Getting the braid monodromy for each branch point

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I want to compute the braid monodromy around each branch point for the projection from a plane algebraic curve onto the complex plane. The command braid_monodromy() is designed for this: it returns a list of the braids around each branch points. However, I then have no way of knowing which braid corresponds to which branch point.

Example of code below:

from sage.schemes.curves.zariski_vankampen import braid_monodromy
R.<x, y> = QQ[]
f = y^3+x^3+x/10+y*x/120
bm = braid_monodromy(f); bm

which returns the list

[(s1*s0)^2*s1^-1*s0^-1*s1^-1, s1*s0*s1*s0^-1*s1^-1, s1*s0, s0, s0^-1*s1*s0]

Moreover, the documentation tells me that it is supposed to return a list of the branch points as well as the list of braids, which it does not.