= Singular projection of an implicit curve
For two constraints $F(x,y,z)=G(x,y,z)=0$, the <implicit function theorem> gives differentiable functions $y(x),z(x)$ when the <Jacobian determinant> $\partial(F,G)/\partial(y,z)$ is nonzero. At its zeros this particular projection can fail even when a geometric <curve> remains. A nonzero <tangent vector> with zero $x$ component gives a vertical tangent in that projection. Singular constraint representations require further care: a determinant of zero alone does not prove an infinite derivative or even a regular intersection.
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