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The following definitions are from lecture notes of Nemethi:

A surface singularity $(X,0)$ is defined by $$(X,0) = (\{ f_1 = \ldots = f_m=0 \}) \subset \mathbb (C^n,0),$$ where $f_i : (\mathbb C^n ,0) \to (\mathbb C ,0)$ are germs of analytic functions with $$r(p) = \mathrm{rank} \left [ \frac{\partial f_i}{\partial z_i} (p) \right ]_{i=1, \ldots, m; j=1, \ldots, N} = N-2$$ for any generic or smooth point $p$ of $X$.

If $r(0) = N-2$, then $(X,0)$ is analytically isomorphic to $\mathbb (C^2,0)$. The singularity $(X,0)$ is called normal, if any bounded holomorphic function $f: X - \{ 0\} \to \mathbb C$ can be extended to a holomorphic function defined on $X$.

Then there is an algorithm in Appendix 1 for finding the resolution graphs of singularities.

I couldn't understand the steps of that algorithm. My question is that is it possible to find an easier algorithmic source for such resolutions or any Magma or Sage code for this purpose?

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