X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-cone.tex;h=78e87415f587dddb5832215cf91aad5079d04fd3;hp=dad432e76b46025182de3c9f808103f54ada6d29;hb=HEAD;hpb=21149d05f0bf33baecfe002704f8dd3d939951e7 diff --git a/mjo-cone.tex b/mjo-cone.tex index dad432e..00a1309 100644 --- a/mjo-cone.tex +++ b/mjo-cone.tex @@ -4,10 +4,16 @@ % 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 -\input{mjo-common} +\ifx\succcurlyeq\undefined + \usepackage{amssymb} % \succcurlyeq, \preccurlyeq +\fi + +\input{mjo-common} % for \of, \Rn, etc. +\input{mjo-linear_algebra} % \Sn and \Hn % The dual of a subset of an inner-product space; always a closed % convex cone. @@ -17,8 +23,10 @@ % Common cones. % -% The nonnegative orthant in the given number of dimensions. +% The nonnegative and strictly positive orthants in the given number +% of dimensions. \newcommand*{\Rnplus}[1][n]{ \Rn[#1]_{+} } +\newcommand*{\Rnplusplus}[1][n]{ \Rn[#1]_{++} } % The Lorentz ``ice-cream'' cone in the given number of dimensions. \newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} } @@ -67,3 +75,6 @@ \newcommand*{\gtcone}{\succ} \newcommand*{\lecone}{\preccurlyeq} \newcommand*{\ltcone}{\prec} + + +\fi