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Refactoring: Improve inconsistent core pickles variable names
As per the Least Authority's audit and subjective experience, it would be a good idea to improve naming of the core Pickles (and Kimchi) variables. This issue is only for the ones that are particularly confusing -- there is much more that can be done.
Examples include (non-exhaustive)
xi/rsame asu/vsame aspolyscale/evalscale-- theu/vcan be used in Latex docs, while code can use justpolyscale/evalscale. I suggest removingxi/rbecause it's less descriptive, and also becauseu/vis already used in the docs + in Plonk paper.bis just a terribly non-descriptive variable name for a quite a complicated thing (a combined evaluation)x_hatis the same aspublic_Inputsand sometimespublic_evals. I prefer the longer descriptions in the code, while the latex docs can have\hat{x}if needed.prev_challenges: PrevChallengesis actually not challenges, but challenges /and/ commitments. It's quite confusing.
Nice ideas