From 7bf768da8e42b26f776e79c99d83a3dbd9816b7e Mon Sep 17 00:00:00 2001 From: Angkur Mondal Date: Fri, 27 Jan 2023 01:28:09 +0600 Subject: [PATCH] Update module-inverse.md --- src/algebra/module-inverse.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/algebra/module-inverse.md b/src/algebra/module-inverse.md index b17b7af78..a744b9da6 100644 --- a/src/algebra/module-inverse.md +++ b/src/algebra/module-inverse.md @@ -120,7 +120,7 @@ Instead of computing the inverse for every number, we can expand the fraction by $$ \begin{align} -x_i^{-1} &= \frac{1}{x^i} = \frac{\overbrace{x_1 \cdot x_2 \cdots x_{i-1}}^{\text{prefix}_{i-1}} \cdot ~1~ \cdot \overbrace{x_{i+1} \cdot x_{i+2} \cdots x_n}^{\text{suffix}_{i+1}}}{x_1 \cdot x_2 \cdots x_{i-1} \cdot x_i \cdot x_{i+1} \cdot x_{i+2} \cdots x_n} \\ +x_i^{-1} &= \frac{1}{x_i} = \frac{\overbrace{x_1 \cdot x_2 \cdots x_{i-1}}^{\text{prefix}_{i-1}} \cdot ~1~ \cdot \overbrace{x_{i+1} \cdot x_{i+2} \cdots x_n}^{\text{suffix}_{i+1}}}{x_1 \cdot x_2 \cdots x_{i-1} \cdot x_i \cdot x_{i+1} \cdot x_{i+2} \cdots x_n} \\ &= \text{prefix}_{i-1} \cdot \text{suffix}_{i+1} \cdot \left(x_1 \cdot x_2 \cdots x_n\right)^{-1} \end{align} $$ pFad - Phonifier reborn

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