X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-cone.tex;h=703ecf44d0d63f2a78ddc51e9a2fac9238adc3f6;hp=6c681e9ebee4a7d0a9b7fef673ac3bf45cd1f1d5;hb=6759e3a5bd5fd13bd239ee851c66d1eac83a7c1b;hpb=d85706cc1efea350df9e957f6583a92d4e05359f diff --git a/mjo-cone.tex b/mjo-cone.tex index 6c681e9..703ecf4 100644 --- a/mjo-cone.tex +++ b/mjo-cone.tex @@ -4,8 +4,13 @@ % The operator families Z(K), LL(K), etc. can technically be defined on % sets other than cones, but nobody cares. % +\ifx\havemjocone\undefined +\def\havemjocone{1} -\usepackage{amssymb} % \succcurlyeq and friends + +\ifx\succcurlyeq\undefined + \usepackage{amssymb} % \succcurlyeq, \preccurlyeq +\fi \input{mjo-common} @@ -24,10 +29,10 @@ \newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} } % The PSD cone in a space of symmetric matrices. -\newcommand*{\Snplus}[1][n]{ \mathcal{S}^{{#1}}_{+} } +\newcommand*{\Snplus}[1][n]{ \Sn[#1]_{+} } % The PSD cone in a space of Hermitian matrices. -\newcommand*{\Hnplus}[1][n]{ \mathcal{H}^{{#1}}_{+} } +\newcommand*{\Hnplus}[1][n]{ \Hn[#1]_{+} } % @@ -62,24 +67,11 @@ % The Lyapunov rank of the given cone. \newcommand*{\lyapunovrank}[1]{ \beta\of{ {#1} } } -% % Cone inequality operators. -% - -% Standard cone inequalities. -\newcommand*{\gek}{\succcurlyeq} -\newcommand*{\gtk}{\succ} -\newcommand*{\lek}{\preccurlyeq} -\newcommand*{\ltk}{\prec} - +\newcommand*{\gecone}{\succcurlyeq} +\newcommand*{\gtcone}{\succ} +\newcommand*{\lecone}{\preccurlyeq} +\newcommand*{\ltcone}{\prec} -% Starred versions of the cone inequality operators. -\newcommand*{\ineqkstar}[1]{ \mathrel{ \overset{ _{\ast} }{ #1 } } } -\newcommand*{\gekstar}{ \ineqkstar{\gek} } -\newcommand*{\gtkstar}{ \ineqkstar{\gtk} } -\newcommand*{\lekstar}{ \ineqkstar{\lek} } -\newcommand*{\ltkstar}{ \ineqkstar{\ltk} } -% And negated versions of some of those... -\newcommand*{\ngeqkstar}{ \ineqkstar{\nsucceq} } -\newcommand*{\ngtrkstar}{ \ineqkstar{\nsucc} } +\fi