%  File: ivl_ess.sty
%
%  Essential definitions for standardizing interval notation.
%  RBK, September 3, 1997.
%

% Commands for intervals, interval vectors, functions and ranges:

\newcommand{\ivl}[1]{\protect{\makebox{\boldmath $#1$}}}
\newcommand{\Inf}[1]{{\underline{#1}}}
\newcommand{\Sup}[1]{{\overline{#1}}}
\newcommand{\midpoint}[1]{\text{\rm m}{\left({#1}\right)}}
\newcommand{\width}[1]{{\text{\rm w}{\left(#1\right)}}}

\newcommand{\pnt}[1]{{\check #1}}
\newcommand{\sol}[1]{{{#1}^{*}}}
\newcommand{\mig}[1]{{\makebox{\large$<$} #1 \makebox{\large$>$}}}

\newcommand{\signum}[1]{{\rm sgn}(#1)}

\newcommand{\slope}{{{\bf S}^\sharp}}
\newcommand{\slopebound}{{\bf S}}
\newcommand{\grad}{{\nabla\phi}}
\newcommand{\gradient}[1]{\nabla {#1}}

\newcommand{\ihull}{{\raise2.25pt\hbox{\framebox[3pt]{\phantom{\tiny|}}}}}

\newcommand{\isin}{\makebox{\bf sin}}
\newcommand{\icos}{\makebox{\bf cos}}

%  Sets of numbers:

% Comment out the following if AMS fonts can be used
%\newcommand{\mathbb}{\bit}

\newcommand{\R}[1]{{\mathbb R}^{#1}}
\newcommand{\C}[1]{{\mathbb C}^{#1}}
\newcommand{\Co}{{\mathbb C}}
\newcommand{\Ro}{{\mathbb R}}
\newcommand{\IR}[1]{{\mathbb{I}\mathbb{R}}^{#1}}
\newcommand{\IRo}{{\mathbb{I}\mathbb{R}}}
\newcommand{\IC}[1]{{\mathbb{I}\mathbb{C}}^{#1}}
\newcommand{\ICo}{{\mathbb{I}\mathbb{C}}}


%  Miscellaneous --

\newcommand {\interior}[1]{{\makebox{{\rm int}}(#1)}}
\newcommand {\bdy}[1]{\makebox{$\ivl\partial$}#1}
\newcommand {\union}{\text{\Large$\cup$}}

\newcommand{\bigoh}[1]{{\cal O}\left({#1}\right)}

\newcommand{\ftn}{\protect{Fortran~90}}


\hyphenation{in-ter-val}
\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}
\hyphenation{Lem-ma}


\newcommand{\cancelminus}{\ominus}
\newcommand{\cancelplus}{\oplus}
\newcommand{\canceldivide}{\oslash}
\newcommand{\cancelop}{\hskip2pt\bigcirc\hskip-10.pt\text{\scriptsize{\mit op}}\hskip3pt}
\newcommand{\canceltimes}{\otimes}
\newcommand{\domain}{{\bf D}}