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Note that this operation is not always well-defined in projective space, e.g., the Hadamard product of the points $[1:0]$ and $[0:1]$ is not well-defined
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Hadamard.m2:205:0.