Unreduced Jones polynomial ($V_L^{\mathrm{un}}(t)=-(t^{1/2}+t^{-1/2})V_L^{\mathrm{red}}(t)$)

Use the Kauffman bracket assigning the empty diagram value $1$ and a disjoint circle factor $-A^2-A^{-2}$. Correct by the writhe of a link diagram and substitute $t=A^{-4}$. Relative to the Jones polynomial normalized to be $1$ on the unknot, this unreduced invariant has an additional factor $-(t^{1/2}+t^{-1/2})$. For a nonempty $l$-component link, its value at $t=1$ is $(-2{)}^l$.