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This is also an interface procedure under the short name blunify. It computes a finite set of generators for an ideal whose blowing up is isomorphic to the sequence of blowing ups computed by the algorithm in the resolution tree (stored in chartHistory).
To unify the sequence of blowing ups of a resolution made by a `desing/dlocpdh` or `desing/pdlocpdh` call over the ith principal open subset of P3 (i=1,2,3,4), set
chartHistory := eval(chartHistorypdh[i]): globalChartCounter := chartHistorypdh[i]:before calling `desing/blunify`().