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Fix typos
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@ -242,7 +242,7 @@ Now, we can write our polynomial as a linear combination of Lagrange basis funct
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$$A(X) = \sum_{i = 0}^{n-1} a_i\mathcal{L_i}(X), X \in \mathcal{H},$$
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which is equivalent to saying that $p(X)$ evaluates to $a_0$ at $\omega^0$,
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which is equivalent to saying that $A(X)$ evaluates to $a_0$ at $\omega^0$,
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to $a_1$ at $\omega^1$, to $a_2$ at $\omega^2, \cdots,$ and so on.
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When working over a multiplicative subgroup, the Lagrange basis function has a convenient
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@ -59,7 +59,7 @@ arguments are independent.)
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Let $c$ be the number of columns that are enabled for equality constraints.
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Let $m$ be the maximum number of columns that can accommodated by a
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Let $m$ be the maximum number of columns that can be accommodated by a
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[column set](permutation.md#spanning-a-large-number-of-columns) without exceeding
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the PLONK configuration's maximum constraint degree.
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@ -55,7 +55,7 @@ $$\mathbf{H} = [\text{Commit}(h_0(X)), \text{Commit}(h_1(X)), \dots, \text{Commi
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## Evaluating the polynomials
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At this point, all properties of the circuit have been committed to. The verifier now
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At this point, we have committed to all properties of the circuit. The verifier now
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wants to see if the prover committed to the correct $h(X)$ polynomial. The verifier
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samples $x$, and the prover produces the purported evaluations of the various polynomials
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at $x$, for all the relative offsets used in the circuit, as well as $h(X)$.
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