imaginary unit and subspaces of the complex polynomial ring?
I am trying to work with the complex, multivariate polynomial ring R.<x,y> = CC['x,y']. When I try to create an element in my ring R f = x + I*y i get parent(f) is a symbolic ring and not R, which seems to happen due to the "I". Is there a way to interpret "I" as an element in my R?
Also if I have a long list "L" of elements in the ring "R" is there an easy way to define a real subspace of R (alternatively R could also be a real polynomial ring) spanned by the elements of L and to check whether a given polynomial f lies in this span?