Changing Coefficient Ring

The ChangeRing function enables the changing of the coefficient ring of a local polynomial ring or ideal.

ChangeRing(I, L): RngMPolLoc, Rng -> RngMPolLoc

Given an ideal \(I\) of a local polynomial ring \(R=K[x_1, \ldots, x_n]\) of rank \(n\) with coefficient ring \(K\), together with a field \(L\), construct the ideal \(J\) of the polynomial field \(S=L[x_1, \ldots, x_n]\) 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 \(J\).