Numerical evaluation of periods matrices of hyperelliptic and superelliptic curves to arbitrary precision by numerical integration.
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gp
Initial projet as gp script, period matrix + Abel-Jacobi map for hyperelliptic curves
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magma
Generalization for superelliptic curves with Christian Neurohr, complete Abel-Jacobi map. Written in magma.
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arb
Rigorous Arb implementation, currently only period matrices.
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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.