 M[1] contains the multiplicities at the respective infinitely near points
p[i,j] (i=step of blowup+1, j=branch)  if branches j=k,...,k+m pass
through the same p[i,j] then the multiplicity is stored in M[1][k,j],
while M[1][k+1]=...=M[1][k+m]=0.
M[2] contains the number of branches meeting at p[i,j] (again, the information
is stored according to the above rule)
M[3] contains the information about the splitting of M[1][i,j] with respect to
different tangents of branches at p[i,j] (information is stored only for
minimal j>=k corresponding to a new tangent direction).
The entries are the sum of multiplicities of all branches with the
respective tangent.
M[4] contains the maximal sum of higher multiplicities for a branch passing
through p[i,j] ( = degree Bound for blowing up)
