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But sometimes, only some of them are needed. In this paper, for a zero-dimensional ideal $I$, we study its complex zeros that locate in another variety $\\textbf{V}(J)$ where $J$ is an arbitrary ideal.\n  The main problem is that for a point in $\\textbf{V}(I) \\cap \\textbf{V}(J)=\\textbf{V}(I+J)$, its multiplicities w.r.t. $I$ and $I+J$ may be different. Therefore, we cannot get the multiplicity of this point w.r.t. $I$ by studying $I + J$. 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