Local Smith form at p : Blackbox
Rank mod p : use Wiedemann on preconditioned matrix
- With high probability the characteristic polynomial can be the minimal polynomial times some power of X
- The non-zero eigenvalues are distinct in the minimum polynomial
- rank = degree(minpoly) - valuation(minpoly)
- Compute the last invariant factor in a p-adic way
- Complete information if needed prime powers are 1
- Rank mod pe
- [Reeds/Sloane] adapt Berlekamp/Massey mod pe
- but not in a memory efficient way ( e ? [rank mod p] )