# Quotient Modules

## Construction of Quotient Modules

### `quo<M | L>: ModTupRng, List -> ModTupRng`

### `quo<M | L>: ModMatRng, List -> ModMatRng`

Given an $R$-module $M$, construct the quotient module $P = M/N$, where $N$ is the submodule generated by the elements of $M$ specified by the list $L$. Each term $L_i$ of the list $L$ must be an expression defining an object of one of the following types:

**(a)**
A sequence of $n$ elements of $R$ defining an element of $M$;

**(b)**
A set or sequence whose terms are elements of $M$;

**(c)**
A submodule of $M$;

**(d)**
A set or sequence whose terms are submodules of $M$.

The generators constructed for $N$ consist of the elements specified by terms $L_i$ together with the stored generators for submodules specified by terms of $L_i$.

The constructor returns the quotient module $P$ and the natural homomorphism $f : M \rightarrow P$.