\ProvidesPackage{sng_style}

% Other packages
\usepackage{amssymb,amsmath,amsfonts,amsthm,bm,enumerate}

% Environment definitions
\newtheoremstyle{tnamed}
	{\topsep}
	{\topsep}
	{}
	{}
	{\bfseries}
	{.}
	{ }
	{\thmname{#1}\thmnumber{ #2}\thmnote{ (#3)}}

\newtheoremstyle{notenamed*}
	{\topsep}
	{\topsep}
	{\slshape}
	{}
	{\bfseries}
	{:}
	{ }
	{\thmnote{#3}}

\theoremstyle{notenamed*}
\newtheorem{note*}{Note}

\theoremstyle{tnamed}
\newtheorem{tnamed}[subsection]{Theorem}
\newtheorem{cnamed}[subsection]{Corollary}

\theoremstyle{definition}
\newtheorem{definition}[subsection]{Definition}
\newtheorem{example}[subsection]{Example}
\newtheorem{corollary}[subsection]{Corollary}
\newtheorem{lemma}[subsection]{Lemma}
\newtheorem{proposition}[subsection]{Proposition}
\newtheorem{exercise}[subsection]{Exercise}

\newcommand{\notebox}[2]{%
\begin{center}
   \fbox{
      \centering
      \parbox{#1}{%
         #2
      }%
   }%
\end{center}
}

\newcommand{\units}[1]{\mathrm{#1}}

% Sets
\newcommand{\N}{\mathbb{N}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}

% Shortcuts
\newcommand{\od}[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}}
\newcommand{\odn}[3]{\frac{\mathrm{d}^{#1} #2}{\mathrm{d} #3^{#1}}}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdn}[3]{\frac{\partial^{#1} #2}{\partial #3^{#1}}}
\newcommand{\then}{\Longrightarrow \quad}
\newcommand{\Then}{\quad \Longrightarrow \quad}
\newcommand{\D}{\,\mathrm{d}}
\newcommand{\ve}{\bm}
\newcommand{\del}{\partial}
\newcommand{\grad}{\nabla}
\renewcommand{\div}{\nabla \cdot}
\newcommand{\curl}{\nabla \times}
\newcommand{\cross}{\times}

% Operators
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\J}{J}
\DeclareMathOperator{\Y}{Y}
\DeclareMathOperator{\Ai}{Ai}
\DeclareMathOperator{\Bi}{Bi}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\e}{e}

% Hat lower case letters
\newcommand{\hta}{\hat{a}}
\newcommand{\htb}{\hat{b}}
\newcommand{\htc}{\hat{c}}
\newcommand{\htd}{\hat{d}}
\newcommand{\hte}{\hat{e}}
\newcommand{\htf}{\hat{f}}
\newcommand{\htg}{\hat{g}}
\newcommand{\hth}{\hat{h}}
\newcommand{\hti}{\hat{\imath}}
\newcommand{\htj}{\hat{\jmath}}
\newcommand{\htk}{\hat{k}}
\newcommand{\htl}{\hat{l}}
\newcommand{\htm}{\hat{m}}
\newcommand{\htn}{\hat{n}}
\newcommand{\hto}{\hat{o}}
\newcommand{\htp}{\hat{p}}
\newcommand{\htq}{\hat{q}}
\newcommand{\htr}{\hat{r}}
\newcommand{\hts}{\hat{s}}
\newcommand{\htt}{\hat{t}}
\newcommand{\htu}{\hat{u}}
\newcommand{\htv}{\hat{v}}
\newcommand{\htw}{\hat{w}}
\newcommand{\htx}{\hat{x}}
\newcommand{\hty}{\hat{y}}
\newcommand{\htz}{\hat{z}}

% Hat upper case letters
\newcommand{\htA}{\hat{A}}
\newcommand{\htB}{\hat{B}}
\newcommand{\htC}{\hat{C}}
\newcommand{\htD}{\hat{D}}
\newcommand{\htE}{\hat{E}}
\newcommand{\htF}{\hat{F}}
\newcommand{\htG}{\hat{G}}
\newcommand{\htH}{\hat{H}}
\newcommand{\htI}{\hat{I}}
\newcommand{\htJ}{\hat{J}}
\newcommand{\htK}{\hat{K}}
\newcommand{\htL}{\hat{L}}
\newcommand{\htM}{\hat{M}}
\newcommand{\htN}{\hat{N}}
\newcommand{\htO}{\hat{O}}
\newcommand{\htP}{\hat{P}}
\newcommand{\htQ}{\hat{Q}}
\newcommand{\htR}{\hat{R}}
\newcommand{\htS}{\hat{S}}
\newcommand{\htT}{\hat{T}}
\newcommand{\htU}{\hat{U}}
\newcommand{\htV}{\hat{V}}
\newcommand{\htW}{\hat{W}}
\newcommand{\htX}{\hat{X}}
\newcommand{\htY}{\hat{Y}}
\newcommand{\htZ}{\hat{Z}}

% Hat lower case Greek letters
\newcommand{\htalpha}{\hat{\alpha}}
\newcommand{\htbeta}{\hat{\beta}}
\newcommand{\htgamma}{\hat{\gamma}}
\newcommand{\htdelta}{\hat{\delta}}
\newcommand{\htepsilon}{\hat{\epsilon}}
\newcommand{\htzeta}{\hat{\zeta}}
\newcommand{\hteta}{\hat{\eta}}
\newcommand{\httheta}{\hat{\theta}}
\newcommand{\htiota}{\hat{\iota}}
\newcommand{\htkappa}{\hat{\kappa}}
\newcommand{\htlambda}{\hat{\lambda}}
\newcommand{\htmu}{\hat{\mu}}
\newcommand{\htnu}{\hat{\nu}}
\newcommand{\htxi}{\hat{\xi}}
\newcommand{\htpi}{\hat{\pi}}
\newcommand{\htrho}{\hat{\rho}}
\newcommand{\htsigma}{\hat{\sigma}}
\newcommand{\httau}{\hat{\htau}}
\newcommand{\htupsilon}{\hat{\upsilon}}
\newcommand{\htphi}{\hat{\phi}}
\newcommand{\htchi}{\hat{\chi}}
\newcommand{\htpsi}{\hat{\psi}}
\newcommand{\htvarphi}{\hat{\varphi}}
\newcommand{\htomega}{\hat{\omega}}

% Hat upper case Greek letters
\newcommand{\htGamma}{\hat{\Gamma}}
\newcommand{\htDelta}{\hat{\Delta}}
\newcommand{\htTheta}{\hat{\Theta}}
\newcommand{\htLambda}{\hat{\Lambda}}
\newcommand{\htXi}{\hat{\Xi}}
\newcommand{\htPi}{\hat{\Pi}}
\newcommand{\htSigma}{\hat{\Sigma}}
\newcommand{\htPhi}{\hat{\phi}}
\newcommand{\htPsi}{\hat{\Psi}}
\newcommand{\htOmega}{\hat{\Omega}}

% Tilde lower case letters
\newcommand{\ta}{\tilde{a}}
\newcommand{\tb}{\tilde{b}}
\newcommand{\tc}{\tilde{c}}
\newcommand{\td}{\tilde{d}}
\newcommand{\te}{\tilde{e}}
\newcommand{\tf}{\tilde{f}}
\newcommand{\tg}{\tilde{g}}
\newcommand{\tlh}{\tilde{h}}
\newcommand{\ti}{\tilde{\imath}}
\newcommand{\tj}{\tilde{\jmath}}
\newcommand{\tk}{\tilde{k}}
\newcommand{\tl}{\tilde{l}}
\newcommand{\tm}{\tilde{m}}
\newcommand{\tn}{\tilde{n}}
\newcommand{\tlo}{\tilde{o}}
\newcommand{\tp}{\tilde{p}}
\newcommand{\tq}{\tilde{q}}
\newcommand{\tr}{\tilde{r}}
\newcommand{\ts}{\tilde{s}}
\newcommand{\tlt}{\tilde{t}}
\newcommand{\tu}{\tilde{u}}
\newcommand{\tv}{\tilde{v}}
\newcommand{\tw}{\tilde{w}}
\newcommand{\tx}{\tilde{x}}
\newcommand{\ty}{\tilde{y}}
\newcommand{\tz}{\tilde{z}}

% Tilde upper case letters
\newcommand{\tA}{\tilde{A}}
\newcommand{\tB}{\tilde{B}}
\newcommand{\tC}{\tilde{C}}
\newcommand{\tD}{\tilde{D}}
\newcommand{\tE}{\tilde{E}}
\newcommand{\tF}{\tilde{F}}
\newcommand{\tG}{\tilde{G}}
\newcommand{\tH}{\tilde{H}}
\newcommand{\tI}{\tilde{I}}
\newcommand{\tJ}{\tilde{J}}
\newcommand{\tK}{\tilde{K}}
\newcommand{\tL}{\tilde{L}}
\newcommand{\tM}{\tilde{M}}
\newcommand{\tN}{\tilde{N}}
\newcommand{\tO}{\tilde{O}}
\newcommand{\tP}{\tilde{P}}
\newcommand{\tQ}{\tilde{Q}}
\newcommand{\tR}{\tilde{R}}
\newcommand{\tS}{\tilde{S}}
\newcommand{\tT}{\tilde{T}}
\newcommand{\tU}{\tilde{U}}
\newcommand{\tV}{\tilde{V}}
\newcommand{\tW}{\tilde{W}}
\newcommand{\tX}{\tilde{X}}
\newcommand{\tY}{\tilde{Y}}
\newcommand{\tZ}{\tilde{Z}}

% Tilde lower case Greek letters
\newcommand{\talpha}{\tilde{\alpha}}
\newcommand{\tbeta}{\tilde{\beta}}
\newcommand{\tgamma}{\tilde{\gamma}}
\newcommand{\tdelta}{\tilde{\delta}}
\newcommand{\tepsilon}{\tilde{\epsilon}}
\newcommand{\tzeta}{\tilde{\zeta}}
\newcommand{\teta}{\tilde{\eta}}
\newcommand{\ttheta}{\tilde{\theta}}
\newcommand{\tiota}{\tilde{\iota}}
\newcommand{\tkappa}{\tilde{\kappa}}
\newcommand{\tlambda}{\tilde{\lambda}}
\newcommand{\tmu}{\tilde{\mu}}
\newcommand{\tnu}{\tilde{\nu}}
\newcommand{\txi}{\tilde{\xi}}
\newcommand{\tpi}{\tilde{\pi}}
\newcommand{\trho}{\tilde{\rho}}
\newcommand{\tsigma}{\tilde{\sigma}}
\newcommand{\ttau}{\tilde{\tau}}
\newcommand{\tupsilon}{\tilde{\upsilon}}
\newcommand{\tphi}{\tilde{\phi}}
\newcommand{\tchi}{\tilde{\chi}}
\newcommand{\tpsi}{\tilde{\psi}}
\newcommand{\tvarphi}{\tilde{\varphi}}
\newcommand{\tomega}{\tilde{\omega}}

% Tilde upper case Greek letters
\newcommand{\tGamma}{\tilde{\Gamma}}
\newcommand{\tDelta}{\tilde{\Delta}}
\newcommand{\tTheta}{\tilde{\Theta}}
\newcommand{\tLambda}{\tilde{\Lambda}}
\newcommand{\tXi}{\tilde{\Xi}}
\newcommand{\tPi}{\tilde{\Pi}}
\newcommand{\tSigma}{\tilde{\Sigma}}
\newcommand{\tPhi}{\tilde{\phi}}
\newcommand{\tPsi}{\tilde{\Psi}}
\newcommand{\tOmega}{\tilde{\Omega}}

% Bar lower case letters
\newcommand{\bra}{\bar{a}}
\newcommand{\brb}{\bar{b}}
\newcommand{\brc}{\bar{c}}
\newcommand{\brd}{\bar{d}}
\newcommand{\bre}{\bar{e}}
\newcommand{\brf}{\bar{f}}
\newcommand{\brg}{\bar{g}}
\newcommand{\brh}{\bar{h}}
\newcommand{\bri}{\bar{\imath}}
\newcommand{\brj}{\bar{\jmath}}
\newcommand{\brk}{\bar{k}}
\newcommand{\brl}{\bar{l}}
\newcommand{\brm}{\bar{m}}
\newcommand{\brn}{\bar{n}}
\newcommand{\bro}{\bar{o}}
\newcommand{\brp}{\bar{p}}
\newcommand{\brq}{\bar{q}}
\newcommand{\brr}{\bar{r}}
\newcommand{\brs}{\bar{s}}
\newcommand{\brt}{\bar{t}}
\newcommand{\bru}{\bar{u}}
\newcommand{\brv}{\bar{v}}
\newcommand{\brw}{\bar{w}}
\newcommand{\brx}{\bar{x}}
\newcommand{\bry}{\bar{y}}
\newcommand{\brz}{\bar{z}}

% Bar upper case letters
\newcommand{\brA}{\bar{A}}
\newcommand{\brB}{\bar{B}}
\newcommand{\brC}{\bar{C}}
\newcommand{\brD}{\bar{D}}
\newcommand{\brE}{\bar{E}}
\newcommand{\brF}{\bar{F}}
\newcommand{\brG}{\bar{G}}
\newcommand{\brH}{\bar{H}}
\newcommand{\brI}{\bar{I}}
\newcommand{\brJ}{\bar{J}}
\newcommand{\brK}{\bar{K}}
\newcommand{\brL}{\bar{L}}
\newcommand{\brM}{\bar{M}}
\newcommand{\brN}{\bar{N}}
\newcommand{\brO}{\bar{O}}
\newcommand{\brP}{\bar{P}}
\newcommand{\brQ}{\bar{Q}}
\newcommand{\brR}{\bar{R}}
\newcommand{\brS}{\bar{S}}
\newcommand{\brT}{\bar{T}}
\newcommand{\brU}{\bar{U}}
\newcommand{\brV}{\bar{V}}
\newcommand{\brW}{\bar{W}}
\newcommand{\brX}{\bar{X}}
\newcommand{\brY}{\bar{Y}}
\newcommand{\brZ}{\bar{Z}}

% Bar lower case Greek letters
\newcommand{\bralpha}{\bar{\alpha}}
\newcommand{\brbeta}{\bar{\beta}}
\newcommand{\brgamma}{\bar{\gamma}}
\newcommand{\brdelta}{\bar{\delta}}
\newcommand{\brepsilon}{\bar{\epsilon}}
\newcommand{\brzeta}{\bar{\zeta}}
\newcommand{\breta}{\bar{\eta}}
\newcommand{\brtheta}{\bar{\brheta}}
\newcommand{\briota}{\bar{\iota}}
\newcommand{\brkappa}{\bar{\kappa}}
\newcommand{\brlambda}{\bar{\lambda}}
\newcommand{\brmu}{\bar{\mu}}
\newcommand{\brnu}{\bar{\nu}}
\newcommand{\brxi}{\bar{\xi}}
\newcommand{\brpi}{\bar{\pi}}
\newcommand{\brrho}{\bar{\rho}}
\newcommand{\brsigma}{\bar{\sigma}}
\newcommand{\brtau}{\bar{\brau}}
\newcommand{\brupsilon}{\bar{\upsilon}}
\newcommand{\brphi}{\bar{\phi}}
\newcommand{\brchi}{\bar{\chi}}
\newcommand{\brpsi}{\bar{\psi}}
\newcommand{\brvarphi}{\bar{\varphi}}
\newcommand{\bromega}{\bar{\omega}}

% Bar upper case Greek letters
\newcommand{\brGamma}{\bar{\Gamma}}
\newcommand{\brDelta}{\bar{\Delta}}
\newcommand{\brTheta}{\bar{\Theta}}
\newcommand{\brLambda}{\bar{\Lambda}}
\newcommand{\brXi}{\bar{\Xi}}
\newcommand{\brPi}{\bar{\Pi}}
\newcommand{\brSigma}{\bar{\Sigma}}
\newcommand{\brPhi}{\bar{\Phi}}
\newcommand{\brPsi}{\bar{\Psi}}
\newcommand{\brOmega}{\bar{\Omega}}