arguments: S:ring f:ringelem >> g:ringelem
Lift f to an element g of S. If R is the base ring of f, then S ---> R should be one of the following extensions: (1) R ---> R (in which case f is returned without change), (2) S ---> R=S/I, (in which case f can always be lifted: note that S itself may be a quotient base ring of R), (3) S ---> R=S[x1..xn], (an error is returned if f is not a scalar), (4) S ---> R=frac S, (an error is returned if f is not an element of S), (5) S=Z/p[x]/(F(x)) ---> GF(p,n). An error indication is returned if the ring extension is not one of these, or in the situations indicated.
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