_gr_ore_poly_divrem, gr_ore_poly_divrem, gr_ore_poly_div, gr_ore_poly_rem

Compute the right Euclidean division $U = QV + R$ with $\operatorname{ord} R < \operatorname{ord} V$, which exists and is unique when the leading coefficient of $V$ and its images under the powers of $\sigma$ are invertible (over a field with $\sigma$ injective, for instance). Each step divides the leading coefficient of the current remainder by $\sigma^k(\operatorname{lc}(V))$ and subtracts $c D^k V$, for $k$ from $\operatorname{ord} U - \operatorname{ord} V$ down to 0; the eliminated coefficients of $R$ are then set to exact zeros (in inexact rings they would otherwise only be approximately zero). The non-underscore functions return GR_DOMAIN if $V = 0$; the underscore version requires $\mathit{lenU} \ge \mathit{lenV} \ge 1$ and writes $\mathit{lenU} - \mathit{lenV} + 1$ coefficients of $Q$ and $\mathit{lenU}$ of $R$. (In FLINT 3.6 and earlier the last step, $k = 0$, was skipped, so that for example $D^2 + D + 1$ divided by $D$ gave $Q = D$ and $R = 1 + D$.)