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D.6.8.5 control_Matrix

Procedure from library equising.lib (see equising_lib).

L is the output of multsequence(hnexpansion(f)).

list M of 4 intmat's:
  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)

the branches are ordered in such a way that only consecutive branches can meet at an infinitely near point.
the final rows of the matrices M[1],...,M[3] is (1,1,1,...,1), and correspond to infinitely near points such that the strict transforms of the branches are smooth and intersect the exceptional divisor transversally.

See also: multsequence.