# Changing Ring

## `ChangeRing(A, R): Mtrx, Rng -> Mtrx`

## `Matrix(R, A): Rng, Mtrx -> Mtrx`

Given a matrix $A$ over a ring $S$ having $m$ rows and $n$ columns, and another ring $R$, return the $m\times n$ matrix over $R$ obtained by coercing the entries of $A$ from $S$ into $R$. The argument order to `ChangeRing(A, R)` here is consistent with other forms of `ChangeRing`, while the `Matrix(R, A)` form of this function is provided to be consistent with the matrix creation functions above, for which the destination ring is the first argument, if supplied.

## `ChangeRing(A, R, f): Mtrx, Rng, Map -> Mtrx`

## `ChangeRing(A, f): Mtrx, Map -> Mtrx`

Given a matrix $A$ over a ring $S$ having $m$ rows and $n$ columns, another ring $R$, and a map $f:S \rightarrow R$, return the $m\times n$ matrix over $R$ obtained by applying $f$ to each of the entries of $A$. The $R$ may be omitted, in which case it is taken to be the codomain of $f$.

## `CanChangeRing(A, R): Mtrx, Rng -> BoolElt, Mtrx`

Return whether the entries in the matrix $A$ can be coerced into $R$ and the matrix resulting from `ChangeRing(A, R)` if so.