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Fixed broken latex in parallel-formulas.md

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Michael Rosenberg 2022-11-26 04:10:21 -05:00
parent ad7c755f49
commit 4b08687093
1 changed files with 4 additions and 4 deletions
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docs/parallel-formulas.md
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@ -145,16 +145,16 @@ This costs \\( 2\mathbf M + 1 \mathbf D\\).
## Readdition
If the point \\( P_2 = (X\_2 : Y\_2 : Z\_2 : T\_2) \\) is fixed, we
If the point \\( P\_2 = (X\_2 : Y\_2 : Z\_2 : T\_2) \\) is fixed, we
can cache the multiplication of the curve constants by computing
$$
\begin{aligned}
(S\_2' &&,&& S\_3' &&,&& Z\_2' &&,&& T\_2' )
(S\_2\' &&,&& S\_3\' &&,&& Z\_2\' &&,&& T\_2\' )
&\gets
(d\_2 \cdot (Y\_2 - X\_2)&&,&& d\_2 \cdot (Y\_1 + X\_1)&&,&& 2d\_2 \cdot Z\_2 &&,&& 2d\_1 \cdot T\_2).
\end{aligned}
$$
This costs \\( 1\mathbf D\\); with \\( (S\_2', S\_3', Z\_2', T\_2')\\)
This costs \\( 1\mathbf D\\); with \\( (S\_2\', S\_3\', Z\_2\', T\_2\')\\)
in hand, the addition formulas above become
$$
\begin{aligned}
@ -164,7 +164,7 @@ $$
\\\\
(S\_8 &&,&& S\_9 &&,&& S\_{10} &&,&& S\_{11} )
&\gets
(S\_0 \cdot S\_2' &&,&& S\_1 \cdot S\_3'&&,&& Z\_1 \cdot Z\_2' &&,&& T\_1 \cdot T\_2')
(S\_0 \cdot S\_2\' &&,&& S\_1 \cdot S\_3\'&&,&& Z\_1 \cdot Z\_2\' &&,&& T\_1 \cdot T\_2\')
\\\\
(S\_{12} &&,&& S\_{13} &&,&& S\_{14} &&,&& S\_{15})
&\gets