Better positive square root symbol.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

protocol/protocol.tex

@@ -458,8 +458,7 @@
 \newcommand{\yy}{\hspace{0.022em}y\hspace{0.021em}}
 
 \newcommand{\hfrac}[2]{\scalebox{0.8}{$\genfrac{}{}{0.5pt}{0}{#1}{#2}$}}
-\newcommand{\ssqrt}[1]{\rlap{\scalebox{0.64}[1]{$\sqrt{\scalebox{1.5625}[1]{${#1}\vphantom{b}$}}$}} %
-             \hspace{0.005em}\scalebox{0.64}[1]{$\sqrt{\scalebox{1.5625}[1]{$\phantom{#1}\vphantom{b}$}}$}}
+\newcommand{\possqrt}[1]{{}^+\hspace{-0.7em}\sqrt{#1\vphantom{b}}}
 
 \newcommand{\sbitbox}[2]{\bitbox{#1}{\strut #2}}
 
@@ -2480,7 +2479,7 @@ $\sxor{i=1}{0} a_i = 0$ or the all-zero bit sequence of length given
 by the type of $a$.
 
 \notsprout{
-$\ssqrt{a}$, where $a \typecolon \GF{q}$, means the positive
+$\possqrt{a}$, where $a \typecolon \GF{q}$, means the positive
 (i.e.\ in the range $\range{0}{\hfrac{q-1}{2}}$)
 square root of $a$ in $\GF{q}$. It is only used in cases where the
 square root must exist.
@@ -10355,6 +10354,9 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
 
 \begin{itemize}
     \item Consistently use ``validating'' for signatures and ``verifying'' for proofs.
+\sapling{
+    \item Use the symbol $\possqrt{\,\paramdot\,}$ for positive square root.
+}
 \end{itemize}
 
 
@@ -10916,7 +10918,7 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
     \item Ensure that \Sprout functions and values are given \Sprout-specific types where appropriate.
     \item Improve cross-referencing.
     \item Clarify the use of \BCTV vs \Groth proofs in \joinSplitStatements.
-    \item Clarify that the $\ssqrt{a}$ notation refers to the positive square root. (This matters for
+    \item Clarify that the $\possqrt{a}$ notation refers to the positive square root. (This matters for
           the conversion in \crossref{cctconversion}.)
     \item Model the group hash as a random oracle. This appears to be unavoidable in order to allow
           proving unlinkability of $\DiversifyHash$. Explain how this relates to the Discrete Logarithm
@@ -12044,7 +12046,7 @@ as follows:
 
 \begin{formulae}
   \item \makebox[25em][l]{$\CtEdwardsToMont(u, \varv) = \left(\hfrac{1 + \varv}{1 - \varv},\,
-                                                              \scalebox{0.8}{$\ssqrt{-40964}$} \mult \hfrac{1 + \varv}{(1 - \varv) \mult u}\right)$}
+                                                              \scalebox{0.8}{$\possqrt{-40964}$} \mult \hfrac{1 + \varv}{(1 - \varv) \mult u}\right)$}
         $[1 - \varv \neq 0 \tand u \neq 0]$
 \end{formulae}
 
@@ -12053,7 +12055,7 @@ Define $\MontToCtEdwards \typecolon \AffineMontJubjub \rightarrow \AffineCtEdwar
 as follows:
 
 \begin{formulae}
-  \item \makebox[25em][l]{$\MontToCtEdwards(x, y) = \left(\scalebox{0.8}{$\ssqrt{-40964}$} \mult \hfrac{x}{y},\,
+  \item \makebox[25em][l]{$\MontToCtEdwards(x, y) = \left(\scalebox{0.8}{$\possqrt{-40964}$} \mult \hfrac{x}{y},\,
                                                           \hfrac{x - 1}{x + 1}\right)$}
         $[x + 1 \neq 0 \tand y \neq 0]$
 \end{formulae}
@@ -12061,7 +12063,7 @@ as follows:
 \introlist
 Either of these conversions can be implemented by the same \quadraticConstraintProgram:
 \begin{formulae}
-  \item $\constraint{y}{u}{\ssqrt{-40964} \mult x}$
+  \item $\constraint{y}{u}{\possqrt{-40964} \mult x}$
         \vspace{-0.5ex}
   \item $\constraint{x + 1}{\varv}{x - 1}$
 \end{formulae}