# Morphism from projective space to product of projective spaces

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?

edit retag close merge delete

Sort by ยป oldest newest most voted

Try to upgrade your version of Sage. This works fine in Sage 9.1:

sage: 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])
....:
Scheme morphism:
From: Projective Space of dimension 2 over Finite Field of size 2
To:   Product of projective spaces P^1 x P^1 over Finite Field of size 2
Defn: Defined on coordinates by sending (x : y : z) to
(x : y , x^2 : y^2)

more