# Changing Coefficient Ring

The `ChangeRing` function enables the changing of the coefficient ring of an algebra or ideal.

## `ChangeRing(I, S): AlgFr, Rng -> AlgFr`

Given an ideal $I$ of an algebra $F=R[x_1, \ldots, x_n]$ of rank $n$ with coefficient ring $R$, together with a ring $S$, construct the ideal $J$ of the algebra $Q=S[x_1, \ldots, x_n]$ obtained by coercing the coefficients of the elements of the basis of $I$ into $S$. It is necessary that all elements of the old coefficient ring $R$ can be automatically coerced into the new coefficient ring $S$. If $R$ and $S$ are fields and $R$ is known to be a subfield of $S$ and the current basis of $I$ is a Gröbner basis, then the basis of $J$ is marked automatically to be a Gröbner basis of $J$.