Often one wishes to change the monomial order of an ideal. Magma allows one to do this by use of the ChangeOrder function.
Given an ideal I of the local polynomial ring R = K[x1, ..., xn], 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.
Given an ideal I of the polynomial ring P = R[x1, ..., xn], together with a monomial order {order} (see Section Elements and Local Monomial Orders), construct the polynomial ring Q = R[x1, ..., xn] 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.