The ChangeRing function enables the changing of the coefficient ring of a local polynomial ring or ideal.
Given an ideal I of a local polynomial ring R=K[x1, ..., xn] of rank n with coefficient ring K, together with a field L, construct the ideal J of the polynomial field S=L[x1, ..., xn] 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.