Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism $\Phi$ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential $D\Phi \left(0\right)$ of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of $D\Phi \left(0\right)$. Singularity classes containing bifurcation points with $\mathrm{c}odim\le 3$, $\mathrm{c}orank=1$ are considered.