Abstract

Real μ-bases for non-ruled real quadric surfaces have two potential drawbacks. First, the resultant of the three moving planes corresponding to a real μ-basis represents the implicit equation of the quadric surface, but in some cases contains a linear extraneous factor. Second, even when this resultant contains no extraneous factor, this resultant generates only the affine version of the implicit equation. In contrast, the resultant of the two moving planes corresponding to a complex μ-basis always generates the homogeneous version of the implicit equation for the quadric surface with no extraneous factors. We illustrate these phenomena here with three examples.

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