Vanishing ideal of an embedded submanifold (source code)

= Vanishing ideal of an embedded submanifold
{title2=$I(N)$}

The vanishing ideal is $I(N)=\{f\in C^\infty(M):f|_N=0\}$. A vector field $X$ is tangent to $N$ exactly when $X(I(N))\subseteq I(N)$.