Let $Y$ be a submanifold of a complex manifold $X$, and $a$ be an ideal on $X$ which does not vanish along the entire $Y$. Consider a point $\xi$ on $Y$, there are the vanishing order $ord_{\xi}a$ and the vanishing order $ord_{\xi}a\cdot O_{Y}$. Is there any relation between the two numbers?
