# Changing Monomial Order

Often one wishes to change the monomial order of an ideal. Magma allows one to do this by use of the `ChangeOrder` function.

## `ChangeOrder(I, Q): RngMPolLoc, RngMPolLoc -> RngMPolLoc, Map`

Given an ideal $I$ of the local polynomial ring $R = K[x_1, \ldots, x_n]$, together with a local polynomial ring $S$ of rank $n$ (with possibly a different order to that of $R$), return the ideal $J$ of $S$ corresponding to $J$ and the isomorphism $f$ from $R$ to $S$. The map $f$ simply maps $R.i$ to $S.i$ for each $i$.

## `ChangeOrder(I, order): RngMPolLoc, ... -> RngMPolLoc, Map`

Given an ideal $I$ of the polynomial ring $P = R[x_1, \ldots, x_n]$, together with a monomial order order (see Section [Elements and Local Monomial Orders](elements-order.md#rngmpolloc-orders)), construct the polynomial ring $Q = R[x_1, \ldots, x_n]$ with order order, and then return the ideal $J$ of $Q$ corresponding to $I$ and the isomorphism $f$ from $P$ to $Q$. See the section on monomial orders for the valid values for the argument order. The map $f$ simply maps $P.i$ to $Q.i$ for each $i$.