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Fix comment for `evaluate_polynomial_in_evaluation_form` to reflect that it can now also be used in the domain

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kevaundray 2023-03-04 19:20:01 +00:00 committed by GitHub
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specs/deneb/polynomial-commitments.md
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@ -303,8 +303,10 @@ def compute_powers(x: BLSFieldElement, n: uint64) -> Sequence[BLSFieldElement]:
def evaluate_polynomial_in_evaluation_form(polynomial: Polynomial,
z: BLSFieldElement) -> BLSFieldElement:
"""
Evaluate a polynomial (in evaluation form) at an arbitrary point ``z`` that is not in the domain.
Uses the barycentric formula:
Evaluate a polynomial (in evaluation form) at an arbitrary point ``z``.
- When ``z`` is in the domain, the evaluation can be found by indexing the polynomial at the
position that ``z`` is in the domain.
- When ``z`` is not in the domain, the barycentric formula is used:
f(z) = (z**WIDTH - 1) / WIDTH * sum_(i=0)^WIDTH (f(DOMAIN[i]) * DOMAIN[i]) / (z - DOMAIN[i])
"""
width = len(polynomial)