Given $f(x_1,\dots,x_n)\in\Bbb Q[x_1,\dots,x_n]$ of form $\prod_{i=1}^df_i(x_1,\dots,x_n)$ where each of $f,f_i$ are homogeneous and each $f_i$ is irreducible what is the best technique to factor such polynomials?

Assume $GCD$ of coefficients is $1$ after removing denominator.

Is there an algorithm that is polynomial time in complexity in degree, variables and logarithm of number of bits in coefficients?


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