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A zero has a multiplicity, which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x  2) has the zeroes x = 3 and x = 2, each occuring once.
1) 'Gini impurity' - it is a standard decision-tree splitting metric (see in the link above); 2) 'Gini coefficient' - each splitting can be assessed based on the AUC criterion. For each splitting scenario we can build a ROC curve and compute AUC metric. According to Wikipedia AUC=(GiniCoeff+1)/2; Question is: are both these measures equivalent? On the one hand, I am informed that Gini coefficient should not be confused with Gini impurity.