% 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}}