I have a problem with creating a rational map from the projective plane to P^1xP^1. The following code gives the error "polys (=[x, y, x^2, y^2]) must be of the same degree":
K = GF(2)
P2.<x,y,z> = ProjectiveSpace(K,2)
P1P1.<x0,x1,y0,y1> = ProductProjectiveSpaces([1,1],K)
H = Hom(P2,P1P1)
H([x,y,x^2,y^2])
On the other hand, creating the "same" map on P^1xP^1 does not give an error:
E = End(P1P1)
E([x0,x1,x0^2,x1^2])
Can someone explain to me why it does not work and how I can go around this problem?
