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+% Needed for \operatorname.
+\usepackage{amsopn}
+
+% The fraction field of its argument, an integral domain. The name
+% "Frac" was chosen here instead of "Quot" because the latter
+% corresponds to the term "quotient field," which can be mistaken in
+% some cases for... a quotient field (something mod something).
+\newcommand*{\Frac}[1]{\operatorname{Frac}\of{{#1}}}
+
+% The polynomial ring whose underlying commutative ring of
+% coefficients is the first argument and whose indeterminates (a
+% comma-separated list) are the second argumnt.
+\newcommand*{\polyring}[2]{{#1}\left[{#2}\right]}