Macaulay2 package TangentCone: This package provides a single function that computes the tangent cone at a point. The algorithm follows the method of Proposition 15.28 in the book ”Commutative Algebra with a View Toward Algebraic Geometry”, by David Eisenbud (Springer, Graduate Texts in Mathematics, volume 150).

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  1. Eisenbud, David: Commutative algebra. With a view toward algebraic geometry (1995)