nf_rnfeq = _nf_rnfeq
```