So I'm using Sage to reduce a bunch of monomials modulo an ideal $I$ in a ring $R = \mathbb{C}[x_1,x_2,...,x_n]$. Sage, however, decides that it should reduce things and use the high index terms as a basis, instead of the lower-index terms. For example, if $I = < x_1 + x_2 + x_3 >$ for $n = 3$, Sage will reduce $x_1$ into $-x_2 - x_3$, and use $x_2$ and $x_3$ as generators, whereas I want it to use $x_1$ and $x_2$ as generators instead, and have it say $x_3 = -x_1 - x_2$. Is there a way to do this?