summary |
shortlog |
log |
commit | commitdiff |
tree
raw |
patch |
inline | side by side (from parent 1:
ce3ce92)
This was a TODO item for a while; a standalone "S" or "H" doesn't have
the same meaning as, say, a standalone \mathbb{R} does. The "n"
doesn't indicate the arity of a Cartesian product, so for example S^2
isn't two copies of S^1. Dropping the superscript was therefore
misleading (and nonstandard notation).
1. Move the set operations from mjo-common and mjo-misc into mjo-set.
1. Move the set operations from mjo-common and mjo-misc into mjo-set.
-
-2. Having S^{n} or H^{n} reduce to simply "S" or "H" in the case where
- n=1 doesn't make sense.
superscript when that superscript would be one: $\Nn[1]$,
$\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
superscript when that superscript would be one: $\Nn[1]$,
$\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
- $\Qn[2]$, $\Rn[2]$, $\Cn[2]$.
+ $\Qn[2]$, $\Rn[2]$, $\Cn[2]$. Likewise we have the $n$-by-$n$
+ real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+ respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+ simplify because the ``$n$'' does not indicate the arity of a
+ Cartesian product in this case.
We also have a few basic set operations, for example the union of
two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
We also have a few basic set operations, for example the union of
two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
-% The space of real symmetric n-by-n matrices.
-\newcommand*{\Sn}[1][n]{
- \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
+% The space of real symmetric n-by-n matrices. Does not reduce to
+% merely "S" when n=1 since S^{n} does not mean an n-fold cartesian
+% product of S^{1}.
+\newcommand*{\Sn}[1][n]{ \mathcal{S}^{#1} }
\ifdefined\newglossaryentry
\newglossaryentry{Sn}{
name={\ensuremath{\Sn}},
\ifdefined\newglossaryentry
\newglossaryentry{Sn}{
name={\ensuremath{\Sn}},
-% The space of complex Hermitian n-by-n matrices.
-\newcommand*{\Hn}[1][n]{
- \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
+% The space of complex Hermitian n-by-n matrices. Does not reduce to
+% merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
+% product of H^{1}.
+\newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
\ifdefined\newglossaryentry
\newglossaryentry{Hn}{
name={\ensuremath{\Hn}},
\ifdefined\newglossaryentry
\newglossaryentry{Hn}{
name={\ensuremath{\Hn}},
%
% Basic set operations
%
%
% Basic set operations
%