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Michael Telatynski
Olm
Commits
4bae4134
Commit
4bae4134
authored
Sep 17, 2020
by
Hubert Chathi
Browse files
partially unindent R_{i,j} derivation
so that we're under GitLab's 1000 character limit for rendering maths
parent
84841a19
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docs/megolm.md
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4bae4134
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@@ -40,30 +40,30 @@ advanced as follows:
```
math
\begin{aligned}
R_{i,0} &=
\begin{cases}
H_0\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
R_{i-1,0} &\text{otherwise}
\end{cases}\\
\begin{cases}
H_0\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
R_{i-1,0} &\text{otherwise}
\end{cases}\\
R_{i,1} &=
\begin{cases}
H_1\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_1\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
R_{i-1,1} &\text{otherwise}
\end{cases}\\
\begin{cases}
H_1\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_1\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
R_{i-1,1} &\text{otherwise}
\end{cases}\\
R_{i,2} &=
\begin{cases}
H_2\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_2\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
R_{i-1,2} &\text{otherwise}
\end{cases}\\
\begin{cases}
H_2\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_2\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
R_{i-1,2} &\text{otherwise}
\end{cases}\\
R_{i,3} &=
\begin{cases}
H_3\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_3\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
H_3\left(R_{i-1,3}\right) &\text{otherwise}
\end{cases}
\begin{cases}
H_3\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
H_3\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
H_3\left(R_{i-1,3}\right) &\text{otherwise}
\end{cases}
\end{aligned}
```
...
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