Commit 4bae4134 authored by Hubert Chathi's avatar 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
...@@ -40,30 +40,30 @@ advanced as follows: ...@@ -40,30 +40,30 @@ advanced as follows:
```math ```math
\begin{aligned} \begin{aligned}
R_{i,0} &= R_{i,0} &=
\begin{cases} \begin{cases}
H_0\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\ H_0\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
R_{i-1,0} &\text{otherwise} R_{i-1,0} &\text{otherwise}
\end{cases}\\ \end{cases}\\
R_{i,1} &= R_{i,1} &=
\begin{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^{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\\ H_1\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
R_{i-1,1} &\text{otherwise} R_{i-1,1} &\text{otherwise}
\end{cases}\\ \end{cases}\\
R_{i,2} &= R_{i,2} &=
\begin{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^{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^{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\\ H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
R_{i-1,2} &\text{otherwise} R_{i-1,2} &\text{otherwise}
\end{cases}\\ \end{cases}\\
R_{i,3} &= R_{i,3} &=
\begin{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^{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^{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_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
H_3\left(R_{i-1,3}\right) &\text{otherwise} H_3\left(R_{i-1,3}\right) &\text{otherwise}
\end{cases} \end{cases}
\end{aligned} \end{aligned}
``` ```
......
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