Let $A=\mathbb{R}[x_1,\dots,x_n]$ be the algebra of real polynomials in $n$ variables. Fix polynomials $p_1,\dots,p_k\in A$.

Consider the subset $$M:=\{(q_1,\dots,q_k)\in A^k|\, p_1q_1+\dots+p_kq_k=0\}.$$ Clearly $M$ is an $A$-submodule of $A^k$. Necessarily $M$ is finitely generated.

**I am wondering if there exists a software which allows to compute explicit generators of $M$ as an $A$-module.**

In my case $n=16,k=10$, and all $p_i$'s are explicit homogeneous polynomials of second degree.