Full Rank Representation of Real Algebraic Sets and Applications

We introduce the notion of the full rank representation of a real algebraic set, which represents it as the projection of a union of real algebraic manifolds \(V_{\mathbb {R}}(F_i)\) of \(\mathbb {R}^m\), \(m\ge n\), such that the rank of the Jacobian matrix of each \(F_i\) at any point of \(V_{\mathbb {R}}(F_i)\) is the same as the number of polynomials in \(F_i\).

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