% macros for latex2e, to be used, e.g., with % \documentclass[a4paper,12pt]{article} % \input intmacros.sty \usepackage{amsfonts} \newcommand{\ivl}[1]{\protect{\makebox{\boldmath $#1$}}} \hyphenation{in-ter-vals} \hyphenation{com-po-nent} \hyphenation{sys-tems} \hyphenation{pol-y-no-mi-als} \hyphenation{pol-y-no-mi-al} \hyphenation{pre-con-di-tion-er} % mathematical functions \def\fct#1{{\mathop{\rm #1}}} % general macro for functions font \def\abs{\fct{abs}} % absolute value function \def\sign{\fct{sign}} % sign function \def\re{\fct{Re\,}} % real part; \Re gives old-fashioned Re \def\im{\fct{Im\,}} % imag. part; \Im gives old-fashioned Im \def\argmax{\mathop{\rm argmax}}% argmax; indices appear below word \def\argmin{\mathop{\rm argmin}}% argmin; indices appear below word % interval functions \def\cch{\fct{cch}\,} % closed convex hull \def\ch{\fct{ch}\,} % convex hull \def\cond{\fct{cond\,}} % condition number \def\dev{\fct{dev\,}} % deviation \def\diag{\fct{diag}} % diagonal vector \def\Diag{\fct{Diag}\,} % diagonal matrix \def\dim{\fct{dim\,}} % dimension of a vector \def\dist{\fct{dist}} % distance \def\Dist{\fct{Dist}} % hyper-distance \def\fl{\fct{fl}} % floating point evaluation \def\flint{\fct{flint}} % outward interval evaluation %RBK 2005/08/13 -- \iint defined in AmSTeX \def\iint{{\fct{int\,}}} %interior; \int is already integral \def\imid{\fct{mid\,}} % midpoint; \mid is already set-| \def\rad{\fct{rad\,}} % radius \def\range{\fct{range}} % range \def\set{\fct{set}} % set (Minkowski) evaluation \def\ivert{\fct{vert\,}} % vertex set; \vert is vertical line \def\wid{\fct{width\,}} % width \def\ol{\overline} % overline (upper bound) \def\ul{\underline} % underline (lower bound) \def\inadd{\oplus} % inner addition \def\insub{\ominus} % inner subtraction \def\<{\langle} % left mignitude \def\>{\rangle} % right mignitude \def\ihull{\raise2.25pt\hbox{\framebox[3pt]{\phantom{\tiny|}}}\,} % interval hull \def\rounddown{{\tt rounddown}} \def\roundup{{\tt roundup}} \def\eps{\varepsilon} \def\phi{\varphi} % open faced letters for special sets \def\Az{\mathbb{A}} \def\Bz{\mathbb{B}} \def\Cz{\mathbb{C}} \def\Dz{\mathbb{D}} \def\Ez{\mathbb{E}} \def\Fz{\mathbb{F}} \def\Gz{\mathbb{G}} \def\Hz{\mathbb{H}} \def\Iz{\mathbb{I}} \def\Jz{\mathbb{J}} \def\Kz{\mathbb{K}} \def\Lz{\mathbb{L}} \def\Mz{\mathbb{M}} \def\Nz{\mathbb{N}} \def\Oz{\mathbb{O}} \def\Pz{\mathbb{P}} \def\Qz{\mathbb{Q}} \def\Rz{\mathbb{R}} \def\Sz{\mathbb{S}} \def\Tz{\mathbb{T}} \def\Uz{\mathbb{U}} \def\Vz{\mathbb{V}} \def\Wz{\mathbb{W}} \def\Xz{\mathbb{X}} \def\Yz{\mathbb{Y}} \def\Zz{\mathbb{Z}} \def\Czr{\Cz_{\mbox{\rm \scriptsize rect}}} % set of complex rectangles \def\Czd{\Cz_{\mbox{\rm \scriptsize disc}}} % set of complex discs % boldface letters for intervals % RBK 2005/08/13 -- modified in an attempt to have subscript sizes % RBK 2005/08/13 -- handled appropriately. %\def\bfm#1{\protect{\makebox{\boldmath $#1$}}} \def\bfm#1{\protect{\textrm{\boldmath $#1$}}} \def\a {\bfm{a}} \def\b {\bfm{b}} \def\cc {\bfm{c}} \def\dd {\bfm{d}} \def\e {\bfm{e}} \def\f {\bfm{f}} \def\g {\bfm{g}} \def\h {\bfm{h}} \def\ii {\bfm{i}} % \i is already 'i without dot' \def\j {\bfm{j}} \def\k {\bfm{k}} \def\l {\bfm{l}} \def\m {\bfm{m}} \def\n {\bfm{n}} \def\o {\bfm{o}} \def\p {\bfm{p}} \def\q {\bfm{q}} \def\rr {\bfm{r}} \def\s {\bfm{s}} \def\t {\bfm{t}} \def\uu {\bfm{u}} \def\vv {\bfm{v}} % \v is already 'check' \def\w {\bfm{w}} \def\x {\bfm{x}} \def\y {\bfm{y}} \def\z {\bfm{z}} \def\A {\bfm{A}} \def\B {\bfm{B}} \def\C {\bfm{C}} \def\DD{\bfm{D}} % \D is already \displaystyle \def\E {\bfm{E}} \def\F {\bfm{F}} \def\G {\bfm{G}} \def\H {\bfm{H}} \def\I {\bfm{I}} \def\J {\bfm{J}} \def\K {\bfm{K}} \def\L {\bfm{L}} \def\M {\bfm{M}} \def\N {\bfm{N}} \def\O {\bfm{O}} \def\P {\bfm{P}} \def\Q {\bfm{Q}} \def\R {\bfm{R}} \def\SSS {\bfm{S}} % \S already "section" \def\T {\bfm{T}} \def\U {\bfm{U}} \def\V {\bfm{V}} \def\W {\bfm{W}} \def\X {\bfm{X}} \def\Y {\bfm{Y}} \def\Z {\bfm{Z}}