Last invariant factor at p : q-adic
For a random vector b, the solution x to Ax=b has in general maximal order, that is to say, orderp(x) = orderp(sr), the exponent of p in the last invariant factor
- It is the case for one of the entries of x
- Precondition A, so that this property is ensured for the first entry
- Computes only the first entry
-
 = p? + qA : locally at p the non-zero invariant factors of A and Â, having exponents lower than ?, are equal
- In a q-adic way, solutions to Âx=b are easy to compute !
x is a vector of reduced integer fractions
orderp(x) = largest exponent in the denominator of the entries of x