Numerical evaluation of periods matrices of hyperelliptic and superelliptic curves to arbitrary precision by numerical integration.
gp
Initial projet as gp script, period matrix + Abel-Jacobi map for hyperelliptic curves
magma
Generalization for superelliptic curves with Christian Neurohr, complete Abel-Jacobi map. Written in magma.
arb
Rigorous Arb implementation, currently only period matrices.
hcperiods.pdf description of the algorithm and proofs
See the magma intructions to use the magma package.
The arb version can be used as follows (needs arb>=v2.12.0 installed)
cd arb && make example
then
build/examples/periods -m 2 --pol 4 1 0 -2 3 0
outputs a period matrix for the curve y^2 = x^4 -2x^2 + 3x
.
Use options -m 5
to switch to the curve y^5 = x^4 -2x^2 + 3x
,
or --prec 1024
for 1024 bits precision.
Other options:
--gp
output fo pari/gp--de
force use of double exponential integration (instead of Gauss, if m = 2).--big
return big period matrices instead of reduced matrix tau.