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Algebraically, \(\text {Sing}(I)\) is computed as the elimination ideal $$\begin{aligned} \text {Sing}(I) \, = \, \left( \text {in}_{(0,1)}(I) \, :\langle \xi _1,\ldots ,\xi _n \rangle ^{(\infty )}\right) \, \cap \, \mathbb {C}[x_1,\ldots ,x_n], \...
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