This function can be called when there is already a completed
resolution stored in chartHistory.
The effect is that the strict transform of J is computed along the map
of the resolution which can be found in chartHistory and new
basic objects are set up over the leaf-charts of the tree. Then the
objects are resolved, such that the existing resolution is
"extended" with the resolution of the strict transform of J.
- a polynomial from k[VAR], defining the scheme to
be desingularized, where VAR is the list of variables of the root
chart in the resolution tree stored in chartHistory.
- The value of the resolvedChartList global
variable, containing the data of the chart covering the final blowing