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Merge pull request #55 from upavloff/patch-3
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Typo in Lagrange's interpolation
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PlanetMacro authored Nov 20, 2023
2 parents 6b854da + 66fab0b commit 98eee2a
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2 changes: 1 addition & 1 deletion chapters/statements-moonmath.tex
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Expand Up @@ -1323,7 +1323,7 @@ \subsubsection{QAP representation} To understand what Quadratic Arithmetic Progr
To compute $A_2$ we note that the set $S_{A_2}$ in our version of Lagrange's interpolation is given by $S_{A_2}=\{(m_1,a^1_2), (m_2,a_2^2)\} = \{(5,1), (7,0)\}$. Using this set we get:
\begin{align*}
A_2(x) & = a^1_2\cdot(\frac{x-m_2}{m_1-m_2}) + a^2_2\cdot(\frac{x-m_1}{m_2-m_2})
A_2(x) & = a^1_2\cdot(\frac{x-m_2}{m_1-m_2}) + a^2_2\cdot(\frac{x-m_1}{m_2-m_1})
= 1\cdot(\frac{x-7}{5-7}) + 0\cdot(\frac{x-5}{7-5}) \\
& = \frac{x-7}{-2}
= \frac{x-7}{11} & \text{\# } 11^{-1}=6 \\
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