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Separating singular loci of different dimension of an SBO. The procedure checks whether the singular locus of the SBO on the top of the stack of a chart-record, w.r.t. a list hypersurfaces defined by elements from the IND member of the chart has components of different dimension. If so, it covers the chart by new charts in which these components are separated.

the chart-record to be checked,
a list of pairwise different indices to the IND member of the chart,
the coefficient ideal of J of the top SBO w.r.t. z.
A list of "clean" charts, with no singular locus components of different dimension w.r.t. z.

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