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Suppose Magma has computed homomorphism $h$ between function fields $F1 \to F2$. Then we have an induced homomorphism $h$ on the divisor group. Now my question is that if there's a better way to compute this homomorphism for $D2 := h(D1)$ than this way which is basically computing the image of the two generators of each place and is very slow.

Ps, Ds := Support(D1);
D2 := Divisor(F2!1);

for i := 1 to #Ps do
  g1,g2 := TwoGenerators(Ps[i]);

  G1 := h(g1);
  G2 := h(g2);

  D2 := D2 + Ds[i]*ZeroDivisor(GCD(Divisor(G1), Divisor(G2)) );

end for;

Thank you very much indeed!

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  • $\begingroup$ There are some Pullback functions in the documentation, but I've never used them. See if anything fits. $\endgroup$
    – Dror Speiser
    Commented Jul 5, 2011 at 8:12
  • $\begingroup$ Ooh, I like that magma tag you just created. $\endgroup$
    – David White
    Commented Jul 6, 2011 at 17:29

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