# Accessing Module Information

## `M . i: ModTupRng, RngIntElt -> ModElt`

Given an $R$-module $M$ and a positive integer $i$, return the $i$-th generator of $M$. The integer $i$ must lie in the range $[1, r]$, where $r$ is the number of generators for $M$.

## `CoefficientRing(M): ModTupRng -> Rng`

## `BaseRing(M): ModTupRng -> Rng`

## `CoefficientRing(M): ModRng -> Rng`

## `BaseRing(M): ModRng -> Rng`

## `CoefficientField(M): ModFld -> Fld`

## `BaseField(M): ModFld -> Fld`

Given an $R$-module $M$ which is defined as a submodule of $S^{(n)}$, return the ring $S$.

## `Generators(M): ModTupRng -> { ModTupRngElt }`

The generators for the $R$-module $M$, returned as a set.

## `OverDimension(M): ModTupRng -> RngIntElt`

Given an $R$-module $M$ which is an embedded submodule of the module $S^{(n)}$, return $n$.

## `OverDimension(u): ModTupRngElt -> RngIntElt`

Given an element $u$ of an embedded submodule of the module $S^{(n)}$, return $n$.

## `Moduli(M): ModTupRng -> [ RngElt ]`

The column moduli of the module $M$ over a euclidean domain.

## `Parent(u): ModTupRngElt -> ModRng`

Given an element $u$ belonging to the $R$-module $M$, return $M$.

## `Generic(M): ModRng -> ModRng`

Given an $R$-module $M$ which is a submodule of the module $R^{(n)}$, return the module $R^{(n)}$ as an $R$-module.