Given two projective spaces Pn and Pm together with m+1 global sections of the invertible sheaf OPn(d) (e.g. m+1 homogeneous polynomials of degree d in the variables x0,⋯,xn, say f0,⋯,fm), we know that there exists a unique morphism [f0,⋯,fm]:Pn→Pm. Assume the projective spaces are considered over a noetherian ring ; the morphisms to the base are both projective, hence proper, which means [f0,⋯,fm] is a proper morphism, hence has closed image.
Question : Does there exist an algorithm already implemented in Sage to find the homogeneous ideal of relations of the image of the map [f0,⋯,fm]? I've been messing around for a few days now and it seems to only involve linear algebra, so in the case where the base is the spectrum of a field there should be an algorithm, I just don't know how efficient it is or if it's implemented at all. I would not mind if the algorithm was slow, I just want it to work in small cases (i.e. small degree and small number of polynomials)!