2021-09-12 09:52:03 +0100 received badge ● Nice Question (source) 2021-09-06 14:48:39 +0100 marked best answer Define morphism of Q[i,w] in terms of i and w I want to construct the field $K=Q[i,w]$ where $w=\sqrt{2}$ and define a field homomorphism such as $w\mapsto iw$, $i\mapsto -i$. I'd like to do K. = NumberField([x^4-2,x^2+1]) H = End(K) H([I*w,-I])  but it doesn't work because $K$ is considered to be the relative field $(Q[i])[w]$. I know I could work with the absolute field K_abs. = K.absolute_field()  but I'd really like to define the morphism in terms of $w,i$. Is it possible? 2021-09-06 14:48:38 +0100 received badge ● Supporter (source) 2021-09-06 11:14:37 +0100 received badge ● Student (source) 2021-09-06 10:35:27 +0100 asked a question Define morphism of Q[i,w] in terms of i and w Define morphism of Q[i,w] in terms of i and w I want to construct the field $K=Q[i,w]$ where $w=\sqrt{2}$ and define 2020-06-12 16:30:06 +0100 received badge ● Scholar (source) 2020-06-10 23:21:36 +0100 asked a question 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. = ProjectiveSpace(K,2) P1P1. = 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?