Changing Coefficient Ring

The ChangeRing function enables the changing of the coefficient ring of an algebra or ideal.

ChangeRing(I, S): AlgFr, Rng -> AlgFr

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