Function having a field as input

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Function having a field as input

Fabio S.-2
I am writing, for didactic purposes, a function which performs
factorization of a square-free polynomial using Berlekamp's algorithm.

As for now, I wrote something like

ber: UP(x,INT) -> List(UP(x,INT))
ber(pol) ==
  car := 5
  GF ==> PF 5
  f : UP(x,GF) := pol

and it works: the function compiles correctly and I get the list of all
irreducible factor of the input polynomials of the input.

Clearly, this works only in the prime field GF(5): if I want to use it
in another prime field, I have to change the "5" in the definition of
the function.

In order to have the prime field also in input I tried something like

ber: (NNI,UP(x,INT)) -> List(UP(x,INT))
ber(p,pol) ==
  car := p
  GF ==> PF p
  f : UP(x,GF) := pol

Putting aside sanity checks on the primality of p, it works but the
function does not compile, it is just interpreted:

(5) -> ber(7,x^6+1)
    Local variable or parameter used in type
    We will attempt to interpret the code.


This makes me guess that I have been somewhat naif: what is wrong? How
can I correct my function?



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