# Changing Ring

The `ChangeRing` function enables the changing of the polynomial ring over which a module is defined.

## `ChangeRing(M, S): RngMPol, Rng -> RngMPol`

Given an $R$-module $M$, where $R$ is a polynomial ring, and another polynomial ring $S$, construct the $S$-module $N$ obtained by coercing the coefficients of the elements of the basis and relations of $M$ into $S$. It is necessary that all elements of the old coefficient ring $R$ can be automatically coerced into the new coefficient ring $S$. Note that $S$ itself must be polynomial ring having the same rank as $R$, so $S$ does not specify the new ring for the underlying coefficients (one can use [`ChangeRing`](../GrobnerBases/change-ring.md#function-gb-changering) for polynomial rings to do that first).