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To make polynomial API ready enough for PLONK, we need following methods:
- polynomial arithmetic (add, sub, div) #28
- evaluation domain #29
- feat: FFT and IFFT based on domain #30
- basis change using FFT (lagrange -> monomial and vice versa) #31
- barycentric evaluation on roots of unity in lagrange basis. Vitalik has an amazing article. #32
- feat: coset lagrange evaluation #33
This article has really concise explanations of common optimisations used throughout proof systems:
- perf: fast polynomial multiplication and division in lagrange domain. #34
- batch polynomial evaluation #35
- feat: coset division #36
Any others I'm missing?
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