Let $\mathbb{C}[x,y]$ be the polynomial ring with variables $x,y$ and coefficient in $\mathbb{C}$.
Let $f,g\in \mathbb{C}[x,y]$.
Let $(f,g)$ be the ideal of $\mathbb{C}[x,y]$ generated by $f,g$.
Given $h\in \mathbb{C}[x,y]$, how to determine whether $h\in (f,g)$ or not?
I have tried some examples by the online programming "sagemath".
Are there any methods that can give a proof?