In Sympy package there is Groebner() function, which allows to find a Groebner basis={$g_1, g_2,..., g_k$} for an ideal I, generated by polynomials $\{f_1, f_2,..., f_n\}$.
I wonder if there is another function, which allows not only to find the Groebner basis, but also find a Groebner representation itself, namely, find the particular polynomials $P_1,P_2,... P_n, Q_1,Q_2, ..., Q_n$ ...etc, such that:
$g_1= P_1\times f_1+...+ P_n\times f_n$
$g_2= Q_1\times f_1+...+ Q_n\times f_n$ .... etc.