Let $H$ be a degree $d$ hypersurface in $\mathbb CP^n$ defined by an explicit equation $F=0$. Let $\varphi: \mathbb P^n \to \mathbb P^n$ be an explicit degree $m$ morphism. In this case $\varphi(H)$ is a degree $d^{n-1}m$ hypersurface. Is there an algorithm to calculate the coefficients of the degree $d^{n-1}m$ polynomial that defines this hypersuface?