How to get the quotients in multivariable polynomial division?
Given a Groebner basis $G=\lbrace f_1,\dots,f_s \rbrace$ and $g$, how can I get the quotients of $g$ on division by $G$ ? I know that when considering the quotients, the ordering we use to list the divisors $f_1,\dots,f_s$ matters. I also know the command p.reduce(I) for remainders. I would appreciate any help with this situation.
Could you please provide the construction of the
fiandgso that we start from something concrete, without having to build our own ?