Lenstra Lenstra Lovasz have a $O((nb)^{11})$ deterministic algorithm to factor primitive polynomials in $\Bbb Q[x]$ where $b$ is total number of bits in the polynomial and $n$ is degree of the polynomial.
What is the current best algorithm?
If the degree of the factors are known apriori can we improve the complexity (assume each irreducible factor occurs only once)?
Is there an implementation available?
