# Changing Coefficient Ring

The `ChangeRing` function enables the changing of the coefficient ring of a local polynomial ring or ideal.

## `ChangeRing(I, L): RngMPolLoc, Rng -> RngMPolLoc`

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