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), 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 \(i\).