Arrabbiata: avoid duplicated code for each curve

[dannywillems]

Initially, it has been decided to go with the KISS method, and avoid as much as possible complex type machinery to not have a Pickles-like version of Arrabbiata.
Over time, we realized that it was adding duplicated code like here or here. There is a consensus in the team that it should be improved. In particular, when introducing the cross-terms computation, we notice that it is getting even worse.

A solution would be to rely on the types to select which fields the environment should use and update.