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I have a polynomial $f\in\mathbb F[x_1,\ldots,x_n]$ and I know that it is an element of the subalgebra generated by $f_1,\ldots,f_k$. In fact, I can confirm this with f.in_subalgebra. However, I'd like the actual expression $h(t_1,\ldots,t_k)$ such that $f=h(f_1,\ldots,f_k)$. I know that the Groebner basis method should produce such $h$.

I'd like to know if there is a ready-to-use functionality in Sage to produce $h$.

I have a polynomial $f\in\mathbb F[x_1,\ldots,x_n]$ and I know that it is an element of the subalgebra generated by $f_1,\ldots,f_k$. In fact, I can confirm this with f.in_subalgebra. However, I'd like the actual expression $h(t_1,\ldots,t_k)$ such that $f=h(f_1,\ldots,f_k)$. I know that the Groebner basis method should produce such $h$.

I'd like to know if there is a ready-to-use functionality in Sage to produce $h$.