There are two ways to present an $R$-module $M$. One way is to take a free module $F$ (whose generators are called the generators) and form the quotient $M = F/H$ by a submodule $H\subset F$ (whose generators are called the relations).
Another way is take a free module $F$, a submodule $G\subset F$ (whose generators are called the generators), a submodule $H\subset F$ (whose generators are called the relations), and form the subquotient module $M = (G+H)/H$, obtained also as the image of $G$ in $F/H$.
The purpose of trim is to minimize presentations of the latter type. This applies also to rings and ideals.
|
|
|
|
|
|
|
|
The object trim is a method function with options.