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Rearranged expanded sums/prods to match Wikipedia
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This form also just seems a bit more readable, with the expansion being
more a sidenote than relevant to the core math.
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geky committed Oct 25, 2024
1 parent affd158 commit a8e82ef
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -143,8 +143,8 @@ points at $g^i$ where $i < n$ like so:

<p align="center">
<img
alt="P(x) = \left(x-1\right)\left(x-g\right)\cdots\left(x-g^{n-1}\right) = \prod_{i=0}^{n-1} \left(x - g^i\right)"
src="https://latex.codecogs.com/svg.image?P%28x%29%20%3d%20%5cleft%28x%2d%31%5cright%29%5cleft%28x%2dg%5cright%29%5ccdots%5cleft%28x%2dg%5e%7bn%2d%31%7d%5cright%29%20%3d%20%5cprod_%7bi%3d%30%7d%5e%7bn%2d%31%7d%20%5cleft%28x%20%2d%20g%5ei%5cright%29"
alt="P(x) = \prod_{i=0}^{n-1} \left(x - g^i\right) = \left(x-1\right)\left(x-g\right)\cdots\left(x-g^{n-1}\right)"
src="https://latex.codecogs.com/svg.image?P%28x%29%20%3d%20%5cprod_%7bi%3d%30%7d%5e%7bn%2d%31%7d%20%5cleft%28x%20%2d%20g%5ei%5cright%29%20%3d%20%5cleft%28x%2d%31%5cright%29%5cleft%28x%2dg%5cright%29%5ccdots%5cleft%28x%2dg%5e%7bn%2d%31%7d%5cright%29"
>
</p>
Expand Down Expand Up @@ -210,8 +210,8 @@ to our original codeword, where $E(x)$ contains up to $e$ non-zero terms:
<p align="center">
<img
alt="E(x) = E_{j_0} x^{j_0} + E_{j_1} x^{j_1} + \cdots + E_{j_{e-1}} x^{j_{e-1}} = \sum_{j \in E} E_j x^j"
src="https://latex.codecogs.com/svg.image?E%28x%29%20%3d%20E_%7bj_%30%7d%20x%5e%7bj_%30%7d%20%2b%20E_%7bj_%31%7d%20x%5e%7bj_%31%7d%20%2b%20%5ccdots%20%2b%20E_%7bj_%7be%2d%31%7d%7d%20x%5e%7bj_%7be%2d%31%7d%7d%20%3d%20%5csum_%7bj%20%5cin%20E%7d%20E_j%20x%5ej"
alt="E(x) = \sum_{j \in E} E_j x^j = E_{j_0} x^{j_0} + E_{j_1} x^{j_1} + \cdots + E_{j_{e-1}} x^{j_{e-1}}"
src="https://latex.codecogs.com/svg.image?E%28x%29%20%3d%20%5csum_%7bj%20%5cin%20E%7d%20E_j%20x%5ej%20%3d%20E_%7bj_%30%7d%20x%5e%7bj_%30%7d%20%2b%20E_%7bj_%31%7d%20x%5e%7bj_%31%7d%20%2b%20%5ccdots%20%2b%20E_%7bj_%7be%2d%31%7d%7d%20x%5e%7bj_%7be%2d%31%7d%7d"
>
</p>
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