Here's how to run the code on one example from Siksek's paper: open MAGMA at the top level, and execeute the following:
Attach("g2-jac.m");
Attach("add.m");
load "JSearch.m";
SetClassGroupBounds("GRH");
Qu<u>:=PolynomialRing(Rationals());
K<t>:=NumberField(u^3-2);
eps:=1-t;
Kx<x>:=PolynomialRing(K);
s := 0;
C:=HyperellipticCurve(3*(4*eps^(-s)*x^5-eps^(2*s)));
pts:=ratPointsC(C);
If all is well, you should see the following:
Chabauty is respectively successful at [ true, true, true, true, true ]
after applying Chabauty with prime 31
W has 0 elements
succeeded in proving that the only K-rational points are [ (1 : 0 : 0), (1 : 3 :
1), (1/3*(t^2 + 2*t + 1) : 1/3*(-10*t^2 - 8*t - 13) : 1), (1 : -3 : 1),
(1/3*(t^2 + 2*t + 1) : 1/3*(10*t^2 + 8*t + 13) : 1) ]
This is a unit test; any changes made to underlying routines should be such that this example still works.
The Coleman integration modules seem to be in g2-jac.m, specifically the integrals and integrationMatrix intrinsics.
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