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The naming conventions seem inconsistent with typical Julia conventions and are all over the place.
Perhaps wp should be named weierstrassp for example, although wp may be fine.
The name halfPeriods is not consistent with Julia naming conventions, it should probably be halfperiods without the capitalization, since capitalization in Julia is usually for structs and types, not for function names. Same with ellipticInvariants.
You could also define const ℘ = wp and export it, since the \wp symbol exists for Julia users.
This isn't a huge issue, but the naming conventions could be more consistent with typical Julia naming conventions.
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