\mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{N}{
+ name={\ensuremath{\Nn[1]}},
+ description={the set of natural numbers},
+ sort=N
+ }
+\fi
+
% The integral n-space, Z x Z x Z x ... x Z.
\newcommand*{\Zn}[1][n]{
\mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Z}{
+ name={\ensuremath{\Zn[1]}},
+ description={the ring of integers},
+ sort=Z
+ }
+\fi
+
% The rational n-space, Q x Q x Q x ... x Q.
\newcommand*{\Qn}[1][n]{
\mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Q}{
+ name={\ensuremath{\Qn[1]}},
+ description={the field of rational numbers},
+ sort=Q
+ }
+\fi
+
% The real n-space, R x R x R x ... x R.
\newcommand*{\Rn}[1][n]{
\mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{R}{
+ name={\ensuremath{\Rn[1]}},
+ description={the field of real numbers},
+ sort=R
+ }
+\fi
+
+
% The complex n-space, C x C x C x ... x C.
\newcommand*{\Cn}[1][n]{
\mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{C}{
+ name={\ensuremath{\Cn[1]}},
+ description={the field of complex numbers},
+ sort=C
+ }
+\fi
+
+
% The space of real symmetric n-by-n matrices.
\newcommand*{\Sn}[1][n]{
\mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Sn}{
+ name={\ensuremath{\Sn}},
+ description={the set of $n$-by-$n$ real symmetric matrices},
+ sort=Sn
+ }
+\fi
+
% The space of complex Hermitian n-by-n matrices.
\newcommand*{\Hn}[1][n]{
\mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Hn}{
+ name={\ensuremath{\Hn}},
+ description={the set of $n$-by-$n$ complex Hermitian matrices},
+ sort=Hn
+ }
+\fi
+
%
% Basic set operations
%