diff --git a/macros.tex b/macros.tex
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+\newcommand{\F}{\mathds{F}}
+
+\newcommand{\Add}{\hyperref[alg:add]{\textsc{Add}}}
+\newcommand{\Double}{\hyperref[alg:double]{\textsc{Double}}}
+
+\newcommand{\sbcaptionextra}{
+    A rule (\rule{4ex}{0.4pt}) denotes a ``dead'' value, i.e.\ one
+    that has no meaning and is unused.
+    \textsc{Red} executes a coefficient-reduction chain.
+}
+\newcommand{\hcaptionextra}{
+    \sbcaptionextra
+    The additions/subtractions with large constants
+    ($2^{32}p$, $4p$ and $2^{37}p$)
+    are to ensure that all the values
+    are in the positive domain after subtraction.
+}
+
+