On Wednesday 31 July 2024 at 07:33:47 UTC-7 Georgi Guninski wrote:
I need non-torsion element of Jacobian of hyperelliptic curve,
would someone give example?
IIRC something very close to the following worked about
5 years ago, but now I get trivial result.
Session:
#Author: Georgi Guninski
K.<x>=QQ[]
C=HyperellipticCurve(x^5+x+5^2-2);
J=C.jacobian();
P=J(1,5);
2*P
#(1) ##is this correct?
Yes, it is correct. To get a non-torsion element:
D=J(x-1,5)
For your other report:
K.<u>=QQ[]
C=HyperellipticCurve(u^5+u+5^2-2);
J=C.jacobian();
print("J=",J);
P=J(1,5); #error here
If you change the last line to P=J(1*u^0,5*u^0) then it does work. It looks
like there is some preprocessing on the arguments that changes constants
into polynomials and it looks like this has been hardcoded to
J.base_ring()['x']. It should use
J.curve().hyperelliptic_polynomials()[0].parent()
instead.
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