B-smooth integer ($m=\pm {\prod }_{p\in B}{p}^{e_p}$)

For a specified finite prime factor base $B$, a nonzero integer is $B$-smooth if every prime dividing its absolute value belongs to $B$. Negative residues are handled by including the sign $-1$ in their exponent vectors. This notation refers to a finite prime set, rather than the alternative convention in which a numerical smoothness bound is called $B$.