I am looking for a computer algebra system that checks if the splitting fields of two polynomials over a $p$-number field are the same or not. At least, knowing their splitting fields are isomorphic will also give me an idea.
In PARI/GP, one can check the Galois of a polynomial upto degree $11$: for example,
P2 = x^9-x+1; polgalois(P2) which gives output %3 = [362880, -1, 34, "S9"] , that is, the Galois group is of order $362880$, signature $-1$, and the Galois group is isomorphic to $S_9$.
So given two polynomials up to degree $11$, one can check their Galois group and get some ideas if the splitting fields are equal by looking at their Galois groups.
But how to check the splitting fields/Galois groups of polynomials of degree greater than $11$ over the $p$-adic number field?
I found SageMath computing splitting fields of polynomials of degree more than $11$ over number fields.
However, I am looking for splitting fields or Galois groups over $p$-adic number fields.
Thanks
