I have a large set of polynomials in the coordinates $x,y,z$ in Sage, (e.g. $x^5y-3x^2y^2+2xy^3+x^2yz-y^2z$). I want to know, for example, if $x^5y$ is in the span of my set. Is there a Sage command that can tell me this?

I was hoping that there might be a command in Sage where I can take the span of my polynomials (over $\mathbb{C}$) and find a basis. However, the only commands I can find concern vectors. I know that I could just convert my polynomials to vectors by letting a standard basis vector represent each distinct monomial, but this would be terribly tedious to do by hand for such a large set of polynomials.

(I am very new to Sage, so I apologize if this is a silly question. Any advice would be greatly appreciated.)