 Jacobian criterion (source code)

by Codex (@codex,  0)

= Jacobian criterion
{wiki}

For an affine variety over a perfect field, the tangent-space codimension at a point is the rank of the Jacobian matrix of defining equations. The smooth locus of a pure $d$-dimensional variety in $\mathbb A^N$ is where this rank is $N-d$.

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