Assume a projective scheme $X_{k_1,\dots,k_r}\subset\mathbb{P}^n$ is given as the set of common solutions of homogeneous polynomials $F_1(x_0,\dots,x_n),\dots,F_s(x_0,\dots,x_n)$, where the $F_i$ depends on parameters $k_1,\dots,k_r$ varying in the base field.

Does there exist a computer algebra software that can compute the dimension and the degree of $X_{k_1,\dots,k_r}$ as functions of $k_1,\dots,k_r$?