Code and instructions related to the paper Automorphisms of the Jacobian, co-authored with Dami Lee.

The necessary packages to run the full program are as follows. Getting the underlying automorphism set of Hom(C_1, C_2) requires SageTrac, Magma, and Costa's endomorphism group package; the group identification uses the GAP SmallGroup package. A very useful collection of documentation at the time of writing may be found in the sagemath github, in the file schemes/riemann_surfaces/riemann_surface.py.

The code in this folder was written almost entirely by Jeroen Sijsling in private correspondence. The implementation is particularly nice for hyperelliptic curves.

f = hyperelliptic curve
S = RiemannSurface(f, prec = 100)
G = S.symplectic_automorphism_group()
print G.order()

For non-hyperellptic curves, we must trick the package for now, by sticking in a "dummy" hyperelliptic curve of the same genus.

Here the code for autperio.sage relies on CullPB.m. The psuedo-code is in section ~\ref{sec:autperio} and ~\ref{sec:find} respectively.

Sijsling's FindPolarizationBasis Magma function plays nicely with the full period matrix big, and not the pre-symmetrized one small. Though one can always create big out of small by appending an identity matrix of the same shape to the small matrix.