The problem I have is the following. I have a subset $S \subseteq \mathbb{R}^4$ which I suspect to be an affine variety. I can generate as many as I would like random points on $S$, but their coordinates are as numpy floats approximations, rather than, say, exact values.
Is there a software that would take these points as inputs, and would give me, if they exist, the polynomial equations satisfied by these points, and thus, hopefully, by $S$? There are some complications due to the fact that the coordinates are approximations. So the software has to be able to handle some round-off errors. Also if someone knows of such a software, could they maybe also give me the name of the relevant command please?