\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{sciencestuff}[2020/04/08 Science related stuff]

\RequirePackage{amsmath} %--------------------- math mode
\RequirePackage{amssymb} %--------------------- math symbols
\RequirePackage{amsfonts} %-------------------- math fonts
\RequirePackage{bm} %-------------------------- boldsymbols
\RequirePackage{mathtools} %------------------- mathematical tools
\RequirePackage{mathrsfs} %-------------------- better cal
\RequirePackage{slashed} %--------------------- slashed characters
\RequirePackage{tensor} %---------------------- write tensors
\RequirePackage{listings} %-------------------- code sections
\RequirePackage[amsmath,
                hyperref,
                framed]{ntheorem} %------------ improved theorem envoronment
\RequirePackage{dsfont} %---------------------- improved math set symbols
\RequirePackage{upgreek} %--------------------- better Greek alphabet
\RequirePackage{physics} %--------------------- full physics-related commands
\RequirePackage[binary-units=true]{siunitx} %-- SI units formatting
\RequirePackage{graphicx} %-------------------- images and figures
\RequirePackage{ifthen} %---------------------- conditionals
\RequirePackage[sort&compress,
                english]{cleveref} %----------- nicer citations and references
\RequirePackage[compat=1.1.0]{tikz-feynman} %-- Feynman diagrams

\ProcessOptions\relax

%---- prepare packages
\tikzfeynmanset{/tikzfeynman/warn luatex=false}

\lstset{%
    language=Python,
    tabsize=4,
    morecomment=[l]{\#},
    basicstyle=\ttfamily\small,
    showstringspaces=false,
    captionpos=b,
    breaklines=true
}
\lstset{escapeinside={(*@}{@*)}}
\lstdefinestyle{boxed}{frame=single, numbers=left}

%---- numbering (number equations, figures and tables within section)

\numberwithin{equation}{section}
\numberwithin{figure}{section}
\numberwithin{table}{section}

%---- abbreviations

\providecommand{\sm}{\textsc{sm}\xspace}
\providecommand{\eom}{\textsc{e.o.m.}\xspace}
\providecommand{\cft}{\textsc{cft}\xspace}
\providecommand{\qft}{\textsc{qft}\xspace}
\providecommand{\qed}{\textsc{qed}\xspace}
\providecommand{\qcd}{\textsc{qcd}\xspace}
\providecommand{\ope}{\textsc{o.p.e.}\xspace}
\providecommand{\ode}{\textsc{o.d.e.}\xspace}
\providecommand{\dof}{\textsc{d.o.f.}\xspace}
\providecommand{\cicy}{\textsc{CICY}\xspace}
\providecommand{\cy}{\textsc{CY}\xspace}
\providecommand{\lhs}{\textsc{lhs}\xspace}
\providecommand{\rhs}{\textsc{rhs}\xspace}
\providecommand{\mse}{\textsc{mse}\xspace}
\providecommand{\mae}{\textsc{mae}\xspace}
\providecommand{\ann}{\textsc{ann}\xspace}
\providecommand{\nn}{\textsc{nn}\xspace}
\providecommand{\cnn}{\textsc{cnn}\xspace}
\providecommand{\ap}{\ensuremath{\alpha'}\xspace}
\providecommand{\sgn}{\ensuremath{\mathrm{sign}}}

%---- remap greek letters

\renewcommand{\alpha}{\ensuremath{\upalpha}\xspace}
\renewcommand{\beta}{\ensuremath{\upbeta}\xspace}
\renewcommand{\gamma}{\ensuremath{\upgamma}\xspace}
\renewcommand{\delta}{\ensuremath{\updelta}\xspace}
\renewcommand{\epsilon}{\ensuremath{\upepsilon}\xspace}
\renewcommand{\zeta}{\ensuremath{\upzeta}\xspace}
\renewcommand{\eta}{\ensuremath{\upeta}\xspace}
\renewcommand{\theta}{\ensuremath{\uptheta}\xspace}
\renewcommand{\iota}{\ensuremath{\upiota}\xspace}
\renewcommand{\kappa}{\ensuremath{\upkappa}\xspace}
\renewcommand{\lambda}{\ensuremath{\uplambda}\xspace}
\renewcommand{\mu}{\ensuremath{\upmu}\xspace}
\renewcommand{\nu}{\ensuremath{\upnu}\xspace}
\renewcommand{\xi}{\ensuremath{\upxi}\xspace}
\renewcommand{\pi}{\ensuremath{\uppi}\xspace}
\renewcommand{\rho}{\ensuremath{\uprho}\xspace}
\renewcommand{\sigma}{\ensuremath{\upsigma}\xspace}
\renewcommand{\tau}{\ensuremath{\uptau}\xspace}
\renewcommand{\upsilon}{\ensuremath{\upupsilon}\xspace}
\renewcommand{\phi}{\ensuremath{\upphi}\xspace}
\renewcommand{\chi}{\ensuremath{\upchi}\xspace}
\renewcommand{\psi}{\ensuremath{\uppsi}\xspace}
\renewcommand{\omega}{\ensuremath{\upomega}\xspace}
\renewcommand{\varepsilon}{\ensuremath{\upvarepsilon}\xspace}
\renewcommand{\vartheta}{\ensuremath{\upvartheta}\xspace}
\renewcommand{\varpi}{\ensuremath{\upvarpi}\xspace}
\renewcommand{\varphi}{\ensuremath{\upvarphi}\xspace}
\renewcommand{\varsigma}{\ensuremath{\upvarsigma}\xspace}
\renewcommand{\Gamma}{\ensuremath{\Upgamma}\xspace}
\renewcommand{\Delta}{\ensuremath{\Updelta}\xspace}
\renewcommand{\Theta}{\ensuremath{\Uptheta}\xspace}
\renewcommand{\Lambda}{\ensuremath{\Uplambda}\xspace}
\renewcommand{\Xi}{\ensuremath{\Upxi}\xspace}
\renewcommand{\Pi}{\ensuremath{\Uppi}\xspace}
\renewcommand{\Sigma}{\ensuremath{\Upsigma}\xspace}
\renewcommand{\Upsilon}{\ensuremath{\Upupsilon}\xspace}
\renewcommand{\Phi}{\ensuremath{\Upphi}\xspace}
\renewcommand{\Psi}{\ensuremath{\Uppsi}\xspace}
\renewcommand{\Omega}{\ensuremath{\Upomega}\xspace}

\providecommand{\dalpha}{\ensuremath{\dot{\upalpha}}\xspace}
\providecommand{\dbeta}{\ensuremath{\dot{\upbeta}}\xspace}
\providecommand{\dgamma}{\ensuremath{\dot{\upgamma}}\xspace}
\providecommand{\ddelta}{\ensuremath{\dot{\updelta}}\xspace}
\providecommand{\depsilon}{\ensuremath{\dot{\upepsilon}}\xspace}
\providecommand{\dzeta}{\ensuremath{\dot{\upzeta}}\xspace}
\providecommand{\deta}{\ensuremath{\dot{\upeta}}\xspace}
\providecommand{\dtheta}{\ensuremath{\dot{\uptheta}}\xspace}
\providecommand{\diota}{\ensuremath{\dot{\upiota}}\xspace}
\providecommand{\dkappa}{\ensuremath{\dot{\upkappa}}\xspace}
\providecommand{\dlambda}{\ensuremath{\dot{\uplambda}}\xspace}
\providecommand{\dmu}{\ensuremath{\dot{\upmu}}\xspace}
\providecommand{\dnu}{\ensuremath{\dot{\upnu}}\xspace}
\providecommand{\dxi}{\ensuremath{\dot{\upxi}}\xspace}
\providecommand{\dpi}{\ensuremath{\dot{\uppi}}\xspace}
\providecommand{\drho}{\ensuremath{\dot{\uprho}}\xspace}
\providecommand{\dsigma}{\ensuremath{\dot{\upsigma}}\xspace}
\providecommand{\dtau}{\ensuremath{\dot{\uptau}}\xspace}
\providecommand{\dupsilon}{\ensuremath{\dot{\upupsilon}}\xspace}
\providecommand{\dphi}{\ensuremath{\dot{\upphi}}\xspace}
\providecommand{\dchi}{\ensuremath{\dot{\upchi}}\xspace}
\providecommand{\dpsi}{\ensuremath{\dot{\uppsi}}\xspace}
\providecommand{\domega}{\ensuremath{\dot{\upomega}}\xspace}
\providecommand{\dvarepsilon}{\ensuremath{\dot{\upvarepsilon}}\xspace}
\providecommand{\dvartheta}{\ensuremath{\dot{\upvartheta}}\xspace}
\providecommand{\dvarpi}{\ensuremath{\dot{\upvarpi}}\xspace}
\providecommand{\dvarphi}{\ensuremath{\dot{\upvarphi}}\xspace}
\providecommand{\dvarsigma}{\ensuremath{\dot{\upvarsigma}}\xspace}
\providecommand{\dGamma}{\ensuremath{\dot{\Upgamma}}\xspace}
\providecommand{\dDelta}{\ensuremath{\dot{\Updelta}}\xspace}
\providecommand{\dTheta}{\ensuremath{\dot{\Uptheta}}\xspace}
\providecommand{\dLambda}{\ensuremath{\dot{\Uplambda}}\xspace}
\providecommand{\dXi}{\ensuremath{\dot{\Upxi}}\xspace}
\providecommand{\dPi}{\ensuremath{\dot{\Uppi}}\xspace}
\providecommand{\dSigma}{\ensuremath{\dot{\Upsigma}}\xspace}
\providecommand{\dUpsilon}{\ensuremath{\dot{\Upupsilon}}\xspace}
\providecommand{\dPhi}{\ensuremath{\dot{\Upphi}}\xspace}
\providecommand{\dPsi}{\ensuremath{\dot{\Uppsi}}\xspace}
\providecommand{\dOmega}{\ensuremath{\dot{\Upomega}}\xspace}

\providecommand{\balpha}{\ensuremath{\overline{\upalpha}}\xspace}
\providecommand{\bbeta}{\ensuremath{\overline{\upbeta}}\xspace}
\providecommand{\bgamma}{\ensuremath{\overline{\upgamma}}\xspace}
\providecommand{\bdelta}{\ensuremath{\overline{\updelta}}\xspace}
\providecommand{\bepsilon}{\ensuremath{\overline{\upepsilon}}\xspace}
\providecommand{\bzeta}{\ensuremath{\overline{\upzeta}}\xspace}
\providecommand{\beta}{\ensuremath{\overline{\upeta}}\xspace}
\providecommand{\btheta}{\ensuremath{\overline{\uptheta}}\xspace}
\providecommand{\biota}{\ensuremath{\overline{\upiota}}\xspace}
\providecommand{\bkappa}{\ensuremath{\overline{\upkappa}}\xspace}
\providecommand{\blambda}{\ensuremath{\overline{\uplambda}}\xspace}
\providecommand{\bmu}{\ensuremath{\overline{\upmu}}\xspace}
\providecommand{\bnu}{\ensuremath{\overline{\upnu}}\xspace}
\providecommand{\bxi}{\ensuremath{\overline{\upxi}}\xspace}
\providecommand{\bpi}{\ensuremath{\overline{\uppi}}\xspace}
\providecommand{\brho}{\ensuremath{\overline{\uprho}}\xspace}
\providecommand{\bsigma}{\ensuremath{\overline{\upsigma}}\xspace}
\providecommand{\btau}{\ensuremath{\overline{\uptau}}\xspace}
\providecommand{\bupsilon}{\ensuremath{\overline{\upupsilon}}\xspace}
\providecommand{\bphi}{\ensuremath{\overline{\upphi}}\xspace}
\providecommand{\bchi}{\ensuremath{\overline{\upchi}}\xspace}
\providecommand{\bpsi}{\ensuremath{\overline{\uppsi}}\xspace}
\providecommand{\bomega}{\ensuremath{\overline{\upomega}}\xspace}
\providecommand{\bvarepsilon}{\ensuremath{\overline{\upvarepsilon}}\xspace}
\providecommand{\bvartheta}{\ensuremath{\overline{\upvartheta}}\xspace}
\providecommand{\bvarpi}{\ensuremath{\overline{\upvarpi}}\xspace}
\providecommand{\bvarphi}{\ensuremath{\overline{\upvarphi}}\xspace}
\providecommand{\bvarsigma}{\ensuremath{\overline{\upvarsigma}}\xspace}
\providecommand{\bGamma}{\ensuremath{\overline{\Upgamma}}\xspace}
\providecommand{\bDelta}{\ensuremath{\overline{\Updelta}}\xspace}
\providecommand{\bTheta}{\ensuremath{\overline{\Uptheta}}\xspace}
\providecommand{\bLambda}{\ensuremath{\overline{\Uplambda}}\xspace}
\providecommand{\bXi}{\ensuremath{\overline{\Upxi}}\xspace}
\providecommand{\bPi}{\ensuremath{\overline{\Uppi}}\xspace}
\providecommand{\bSigma}{\ensuremath{\overline{\Upsigma}}\xspace}
\providecommand{\bUpsilon}{\ensuremath{\overline{\Upupsilon}}\xspace}
\providecommand{\bPhi}{\ensuremath{\overline{\Upphi}}\xspace}
\providecommand{\bPsi}{\ensuremath{\overline{\Uppsi}}\xspace}
\providecommand{\bOmega}{\ensuremath{\overline{\Upomega}}\xspace}

\providecommand{\talpha}{\ensuremath{\widetilde{\upalpha}}\xspace}
\providecommand{\tbeta}{\ensuremath{\widetilde{\upbeta}}\xspace}
\providecommand{\tgamma}{\ensuremath{\widetilde{\upgamma}}\xspace}
\providecommand{\tdelta}{\ensuremath{\widetilde{\updelta}}\xspace}
\providecommand{\tepsilon}{\ensuremath{\widetilde{\upepsilon}}\xspace}
\providecommand{\tzeta}{\ensuremath{\widetilde{\upzeta}}\xspace}
\providecommand{\teta}{\ensuremath{\widetilde{\upeta}}\xspace}
\providecommand{\ttheta}{\ensuremath{\widetilde{\uptheta}}\xspace}
\providecommand{\tiota}{\ensuremath{\widetilde{\upiota}}\xspace}
\providecommand{\tkappa}{\ensuremath{\widetilde{\upkappa}}\xspace}
\providecommand{\tlambda}{\ensuremath{\widetilde{\uplambda}}\xspace}
\providecommand{\tmu}{\ensuremath{\widetilde{\upmu}}\xspace}
\providecommand{\tnu}{\ensuremath{\widetilde{\upnu}}\xspace}
\providecommand{\txi}{\ensuremath{\widetilde{\upxi}}\xspace}
\providecommand{\tpi}{\ensuremath{\widetilde{\uppi}}\xspace}
\providecommand{\trho}{\ensuremath{\widetilde{\uprho}}\xspace}
\providecommand{\tsigma}{\ensuremath{\widetilde{\upsigma}}\xspace}
\providecommand{\ttau}{\ensuremath{\widetilde{\uptau}}\xspace}
\providecommand{\tupsilon}{\ensuremath{\widetilde{\upupsilon}}\xspace}
\providecommand{\tphi}{\ensuremath{\widetilde{\upphi}}\xspace}
\providecommand{\tchi}{\ensuremath{\widetilde{\upchi}}\xspace}
\providecommand{\tpsi}{\ensuremath{\widetilde{\uppsi}}\xspace}
\providecommand{\tomega}{\ensuremath{\widetilde{\upomega}}\xspace}
\providecommand{\tvarepsilon}{\ensuremath{\widetilde{\upvarepsilon}}\xspace}
\providecommand{\tvartheta}{\ensuremath{\widetilde{\upvartheta}}\xspace}
\providecommand{\tvarpi}{\ensuremath{\widetilde{\upvarpi}}\xspace}
\providecommand{\tvarphi}{\ensuremath{\widetilde{\upvarphi}}\xspace}
\providecommand{\tvarsigma}{\ensuremath{\widetilde{\upvarsigma}}\xspace}
\providecommand{\tGamma}{\ensuremath{\widetilde{\Upgamma}}\xspace}
\providecommand{\tDelta}{\ensuremath{\widetilde{\Updelta}}\xspace}
\providecommand{\tTheta}{\ensuremath{\widetilde{\Uptheta}}\xspace}
\providecommand{\tLambda}{\ensuremath{\widetilde{\Uplambda}}\xspace}
\providecommand{\tXi}{\ensuremath{\widetilde{\Upxi}}\xspace}
\providecommand{\tPi}{\ensuremath{\widetilde{\Uppi}}\xspace}
\providecommand{\tSigma}{\ensuremath{\widetilde{\Upsigma}}\xspace}
\providecommand{\tUpsilon}{\ensuremath{\widetilde{\Upupsilon}}\xspace}
\providecommand{\tPhi}{\ensuremath{\widetilde{\Upphi}}\xspace}
\providecommand{\tPsi}{\ensuremath{\widetilde{\Uppsi}}\xspace}
\providecommand{\tOmega}{\ensuremath{\widetilde{\Upomega}}\xspace}

\providecommand{\halpha}{\ensuremath{\widehat{\upalpha}}\xspace}
\providecommand{\hbeta}{\ensuremath{\widehat{\upbeta}}\xspace}
\providecommand{\hgamma}{\ensuremath{\widehat{\upgamma}}\xspace}
\providecommand{\hdelta}{\ensuremath{\widehat{\updelta}}\xspace}
\providecommand{\hepsilon}{\ensuremath{\widehat{\upepsilon}}\xspace}
\providecommand{\hzeta}{\ensuremath{\widehat{\upzeta}}\xspace}
\providecommand{\heta}{\ensuremath{\widehat{\upeta}}\xspace}
\providecommand{\htheta}{\ensuremath{\widehat{\uptheta}}\xspace}
\providecommand{\hiota}{\ensuremath{\widehat{\upiota}}\xspace}
\providecommand{\hkappa}{\ensuremath{\widehat{\upkappa}}\xspace}
\providecommand{\hlambda}{\ensuremath{\widehat{\uplambda}}\xspace}
\providecommand{\hmu}{\ensuremath{\widehat{\upmu}}\xspace}
\providecommand{\hnu}{\ensuremath{\widehat{\upnu}}\xspace}
\providecommand{\hxi}{\ensuremath{\widehat{\upxi}}\xspace}
\providecommand{\hpi}{\ensuremath{\widehat{\uppi}}\xspace}
\providecommand{\hrho}{\ensuremath{\widehat{\uprho}}\xspace}
\providecommand{\hsigma}{\ensuremath{\widehat{\upsigma}}\xspace}
\providecommand{\htau}{\ensuremath{\widehat{\uptau}}\xspace}
\providecommand{\hupsilon}{\ensuremath{\widehat{\upupsilon}}\xspace}
\providecommand{\hphi}{\ensuremath{\widehat{\upphi}}\xspace}
\providecommand{\hchi}{\ensuremath{\widehat{\upchi}}\xspace}
\providecommand{\hpsi}{\ensuremath{\widehat{\uppsi}}\xspace}
\providecommand{\homega}{\ensuremath{\widehat{\upomega}}\xspace}
\providecommand{\hvarepsilon}{\ensuremath{\widehat{\upvarepsilon}}\xspace}
\providecommand{\hvartheta}{\ensuremath{\widehat{\upvartheta}}\xspace}
\providecommand{\hvarpi}{\ensuremath{\widehat{\upvarpi}}\xspace}
\providecommand{\hvarphi}{\ensuremath{\widehat{\upvarphi}}\xspace}
\providecommand{\hvarsigma}{\ensuremath{\widehat{\upvarsigma}}\xspace}
\providecommand{\hGamma}{\ensuremath{\widehat{\Upgamma}}\xspace}
\providecommand{\hDelta}{\ensuremath{\widehat{\Updelta}}\xspace}
\providecommand{\hTheta}{\ensuremath{\widehat{\Uptheta}}\xspace}
\providecommand{\hLambda}{\ensuremath{\widehat{\Uplambda}}\xspace}
\providecommand{\hXi}{\ensuremath{\widehat{\Upxi}}\xspace}
\providecommand{\hPi}{\ensuremath{\widehat{\Uppi}}\xspace}
\providecommand{\hSigma}{\ensuremath{\widehat{\Upsigma}}\xspace}
\providecommand{\hUpsilon}{\ensuremath{\widehat{\Upupsilon}}\xspace}
\providecommand{\hPhi}{\ensuremath{\widehat{\Upphi}}\xspace}
\providecommand{\hPsi}{\ensuremath{\widehat{\Uppsi}}\xspace}
\providecommand{\hOmega}{\ensuremath{\widehat{\Upomega}}\xspace}

\providecommand{\ualpha}{\ensuremath{\underline{\upalpha}}\xspace}
\providecommand{\ubeta}{\ensuremath{\underline{\upbeta}}\xspace}
\providecommand{\ugamma}{\ensuremath{\underline{\upgamma}}\xspace}
\providecommand{\udelta}{\ensuremath{\underline{\updelta}}\xspace}
\providecommand{\uepsilon}{\ensuremath{\underline{\upepsilon}}\xspace}
\providecommand{\uzeta}{\ensuremath{\underline{\upzeta}}\xspace}
\providecommand{\ueta}{\ensuremath{\underline{\upeta}}\xspace}
\providecommand{\utheta}{\ensuremath{\underline{\uptheta}}\xspace}
\providecommand{\uiota}{\ensuremath{\underline{\upiota}}\xspace}
\providecommand{\ukappa}{\ensuremath{\underline{\upkappa}}\xspace}
\providecommand{\ulambda}{\ensuremath{\underline{\uplambda}}\xspace}
\providecommand{\umu}{\ensuremath{\underline{\upmu}}\xspace}
\providecommand{\unu}{\ensuremath{\underline{\upnu}}\xspace}
\providecommand{\uxi}{\ensuremath{\underline{\upxi}}\xspace}
\providecommand{\upi}{\ensuremath{\underline{\uppi}}\xspace}
\providecommand{\urho}{\ensuremath{\underline{\uprho}}\xspace}
\providecommand{\usigma}{\ensuremath{\underline{\upsigma}}\xspace}
\providecommand{\utau}{\ensuremath{\underline{\uptau}}\xspace}
\providecommand{\uupsilon}{\ensuremath{\underline{\upupsilon}}\xspace}
\providecommand{\uphi}{\ensuremath{\underline{\upphi}}\xspace}
\providecommand{\uchi}{\ensuremath{\underline{\upchi}}\xspace}
\providecommand{\upsi}{\ensuremath{\underline{\uppsi}}\xspace}
\providecommand{\uomega}{\ensuremath{\underline{\upomega}}\xspace}
\providecommand{\uvarepsilon}{\ensuremath{\underline{\upvarepsilon}}\xspace}
\providecommand{\uvartheta}{\ensuremath{\underline{\upvartheta}}\xspace}
\providecommand{\uvarpi}{\ensuremath{\underline{\upvarpi}}\xspace}
\providecommand{\uvarphi}{\ensuremath{\underline{\upvarphi}}\xspace}
\providecommand{\uvarsigma}{\ensuremath{\underline{\upvarsigma}}\xspace}
\providecommand{\uGamma}{\ensuremath{\underline{\Upgamma}}\xspace}
\providecommand{\uDelta}{\ensuremath{\underline{\Updelta}}\xspace}
\providecommand{\uTheta}{\ensuremath{\underline{\Uptheta}}\xspace}
\providecommand{\uLambda}{\ensuremath{\underline{\Uplambda}}\xspace}
\providecommand{\uXi}{\ensuremath{\underline{\Upxi}}\xspace}
\providecommand{\uPi}{\ensuremath{\underline{\Uppi}}\xspace}
\providecommand{\uSigma}{\ensuremath{\underline{\Upsigma}}\xspace}
\providecommand{\uUpsilon}{\ensuremath{\underline{\Upupsilon}}\xspace}
\providecommand{\uPhi}{\ensuremath{\underline{\Upphi}}\xspace}
\providecommand{\uPsi}{\ensuremath{\underline{\Uppsi}}\xspace}
\providecommand{\uOmega}{\ensuremath{\underline{\Upomega}}\xspace}

%---- numerical sets

\providecommand{\1}{\ensuremath{\mathds{1}}\xspace}
\providecommand{\N}{\ensuremath{\mathds{N}}\xspace}
\providecommand{\Q}{\ensuremath{\mathds{Q}}\xspace}
\providecommand{\R}{\ensuremath{\mathds{R}}\xspace}
\providecommand{\Z}{\ensuremath{\mathds{Z}}\xspace}
\providecommand{\C}{\ensuremath{\mathds{C}}\xspace}

%---- dot, bar, tilde, hat

\providecommand{\dota}{\ensuremath{\dot{a}}\xspace}
\providecommand{\dotb}{\ensuremath{\dot{b}}\xspace}
\providecommand{\dotc}{\ensuremath{\dot{c}}\xspace}
\providecommand{\dotd}{\ensuremath{\dot{d}}\xspace}
\providecommand{\dote}{\ensuremath{\dot{e}}\xspace}
\providecommand{\dotf}{\ensuremath{\dot{f}}\xspace}
\providecommand{\dotg}{\ensuremath{\dot{g}}\xspace}
\providecommand{\doth}{\ensuremath{\dot{h}}\xspace}
\providecommand{\doti}{\ensuremath{\dot{i}}\xspace}
\providecommand{\dotj}{\ensuremath{\dot{j}}\xspace}
\providecommand{\dotk}{\ensuremath{\dot{k}}\xspace}
\providecommand{\dotl}{\ensuremath{\dot{l}}\xspace}
\providecommand{\dotm}{\ensuremath{\dot{m}}\xspace}
\providecommand{\dotn}{\ensuremath{\dot{n}}\xspace}
\providecommand{\doto}{\ensuremath{\dot{o}}\xspace}
\providecommand{\dotp}{\ensuremath{\dot{p}}\xspace}
\providecommand{\dotq}{\ensuremath{\dot{q}}\xspace}
\providecommand{\dotr}{\ensuremath{\dot{r}}\xspace}
\providecommand{\dots}{\ensuremath{\dot{s}}\xspace}
\providecommand{\dott}{\ensuremath{\dot{t}}\xspace}
\providecommand{\dotu}{\ensuremath{\dot{u}}\xspace}
\providecommand{\dotv}{\ensuremath{\dot{v}}\xspace}
\providecommand{\dotw}{\ensuremath{\dot{w}}\xspace}
\providecommand{\dotx}{\ensuremath{\dot{x}}\xspace}
\providecommand{\doty}{\ensuremath{\dot{y}}\xspace}
\providecommand{\dotz}{\ensuremath{\dot{z}}\xspace}
\providecommand{\dotA}{\ensuremath{\dot{A}}\xspace}
\providecommand{\dotB}{\ensuremath{\dot{B}}\xspace}
\providecommand{\dotC}{\ensuremath{\dot{C}}\xspace}
\providecommand{\dotD}{\ensuremath{\dot{D}}\xspace}
\providecommand{\dotE}{\ensuremath{\dot{E}}\xspace}
\providecommand{\dotF}{\ensuremath{\dot{F}}\xspace}
\providecommand{\dotG}{\ensuremath{\dot{G}}\xspace}
\providecommand{\dotH}{\ensuremath{\dot{H}}\xspace}
\providecommand{\dotI}{\ensuremath{\dot{I}}\xspace}
\providecommand{\dotJ}{\ensuremath{\dot{J}}\xspace}
\providecommand{\dotK}{\ensuremath{\dot{K}}\xspace}
\providecommand{\dotL}{\ensuremath{\dot{L}}\xspace}
\providecommand{\dotM}{\ensuremath{\dot{M}}\xspace}
\providecommand{\dotN}{\ensuremath{\dot{N}}\xspace}
\providecommand{\dotO}{\ensuremath{\dot{O}}\xspace}
\providecommand{\dotP}{\ensuremath{\dot{P}}\xspace}
\providecommand{\dotQ}{\ensuremath{\dot{Q}}\xspace}
\providecommand{\dotR}{\ensuremath{\dot{R}}\xspace}
\providecommand{\dotS}{\ensuremath{\dot{S}}\xspace}
\providecommand{\dotT}{\ensuremath{\dot{T}}\xspace}
\providecommand{\dotU}{\ensuremath{\dot{U}}\xspace}
\providecommand{\dotV}{\ensuremath{\dot{V}}\xspace}
\providecommand{\dotW}{\ensuremath{\dot{W}}\xspace}
\providecommand{\dotX}{\ensuremath{\dot{X}}\xspace}
\providecommand{\dotY}{\ensuremath{\dot{Y}}\xspace}
\providecommand{\dotZ}{\ensuremath{\dot{Z}}\xspace}

\providecommand{\bara}{\ensuremath{\overline{a}}\xspace}
\providecommand{\barb}{\ensuremath{\overline{b}}\xspace}
\providecommand{\barc}{\ensuremath{\overline{c}}\xspace}
\providecommand{\bard}{\ensuremath{\overline{d}}\xspace}
\providecommand{\bare}{\ensuremath{\overline{e}}\xspace}
\providecommand{\barf}{\ensuremath{\overline{f}}\xspace}
\providecommand{\barg}{\ensuremath{\overline{g}}\xspace}
\providecommand{\barh}{\ensuremath{\overline{h}}\xspace}
\providecommand{\bari}{\ensuremath{\overline{i}}\xspace}
\providecommand{\barj}{\ensuremath{\overline{j}}\xspace}
\providecommand{\bark}{\ensuremath{\overline{k}}\xspace}
\providecommand{\barl}{\ensuremath{\overline{l}}\xspace}
\providecommand{\barm}{\ensuremath{\overline{m}}\xspace}
\providecommand{\barn}{\ensuremath{\overline{n}}\xspace}
\providecommand{\baro}{\ensuremath{\overline{o}}\xspace}
\providecommand{\barp}{\ensuremath{\overline{p}}\xspace}
\providecommand{\barq}{\ensuremath{\overline{q}}\xspace}
\providecommand{\barr}{\ensuremath{\overline{r}}\xspace}
\providecommand{\bars}{\ensuremath{\overline{s}}\xspace}
\providecommand{\bart}{\ensuremath{\overline{t}}\xspace}
\providecommand{\baru}{\ensuremath{\overline{u}}\xspace}
\providecommand{\barv}{\ensuremath{\overline{v}}\xspace}
\providecommand{\barw}{\ensuremath{\overline{w}}\xspace}
\providecommand{\barx}{\ensuremath{\overline{x}}\xspace}
\providecommand{\bary}{\ensuremath{\overline{y}}\xspace}
\providecommand{\barz}{\ensuremath{\overline{z}}\xspace}
\providecommand{\barA}{\ensuremath{\overline{A}}\xspace}
\providecommand{\barB}{\ensuremath{\overline{B}}\xspace}
\providecommand{\barC}{\ensuremath{\overline{C}}\xspace}
\providecommand{\barD}{\ensuremath{\overline{D}}\xspace}
\providecommand{\barE}{\ensuremath{\overline{E}}\xspace}
\providecommand{\barF}{\ensuremath{\overline{F}}\xspace}
\providecommand{\barG}{\ensuremath{\overline{G}}\xspace}
\providecommand{\barH}{\ensuremath{\overline{H}}\xspace}
\providecommand{\barI}{\ensuremath{\overline{I}}\xspace}
\providecommand{\barJ}{\ensuremath{\overline{J}}\xspace}
\providecommand{\barK}{\ensuremath{\overline{K}}\xspace}
\providecommand{\barL}{\ensuremath{\overline{L}}\xspace}
\providecommand{\barM}{\ensuremath{\overline{M}}\xspace}
\providecommand{\barN}{\ensuremath{\overline{N}}\xspace}
\providecommand{\barO}{\ensuremath{\overline{O}}\xspace}
\providecommand{\barP}{\ensuremath{\overline{P}}\xspace}
\providecommand{\barQ}{\ensuremath{\overline{Q}}\xspace}
\providecommand{\barR}{\ensuremath{\overline{R}}\xspace}
\providecommand{\barS}{\ensuremath{\overline{S}}\xspace}
\providecommand{\barT}{\ensuremath{\overline{T}}\xspace}
\providecommand{\barU}{\ensuremath{\overline{U}}\xspace}
\providecommand{\barV}{\ensuremath{\overline{V}}\xspace}
\providecommand{\barW}{\ensuremath{\overline{W}}\xspace}
\providecommand{\barX}{\ensuremath{\overline{X}}\xspace}
\providecommand{\barY}{\ensuremath{\overline{Y}}\xspace}
\providecommand{\barZ}{\ensuremath{\overline{Z}}\xspace}

\providecommand{\tildea}{\ensuremath{\widetilde{a}}\xspace}
\providecommand{\tildeb}{\ensuremath{\widetilde{b}}\xspace}
\providecommand{\tildec}{\ensuremath{\widetilde{c}}\xspace}
\providecommand{\tilded}{\ensuremath{\widetilde{d}}\xspace}
\providecommand{\tildee}{\ensuremath{\widetilde{e}}\xspace}
\providecommand{\tildef}{\ensuremath{\widetilde{f}}\xspace}
\providecommand{\tildeg}{\ensuremath{\widetilde{g}}\xspace}
\providecommand{\tildeh}{\ensuremath{\widetilde{h}}\xspace}
\providecommand{\tildei}{\ensuremath{\widetilde{i}}\xspace}
\providecommand{\tildej}{\ensuremath{\widetilde{j}}\xspace}
\providecommand{\tildek}{\ensuremath{\widetilde{k}}\xspace}
\providecommand{\tildel}{\ensuremath{\widetilde{l}}\xspace}
\providecommand{\tildem}{\ensuremath{\widetilde{m}}\xspace}
\providecommand{\tilden}{\ensuremath{\widetilde{n}}\xspace}
\providecommand{\tildeo}{\ensuremath{\widetilde{o}}\xspace}
\providecommand{\tildep}{\ensuremath{\widetilde{p}}\xspace}
\providecommand{\tildeq}{\ensuremath{\widetilde{q}}\xspace}
\providecommand{\tilder}{\ensuremath{\widetilde{r}}\xspace}
\providecommand{\tildes}{\ensuremath{\widetilde{s}}\xspace}
\providecommand{\tildet}{\ensuremath{\widetilde{t}}\xspace}
\providecommand{\tildeu}{\ensuremath{\widetilde{u}}\xspace}
\providecommand{\tildev}{\ensuremath{\widetilde{v}}\xspace}
\providecommand{\tildew}{\ensuremath{\widetilde{w}}\xspace}
\providecommand{\tildex}{\ensuremath{\widetilde{x}}\xspace}
\providecommand{\tildey}{\ensuremath{\widetilde{y}}\xspace}
\providecommand{\tildez}{\ensuremath{\widetilde{z}}\xspace}
\providecommand{\tildeA}{\ensuremath{\widetilde{A}}\xspace}
\providecommand{\tildeB}{\ensuremath{\widetilde{B}}\xspace}
\providecommand{\tildeC}{\ensuremath{\widetilde{C}}\xspace}
\providecommand{\tildeD}{\ensuremath{\widetilde{D}}\xspace}
\providecommand{\tildeE}{\ensuremath{\widetilde{E}}\xspace}
\providecommand{\tildeF}{\ensuremath{\widetilde{F}}\xspace}
\providecommand{\tildeG}{\ensuremath{\widetilde{G}}\xspace}
\providecommand{\tildeH}{\ensuremath{\widetilde{H}}\xspace}
\providecommand{\tildeI}{\ensuremath{\widetilde{I}}\xspace}
\providecommand{\tildeJ}{\ensuremath{\widetilde{J}}\xspace}
\providecommand{\tildeK}{\ensuremath{\widetilde{K}}\xspace}
\providecommand{\tildeL}{\ensuremath{\widetilde{L}}\xspace}
\providecommand{\tildeM}{\ensuremath{\widetilde{M}}\xspace}
\providecommand{\tildeN}{\ensuremath{\widetilde{N}}\xspace}
\providecommand{\tildeO}{\ensuremath{\widetilde{O}}\xspace}
\providecommand{\tildeP}{\ensuremath{\widetilde{P}}\xspace}
\providecommand{\tildeQ}{\ensuremath{\widetilde{Q}}\xspace}
\providecommand{\tildeR}{\ensuremath{\widetilde{R}}\xspace}
\providecommand{\tildeS}{\ensuremath{\widetilde{S}}\xspace}
\providecommand{\tildeT}{\ensuremath{\widetilde{T}}\xspace}
\providecommand{\tildeU}{\ensuremath{\widetilde{U}}\xspace}
\providecommand{\tildeV}{\ensuremath{\widetilde{V}}\xspace}
\providecommand{\tildeW}{\ensuremath{\widetilde{W}}\xspace}
\providecommand{\tildeX}{\ensuremath{\widetilde{X}}\xspace}
\providecommand{\tildeY}{\ensuremath{\widetilde{Y}}\xspace}
\providecommand{\tildeZ}{\ensuremath{\widetilde{Z}}\xspace}

\providecommand{\hata}{\ensuremath{\widehat{a}}\xspace}
\providecommand{\hatb}{\ensuremath{\widehat{b}}\xspace}
\providecommand{\hatc}{\ensuremath{\widehat{c}}\xspace}
\providecommand{\hatd}{\ensuremath{\widehat{d}}\xspace}
\providecommand{\hate}{\ensuremath{\widehat{e}}\xspace}
\providecommand{\hatf}{\ensuremath{\widehat{f}}\xspace}
\providecommand{\hatg}{\ensuremath{\widehat{g}}\xspace}
\providecommand{\hath}{\ensuremath{\widehat{h}}\xspace}
\providecommand{\hati}{\ensuremath{\widehat{i}}\xspace}
\providecommand{\hatj}{\ensuremath{\widehat{j}}\xspace}
\providecommand{\hatk}{\ensuremath{\widehat{k}}\xspace}
\providecommand{\hatl}{\ensuremath{\widehat{l}}\xspace}
\providecommand{\hatm}{\ensuremath{\widehat{m}}\xspace}
\providecommand{\hatn}{\ensuremath{\widehat{n}}\xspace}
\providecommand{\hato}{\ensuremath{\widehat{o}}\xspace}
\providecommand{\hatp}{\ensuremath{\widehat{p}}\xspace}
\providecommand{\hatq}{\ensuremath{\widehat{q}}\xspace}
\providecommand{\hatr}{\ensuremath{\widehat{r}}\xspace}
\providecommand{\hats}{\ensuremath{\widehat{s}}\xspace}
\providecommand{\hatt}{\ensuremath{\widehat{t}}\xspace}
\providecommand{\hatu}{\ensuremath{\widehat{u}}\xspace}
\providecommand{\hatv}{\ensuremath{\widehat{v}}\xspace}
\providecommand{\hatw}{\ensuremath{\widehat{w}}\xspace}
\providecommand{\hatx}{\ensuremath{\widehat{x}}\xspace}
\providecommand{\haty}{\ensuremath{\widehat{y}}\xspace}
\providecommand{\hatz}{\ensuremath{\widehat{z}}\xspace}
\providecommand{\hatA}{\ensuremath{\widehat{A}}\xspace}
\providecommand{\hatB}{\ensuremath{\widehat{B}}\xspace}
\providecommand{\hatC}{\ensuremath{\widehat{C}}\xspace}
\providecommand{\hatD}{\ensuremath{\widehat{D}}\xspace}
\providecommand{\hatE}{\ensuremath{\widehat{E}}\xspace}
\providecommand{\hatF}{\ensuremath{\widehat{F}}\xspace}
\providecommand{\hatG}{\ensuremath{\widehat{G}}\xspace}
\providecommand{\hatH}{\ensuremath{\widehat{H}}\xspace}
\providecommand{\hatI}{\ensuremath{\widehat{I}}\xspace}
\providecommand{\hatJ}{\ensuremath{\widehat{J}}\xspace}
\providecommand{\hatK}{\ensuremath{\widehat{K}}\xspace}
\providecommand{\hatL}{\ensuremath{\widehat{L}}\xspace}
\providecommand{\hatM}{\ensuremath{\widehat{M}}\xspace}
\providecommand{\hatN}{\ensuremath{\widehat{N}}\xspace}
\providecommand{\hatO}{\ensuremath{\widehat{O}}\xspace}
\providecommand{\hatP}{\ensuremath{\widehat{P}}\xspace}
\providecommand{\hatQ}{\ensuremath{\widehat{Q}}\xspace}
\providecommand{\hatR}{\ensuremath{\widehat{R}}\xspace}
\providecommand{\hatS}{\ensuremath{\widehat{S}}\xspace}
\providecommand{\hatT}{\ensuremath{\widehat{T}}\xspace}
\providecommand{\hatU}{\ensuremath{\widehat{U}}\xspace}
\providecommand{\hatV}{\ensuremath{\widehat{V}}\xspace}
\providecommand{\hatW}{\ensuremath{\widehat{W}}\xspace}
\providecommand{\hatX}{\ensuremath{\widehat{X}}\xspace}
\providecommand{\hatY}{\ensuremath{\widehat{Y}}\xspace}
\providecommand{\hatZ}{\ensuremath{\widehat{Z}}\xspace}

\providecommand{\undera}{\ensuremath{\underline{a}}\xspace}
\providecommand{\underb}{\ensuremath{\underline{b}}\xspace}
\providecommand{\underc}{\ensuremath{\underline{c}}\xspace}
\providecommand{\underd}{\ensuremath{\underline{d}}\xspace}
\providecommand{\undere}{\ensuremath{\underline{e}}\xspace}
\providecommand{\underf}{\ensuremath{\underline{f}}\xspace}
\providecommand{\underg}{\ensuremath{\underline{g}}\xspace}
\providecommand{\underh}{\ensuremath{\underline{h}}\xspace}
\providecommand{\underi}{\ensuremath{\underline{i}}\xspace}
\providecommand{\underj}{\ensuremath{\underline{j}}\xspace}
\providecommand{\underk}{\ensuremath{\underline{k}}\xspace}
\providecommand{\underl}{\ensuremath{\underline{l}}\xspace}
\providecommand{\underm}{\ensuremath{\underline{m}}\xspace}
\providecommand{\undern}{\ensuremath{\underline{n}}\xspace}
\providecommand{\undero}{\ensuremath{\underline{o}}\xspace}
\providecommand{\underp}{\ensuremath{\underline{p}}\xspace}
\providecommand{\underq}{\ensuremath{\underline{q}}\xspace}
\providecommand{\underr}{\ensuremath{\underline{r}}\xspace}
\providecommand{\unders}{\ensuremath{\underline{s}}\xspace}
\providecommand{\undert}{\ensuremath{\underline{t}}\xspace}
\providecommand{\underu}{\ensuremath{\underline{u}}\xspace}
\providecommand{\underv}{\ensuremath{\underline{v}}\xspace}
\providecommand{\underw}{\ensuremath{\underline{w}}\xspace}
\providecommand{\underx}{\ensuremath{\underline{x}}\xspace}
\providecommand{\undery}{\ensuremath{\underline{y}}\xspace}
\providecommand{\underz}{\ensuremath{\underline{z}}\xspace}
\providecommand{\underA}{\ensuremath{\underline{A}}\xspace}
\providecommand{\underB}{\ensuremath{\underline{B}}\xspace}
\providecommand{\underC}{\ensuremath{\underline{C}}\xspace}
\providecommand{\underD}{\ensuremath{\underline{D}}\xspace}
\providecommand{\underE}{\ensuremath{\underline{E}}\xspace}
\providecommand{\underF}{\ensuremath{\underline{F}}\xspace}
\providecommand{\underG}{\ensuremath{\underline{G}}\xspace}
\providecommand{\underH}{\ensuremath{\underline{H}}\xspace}
\providecommand{\underI}{\ensuremath{\underline{I}}\xspace}
\providecommand{\underJ}{\ensuremath{\underline{J}}\xspace}
\providecommand{\underK}{\ensuremath{\underline{K}}\xspace}
\providecommand{\underL}{\ensuremath{\underline{L}}\xspace}
\providecommand{\underM}{\ensuremath{\underline{M}}\xspace}
\providecommand{\underN}{\ensuremath{\underline{N}}\xspace}
\providecommand{\underO}{\ensuremath{\underline{O}}\xspace}
\providecommand{\underP}{\ensuremath{\underline{P}}\xspace}
\providecommand{\underQ}{\ensuremath{\underline{Q}}\xspace}
\providecommand{\underR}{\ensuremath{\underline{R}}\xspace}
\providecommand{\underS}{\ensuremath{\underline{S}}\xspace}
\providecommand{\underT}{\ensuremath{\underline{T}}\xspace}
\providecommand{\underU}{\ensuremath{\underline{U}}\xspace}
\providecommand{\underV}{\ensuremath{\underline{V}}\xspace}
\providecommand{\underW}{\ensuremath{\underline{W}}\xspace}
\providecommand{\underX}{\ensuremath{\underline{X}}\xspace}
\providecommand{\underY}{\ensuremath{\underline{Y}}\xspace}
\providecommand{\underZ}{\ensuremath{\underline{Z}}\xspace}

%---- calligraphic letters

\providecommand{\cA}{\ensuremath{\mathcal{A}}\xspace}
\providecommand{\cB}{\ensuremath{\mathcal{B}}\xspace}
\providecommand{\cC}{\ensuremath{\mathcal{C}}\xspace}
\providecommand{\cD}{\ensuremath{\mathcal{D}}\xspace}
\providecommand{\cE}{\ensuremath{\mathcal{E}}\xspace}
\providecommand{\cF}{\ensuremath{\mathcal{F}}\xspace}
\providecommand{\cG}{\ensuremath{\mathcal{G}}\xspace}
\providecommand{\cH}{\ensuremath{\mathcal{H}}\xspace}
\providecommand{\cI}{\ensuremath{\mathcal{I}}\xspace}
\providecommand{\cJ}{\ensuremath{\mathcal{J}}\xspace}
\providecommand{\cK}{\ensuremath{\mathcal{K}}\xspace}
\providecommand{\cL}{\ensuremath{\mathcal{L}}\xspace}
\providecommand{\cM}{\ensuremath{\mathcal{M}}\xspace}
\providecommand{\cN}{\ensuremath{\mathcal{N}}\xspace}
\providecommand{\cO}{\ensuremath{\mathcal{O}}\xspace}
\providecommand{\cP}{\ensuremath{\mathcal{P}}\xspace}
\providecommand{\cQ}{\ensuremath{\mathcal{Q}}\xspace}
\providecommand{\cR}{\ensuremath{\mathcal{R}}\xspace}
\providecommand{\cS}{\ensuremath{\mathcal{S}}\xspace}
\providecommand{\cT}{\ensuremath{\mathcal{T}}\xspace}
\providecommand{\cU}{\ensuremath{\mathcal{U}}\xspace}
\providecommand{\cV}{\ensuremath{\mathcal{V}}\xspace}
\providecommand{\cW}{\ensuremath{\mathcal{W}}\xspace}
\providecommand{\cX}{\ensuremath{\mathcal{X}}\xspace}
\providecommand{\cY}{\ensuremath{\mathcal{Y}}\xspace}
\providecommand{\cZ}{\ensuremath{\mathcal{Z}}\xspace}

\providecommand{\ccA}{\ensuremath{\mathscr{A}}\xspace}
\providecommand{\ccB}{\ensuremath{\mathscr{B}}\xspace}
\providecommand{\ccC}{\ensuremath{\mathscr{C}}\xspace}
\providecommand{\ccD}{\ensuremath{\mathscr{D}}\xspace}
\providecommand{\ccE}{\ensuremath{\mathscr{E}}\xspace}
\providecommand{\ccF}{\ensuremath{\mathscr{F}}\xspace}
\providecommand{\ccG}{\ensuremath{\mathscr{G}}\xspace}
\providecommand{\ccH}{\ensuremath{\mathscr{H}}\xspace}
\providecommand{\ccI}{\ensuremath{\mathscr{I}}\xspace}
\providecommand{\ccJ}{\ensuremath{\mathscr{J}}\xspace}
\providecommand{\ccK}{\ensuremath{\mathscr{K}}\xspace}
\providecommand{\ccL}{\ensuremath{\mathscr{L}}\xspace}
\providecommand{\ccM}{\ensuremath{\mathscr{M}}\xspace}
\providecommand{\ccN}{\ensuremath{\mathscr{N}}\xspace}
\providecommand{\ccO}{\ensuremath{\mathscr{O}}\xspace}
\providecommand{\ccP}{\ensuremath{\mathscr{P}}\xspace}
\providecommand{\ccQ}{\ensuremath{\mathscr{Q}}\xspace}
\providecommand{\ccR}{\ensuremath{\mathscr{R}}\xspace}
\providecommand{\ccS}{\ensuremath{\mathscr{S}}\xspace}
\providecommand{\ccT}{\ensuremath{\mathscr{T}}\xspace}
\providecommand{\ccU}{\ensuremath{\mathscr{U}}\xspace}
\providecommand{\ccV}{\ensuremath{\mathscr{V}}\xspace}
\providecommand{\ccW}{\ensuremath{\mathscr{W}}\xspace}
\providecommand{\ccX}{\ensuremath{\mathscr{X}}\xspace}
\providecommand{\ccY}{\ensuremath{\mathscr{Y}}\xspace}
\providecommand{\ccZ}{\ensuremath{\mathscr{Z}}\xspace}

\providecommand{\dcA}{\ensuremath{\dot{\mathcal{A}}}\xspace}
\providecommand{\dcB}{\ensuremath{\dot{\mathcal{B}}}\xspace}
\providecommand{\dcC}{\ensuremath{\dot{\mathcal{C}}}\xspace}
\providecommand{\dcD}{\ensuremath{\dot{\mathcal{D}}}\xspace}
\providecommand{\dcE}{\ensuremath{\dot{\mathcal{E}}}\xspace}
\providecommand{\dcF}{\ensuremath{\dot{\mathcal{F}}}\xspace}
\providecommand{\dcG}{\ensuremath{\dot{\mathcal{G}}}\xspace}
\providecommand{\dcH}{\ensuremath{\dot{\mathcal{H}}}\xspace}
\providecommand{\dcI}{\ensuremath{\dot{\mathcal{I}}}\xspace}
\providecommand{\dcJ}{\ensuremath{\dot{\mathcal{J}}}\xspace}
\providecommand{\dcK}{\ensuremath{\dot{\mathcal{K}}}\xspace}
\providecommand{\dcL}{\ensuremath{\dot{\mathcal{L}}}\xspace}
\providecommand{\dcM}{\ensuremath{\dot{\mathcal{M}}}\xspace}
\providecommand{\dcN}{\ensuremath{\dot{\mathcal{N}}}\xspace}
\providecommand{\dcO}{\ensuremath{\dot{\mathcal{O}}}\xspace}
\providecommand{\dcP}{\ensuremath{\dot{\mathcal{P}}}\xspace}
\providecommand{\dcQ}{\ensuremath{\dot{\mathcal{Q}}}\xspace}
\providecommand{\dcR}{\ensuremath{\dot{\mathcal{R}}}\xspace}
\providecommand{\dcS}{\ensuremath{\dot{\mathcal{S}}}\xspace}
\providecommand{\dcT}{\ensuremath{\dot{\mathcal{T}}}\xspace}
\providecommand{\dcU}{\ensuremath{\dot{\mathcal{U}}}\xspace}
\providecommand{\dcV}{\ensuremath{\dot{\mathcal{V}}}\xspace}
\providecommand{\dcW}{\ensuremath{\dot{\mathcal{W}}}\xspace}
\providecommand{\dcX}{\ensuremath{\dot{\mathcal{X}}}\xspace}
\providecommand{\dcY}{\ensuremath{\dot{\mathcal{Y}}}\xspace}
\providecommand{\dcZ}{\ensuremath{\dot{\mathcal{Z}}}\xspace}

\providecommand{\dccA}{\ensuremath{\dot{\mathscr{A}}}\xspace}
\providecommand{\dccB}{\ensuremath{\dot{\mathscr{B}}}\xspace}
\providecommand{\dccC}{\ensuremath{\dot{\mathscr{C}}}\xspace}
\providecommand{\dccD}{\ensuremath{\dot{\mathscr{D}}}\xspace}
\providecommand{\dccE}{\ensuremath{\dot{\mathscr{E}}}\xspace}
\providecommand{\dccF}{\ensuremath{\dot{\mathscr{F}}}\xspace}
\providecommand{\dccG}{\ensuremath{\dot{\mathscr{G}}}\xspace}
\providecommand{\dccH}{\ensuremath{\dot{\mathscr{H}}}\xspace}
\providecommand{\dccI}{\ensuremath{\dot{\mathscr{I}}}\xspace}
\providecommand{\dccJ}{\ensuremath{\dot{\mathscr{J}}}\xspace}
\providecommand{\dccK}{\ensuremath{\dot{\mathscr{K}}}\xspace}
\providecommand{\dccL}{\ensuremath{\dot{\mathscr{L}}}\xspace}
\providecommand{\dccM}{\ensuremath{\dot{\mathscr{M}}}\xspace}
\providecommand{\dccN}{\ensuremath{\dot{\mathscr{N}}}\xspace}
\providecommand{\dccO}{\ensuremath{\dot{\mathscr{O}}}\xspace}
\providecommand{\dccP}{\ensuremath{\dot{\mathscr{P}}}\xspace}
\providecommand{\dccQ}{\ensuremath{\dot{\mathscr{Q}}}\xspace}
\providecommand{\dccR}{\ensuremath{\dot{\mathscr{R}}}\xspace}
\providecommand{\dccS}{\ensuremath{\dot{\mathscr{S}}}\xspace}
\providecommand{\dccT}{\ensuremath{\dot{\mathscr{T}}}\xspace}
\providecommand{\dccU}{\ensuremath{\dot{\mathscr{U}}}\xspace}
\providecommand{\dccV}{\ensuremath{\dot{\mathscr{V}}}\xspace}
\providecommand{\dccW}{\ensuremath{\dot{\mathscr{W}}}\xspace}
\providecommand{\dccX}{\ensuremath{\dot{\mathscr{X}}}\xspace}
\providecommand{\dccY}{\ensuremath{\dot{\mathscr{Y}}}\xspace}
\providecommand{\dccZ}{\ensuremath{\dot{\mathscr{Z}}}\xspace}

\providecommand{\tcA}{\ensuremath{\widetilde{\mathcal{A}}}\xspace}
\providecommand{\tcB}{\ensuremath{\widetilde{\mathcal{B}}}\xspace}
\providecommand{\tcC}{\ensuremath{\widetilde{\mathcal{C}}}\xspace}
\providecommand{\tcD}{\ensuremath{\widetilde{\mathcal{D}}}\xspace}
\providecommand{\tcE}{\ensuremath{\widetilde{\mathcal{E}}}\xspace}
\providecommand{\tcF}{\ensuremath{\widetilde{\mathcal{F}}}\xspace}
\providecommand{\tcG}{\ensuremath{\widetilde{\mathcal{G}}}\xspace}
\providecommand{\tcH}{\ensuremath{\widetilde{\mathcal{H}}}\xspace}
\providecommand{\tcI}{\ensuremath{\widetilde{\mathcal{I}}}\xspace}
\providecommand{\tcJ}{\ensuremath{\widetilde{\mathcal{J}}}\xspace}
\providecommand{\tcK}{\ensuremath{\widetilde{\mathcal{K}}}\xspace}
\providecommand{\tcL}{\ensuremath{\widetilde{\mathcal{L}}}\xspace}
\providecommand{\tcM}{\ensuremath{\widetilde{\mathcal{M}}}\xspace}
\providecommand{\tcN}{\ensuremath{\widetilde{\mathcal{N}}}\xspace}
\providecommand{\tcO}{\ensuremath{\widetilde{\mathcal{O}}}\xspace}
\providecommand{\tcP}{\ensuremath{\widetilde{\mathcal{P}}}\xspace}
\providecommand{\tcQ}{\ensuremath{\widetilde{\mathcal{Q}}}\xspace}
\providecommand{\tcR}{\ensuremath{\widetilde{\mathcal{R}}}\xspace}
\providecommand{\tcS}{\ensuremath{\widetilde{\mathcal{S}}}\xspace}
\providecommand{\tcT}{\ensuremath{\widetilde{\mathcal{T}}}\xspace}
\providecommand{\tcU}{\ensuremath{\widetilde{\mathcal{U}}}\xspace}
\providecommand{\tcV}{\ensuremath{\widetilde{\mathcal{V}}}\xspace}
\providecommand{\tcW}{\ensuremath{\widetilde{\mathcal{W}}}\xspace}
\providecommand{\tcX}{\ensuremath{\widetilde{\mathcal{X}}}\xspace}
\providecommand{\tcY}{\ensuremath{\widetilde{\mathcal{Y}}}\xspace}
\providecommand{\tcZ}{\ensuremath{\widetilde{\mathcal{Z}}}\xspace}

\providecommand{\tccA}{\ensuremath{\widetilde{\mathscr{A}}}\xspace}
\providecommand{\tccB}{\ensuremath{\widetilde{\mathscr{B}}}\xspace}
\providecommand{\tccC}{\ensuremath{\widetilde{\mathscr{C}}}\xspace}
\providecommand{\tccD}{\ensuremath{\widetilde{\mathscr{D}}}\xspace}
\providecommand{\tccE}{\ensuremath{\widetilde{\mathscr{E}}}\xspace}
\providecommand{\tccF}{\ensuremath{\widetilde{\mathscr{F}}}\xspace}
\providecommand{\tccG}{\ensuremath{\widetilde{\mathscr{G}}}\xspace}
\providecommand{\tccH}{\ensuremath{\widetilde{\mathscr{H}}}\xspace}
\providecommand{\tccI}{\ensuremath{\widetilde{\mathscr{I}}}\xspace}
\providecommand{\tccJ}{\ensuremath{\widetilde{\mathscr{J}}}\xspace}
\providecommand{\tccK}{\ensuremath{\widetilde{\mathscr{K}}}\xspace}
\providecommand{\tccL}{\ensuremath{\widetilde{\mathscr{L}}}\xspace}
\providecommand{\tccM}{\ensuremath{\widetilde{\mathscr{M}}}\xspace}
\providecommand{\tccN}{\ensuremath{\widetilde{\mathscr{N}}}\xspace}
\providecommand{\tccO}{\ensuremath{\widetilde{\mathscr{O}}}\xspace}
\providecommand{\tccP}{\ensuremath{\widetilde{\mathscr{P}}}\xspace}
\providecommand{\tccQ}{\ensuremath{\widetilde{\mathscr{Q}}}\xspace}
\providecommand{\tccR}{\ensuremath{\widetilde{\mathscr{R}}}\xspace}
\providecommand{\tccS}{\ensuremath{\widetilde{\mathscr{S}}}\xspace}
\providecommand{\tccT}{\ensuremath{\widetilde{\mathscr{T}}}\xspace}
\providecommand{\tccU}{\ensuremath{\widetilde{\mathscr{U}}}\xspace}
\providecommand{\tccV}{\ensuremath{\widetilde{\mathscr{V}}}\xspace}
\providecommand{\tccW}{\ensuremath{\widetilde{\mathscr{W}}}\xspace}
\providecommand{\tccX}{\ensuremath{\widetilde{\mathscr{X}}}\xspace}
\providecommand{\tccY}{\ensuremath{\widetilde{\mathscr{Y}}}\xspace}
\providecommand{\tccZ}{\ensuremath{\widetilde{\mathscr{Z}}}\xspace}

\providecommand{\hcA}{\ensuremath{\widehat{\mathcal{A}}}\xspace}
\providecommand{\hcB}{\ensuremath{\widehat{\mathcal{B}}}\xspace}
\providecommand{\hcC}{\ensuremath{\widehat{\mathcal{C}}}\xspace}
\providecommand{\hcD}{\ensuremath{\widehat{\mathcal{D}}}\xspace}
\providecommand{\hcE}{\ensuremath{\widehat{\mathcal{E}}}\xspace}
\providecommand{\hcF}{\ensuremath{\widehat{\mathcal{F}}}\xspace}
\providecommand{\hcG}{\ensuremath{\widehat{\mathcal{G}}}\xspace}
\providecommand{\hcH}{\ensuremath{\widehat{\mathcal{H}}}\xspace}
\providecommand{\hcI}{\ensuremath{\widehat{\mathcal{I}}}\xspace}
\providecommand{\hcJ}{\ensuremath{\widehat{\mathcal{J}}}\xspace}
\providecommand{\hcK}{\ensuremath{\widehat{\mathcal{K}}}\xspace}
\providecommand{\hcL}{\ensuremath{\widehat{\mathcal{L}}}\xspace}
\providecommand{\hcM}{\ensuremath{\widehat{\mathcal{M}}}\xspace}
\providecommand{\hcN}{\ensuremath{\widehat{\mathcal{N}}}\xspace}
\providecommand{\hcO}{\ensuremath{\widehat{\mathcal{O}}}\xspace}
\providecommand{\hcP}{\ensuremath{\widehat{\mathcal{P}}}\xspace}
\providecommand{\hcQ}{\ensuremath{\widehat{\mathcal{Q}}}\xspace}
\providecommand{\hcR}{\ensuremath{\widehat{\mathcal{R}}}\xspace}
\providecommand{\hcS}{\ensuremath{\widehat{\mathcal{S}}}\xspace}
\providecommand{\hcT}{\ensuremath{\widehat{\mathcal{T}}}\xspace}
\providecommand{\hcU}{\ensuremath{\widehat{\mathcal{U}}}\xspace}
\providecommand{\hcV}{\ensuremath{\widehat{\mathcal{V}}}\xspace}
\providecommand{\hcW}{\ensuremath{\widehat{\mathcal{W}}}\xspace}
\providecommand{\hcX}{\ensuremath{\widehat{\mathcal{X}}}\xspace}
\providecommand{\hcY}{\ensuremath{\widehat{\mathcal{Y}}}\xspace}
\providecommand{\hcZ}{\ensuremath{\widehat{\mathcal{Z}}}\xspace}

\providecommand{\hccA}{\ensuremath{\widehat{\mathscr{A}}}\xspace}
\providecommand{\hccB}{\ensuremath{\widehat{\mathscr{B}}}\xspace}
\providecommand{\hccC}{\ensuremath{\widehat{\mathscr{C}}}\xspace}
\providecommand{\hccD}{\ensuremath{\widehat{\mathscr{D}}}\xspace}
\providecommand{\hccE}{\ensuremath{\widehat{\mathscr{E}}}\xspace}
\providecommand{\hccF}{\ensuremath{\widehat{\mathscr{F}}}\xspace}
\providecommand{\hccG}{\ensuremath{\widehat{\mathscr{G}}}\xspace}
\providecommand{\hccH}{\ensuremath{\widehat{\mathscr{H}}}\xspace}
\providecommand{\hccI}{\ensuremath{\widehat{\mathscr{I}}}\xspace}
\providecommand{\hccJ}{\ensuremath{\widehat{\mathscr{J}}}\xspace}
\providecommand{\hccK}{\ensuremath{\widehat{\mathscr{K}}}\xspace}
\providecommand{\hccL}{\ensuremath{\widehat{\mathscr{L}}}\xspace}
\providecommand{\hccM}{\ensuremath{\widehat{\mathscr{M}}}\xspace}
\providecommand{\hccN}{\ensuremath{\widehat{\mathscr{N}}}\xspace}
\providecommand{\hccO}{\ensuremath{\widehat{\mathscr{O}}}\xspace}
\providecommand{\hccP}{\ensuremath{\widehat{\mathscr{P}}}\xspace}
\providecommand{\hccQ}{\ensuremath{\widehat{\mathscr{Q}}}\xspace}
\providecommand{\hccR}{\ensuremath{\widehat{\mathscr{R}}}\xspace}
\providecommand{\hccS}{\ensuremath{\widehat{\mathscr{S}}}\xspace}
\providecommand{\hccT}{\ensuremath{\widehat{\mathscr{T}}}\xspace}
\providecommand{\hccU}{\ensuremath{\widehat{\mathscr{U}}}\xspace}
\providecommand{\hccV}{\ensuremath{\widehat{\mathscr{V}}}\xspace}
\providecommand{\hccW}{\ensuremath{\widehat{\mathscr{W}}}\xspace}
\providecommand{\hccX}{\ensuremath{\widehat{\mathscr{X}}}\xspace}
\providecommand{\hccY}{\ensuremath{\widehat{\mathscr{Y}}}\xspace}
\providecommand{\hccZ}{\ensuremath{\widehat{\mathscr{Z}}}\xspace}

\providecommand{\bcA}{\ensuremath{\overline{\mathcal{A}}}\xspace}
\providecommand{\bcB}{\ensuremath{\overline{\mathcal{B}}}\xspace}
\providecommand{\bcC}{\ensuremath{\overline{\mathcal{C}}}\xspace}
\providecommand{\bcD}{\ensuremath{\overline{\mathcal{D}}}\xspace}
\providecommand{\bcE}{\ensuremath{\overline{\mathcal{E}}}\xspace}
\providecommand{\bcF}{\ensuremath{\overline{\mathcal{F}}}\xspace}
\providecommand{\bcG}{\ensuremath{\overline{\mathcal{G}}}\xspace}
\providecommand{\bcH}{\ensuremath{\overline{\mathcal{H}}}\xspace}
\providecommand{\bcI}{\ensuremath{\overline{\mathcal{I}}}\xspace}
\providecommand{\bcJ}{\ensuremath{\overline{\mathcal{J}}}\xspace}
\providecommand{\bcK}{\ensuremath{\overline{\mathcal{K}}}\xspace}
\providecommand{\bcL}{\ensuremath{\overline{\mathcal{L}}}\xspace}
\providecommand{\bcM}{\ensuremath{\overline{\mathcal{M}}}\xspace}
\providecommand{\bcN}{\ensuremath{\overline{\mathcal{N}}}\xspace}
\providecommand{\bcO}{\ensuremath{\overline{\mathcal{O}}}\xspace}
\providecommand{\bcP}{\ensuremath{\overline{\mathcal{P}}}\xspace}
\providecommand{\bcQ}{\ensuremath{\overline{\mathcal{Q}}}\xspace}
\providecommand{\bcR}{\ensuremath{\overline{\mathcal{R}}}\xspace}
\providecommand{\bcS}{\ensuremath{\overline{\mathcal{S}}}\xspace}
\providecommand{\bcT}{\ensuremath{\overline{\mathcal{T}}}\xspace}
\providecommand{\bcU}{\ensuremath{\overline{\mathcal{U}}}\xspace}
\providecommand{\bcV}{\ensuremath{\overline{\mathcal{V}}}\xspace}
\providecommand{\bcW}{\ensuremath{\overline{\mathcal{W}}}\xspace}
\providecommand{\bcX}{\ensuremath{\overline{\mathcal{X}}}\xspace}
\providecommand{\bcY}{\ensuremath{\overline{\mathcal{Y}}}\xspace}
\providecommand{\bcZ}{\ensuremath{\overline{\mathcal{Z}}}\xspace}

\providecommand{\bccA}{\ensuremath{\overline{\mathscr{A}}}\xspace}
\providecommand{\bccB}{\ensuremath{\overline{\mathscr{B}}}\xspace}
\providecommand{\bccC}{\ensuremath{\overline{\mathscr{C}}}\xspace}
\providecommand{\bccD}{\ensuremath{\overline{\mathscr{D}}}\xspace}
\providecommand{\bccE}{\ensuremath{\overline{\mathscr{E}}}\xspace}
\providecommand{\bccF}{\ensuremath{\overline{\mathscr{F}}}\xspace}
\providecommand{\bccG}{\ensuremath{\overline{\mathscr{G}}}\xspace}
\providecommand{\bccH}{\ensuremath{\overline{\mathscr{H}}}\xspace}
\providecommand{\bccI}{\ensuremath{\overline{\mathscr{I}}}\xspace}
\providecommand{\bccJ}{\ensuremath{\overline{\mathscr{J}}}\xspace}
\providecommand{\bccK}{\ensuremath{\overline{\mathscr{K}}}\xspace}
\providecommand{\bccL}{\ensuremath{\overline{\mathscr{L}}}\xspace}
\providecommand{\bccM}{\ensuremath{\overline{\mathscr{M}}}\xspace}
\providecommand{\bccN}{\ensuremath{\overline{\mathscr{N}}}\xspace}
\providecommand{\bccO}{\ensuremath{\overline{\mathscr{O}}}\xspace}
\providecommand{\bccP}{\ensuremath{\overline{\mathscr{P}}}\xspace}
\providecommand{\bccQ}{\ensuremath{\overline{\mathscr{Q}}}\xspace}
\providecommand{\bccR}{\ensuremath{\overline{\mathscr{R}}}\xspace}
\providecommand{\bccS}{\ensuremath{\overline{\mathscr{S}}}\xspace}
\providecommand{\bccT}{\ensuremath{\overline{\mathscr{T}}}\xspace}
\providecommand{\bccU}{\ensuremath{\overline{\mathscr{U}}}\xspace}
\providecommand{\bccV}{\ensuremath{\overline{\mathscr{V}}}\xspace}
\providecommand{\bccW}{\ensuremath{\overline{\mathscr{W}}}\xspace}
\providecommand{\bccX}{\ensuremath{\overline{\mathscr{X}}}\xspace}
\providecommand{\bccY}{\ensuremath{\overline{\mathscr{Y}}}\xspace}
\providecommand{\bccZ}{\ensuremath{\overline{\mathscr{Z}}}\xspace}

\providecommand{\ucA}{\ensuremath{\underline{\mathcal{A}}}\xspace}
\providecommand{\ucB}{\ensuremath{\underline{\mathcal{B}}}\xspace}
\providecommand{\ucC}{\ensuremath{\underline{\mathcal{C}}}\xspace}
\providecommand{\ucD}{\ensuremath{\underline{\mathcal{D}}}\xspace}
\providecommand{\ucE}{\ensuremath{\underline{\mathcal{E}}}\xspace}
\providecommand{\ucF}{\ensuremath{\underline{\mathcal{F}}}\xspace}
\providecommand{\ucG}{\ensuremath{\underline{\mathcal{G}}}\xspace}
\providecommand{\ucH}{\ensuremath{\underline{\mathcal{H}}}\xspace}
\providecommand{\ucI}{\ensuremath{\underline{\mathcal{I}}}\xspace}
\providecommand{\ucJ}{\ensuremath{\underline{\mathcal{J}}}\xspace}
\providecommand{\ucK}{\ensuremath{\underline{\mathcal{K}}}\xspace}
\providecommand{\ucL}{\ensuremath{\underline{\mathcal{L}}}\xspace}
\providecommand{\ucM}{\ensuremath{\underline{\mathcal{M}}}\xspace}
\providecommand{\ucN}{\ensuremath{\underline{\mathcal{N}}}\xspace}
\providecommand{\ucO}{\ensuremath{\underline{\mathcal{O}}}\xspace}
\providecommand{\ucP}{\ensuremath{\underline{\mathcal{P}}}\xspace}
\providecommand{\ucQ}{\ensuremath{\underline{\mathcal{Q}}}\xspace}
\providecommand{\ucR}{\ensuremath{\underline{\mathcal{R}}}\xspace}
\providecommand{\ucS}{\ensuremath{\underline{\mathcal{S}}}\xspace}
\providecommand{\ucT}{\ensuremath{\underline{\mathcal{T}}}\xspace}
\providecommand{\ucU}{\ensuremath{\underline{\mathcal{U}}}\xspace}
\providecommand{\ucV}{\ensuremath{\underline{\mathcal{V}}}\xspace}
\providecommand{\ucW}{\ensuremath{\underline{\mathcal{W}}}\xspace}
\providecommand{\ucX}{\ensuremath{\underline{\mathcal{X}}}\xspace}
\providecommand{\ucY}{\ensuremath{\underline{\mathcal{Y}}}\xspace}
\providecommand{\ucZ}{\ensuremath{\underline{\mathcal{Z}}}\xspace}

\providecommand{\uccA}{\ensuremath{\underline{\mathscr{A}}}\xspace}
\providecommand{\uccB}{\ensuremath{\underline{\mathscr{B}}}\xspace}
\providecommand{\uccC}{\ensuremath{\underline{\mathscr{C}}}\xspace}
\providecommand{\uccD}{\ensuremath{\underline{\mathscr{D}}}\xspace}
\providecommand{\uccE}{\ensuremath{\underline{\mathscr{E}}}\xspace}
\providecommand{\uccF}{\ensuremath{\underline{\mathscr{F}}}\xspace}
\providecommand{\uccG}{\ensuremath{\underline{\mathscr{G}}}\xspace}
\providecommand{\uccH}{\ensuremath{\underline{\mathscr{H}}}\xspace}
\providecommand{\uccI}{\ensuremath{\underline{\mathscr{I}}}\xspace}
\providecommand{\uccJ}{\ensuremath{\underline{\mathscr{J}}}\xspace}
\providecommand{\uccK}{\ensuremath{\underline{\mathscr{K}}}\xspace}
\providecommand{\uccL}{\ensuremath{\underline{\mathscr{L}}}\xspace}
\providecommand{\uccM}{\ensuremath{\underline{\mathscr{M}}}\xspace}
\providecommand{\uccN}{\ensuremath{\underline{\mathscr{N}}}\xspace}
\providecommand{\uccO}{\ensuremath{\underline{\mathscr{O}}}\xspace}
\providecommand{\uccP}{\ensuremath{\underline{\mathscr{P}}}\xspace}
\providecommand{\uccQ}{\ensuremath{\underline{\mathscr{Q}}}\xspace}
\providecommand{\uccR}{\ensuremath{\underline{\mathscr{R}}}\xspace}
\providecommand{\uccS}{\ensuremath{\underline{\mathscr{S}}}\xspace}
\providecommand{\uccT}{\ensuremath{\underline{\mathscr{T}}}\xspace}
\providecommand{\uccU}{\ensuremath{\underline{\mathscr{U}}}\xspace}
\providecommand{\uccV}{\ensuremath{\underline{\mathscr{V}}}\xspace}
\providecommand{\uccW}{\ensuremath{\underline{\mathscr{W}}}\xspace}
\providecommand{\uccX}{\ensuremath{\underline{\mathscr{X}}}\xspace}
\providecommand{\uccY}{\ensuremath{\underline{\mathscr{Y}}}\xspace}
\providecommand{\uccZ}{\ensuremath{\underline{\mathscr{Z}}}\xspace}

%---- roman letters

\providecommand{\rA}{\ensuremath{\mathrm{A}}\xspace}
\providecommand{\rB}{\ensuremath{\mathrm{B}}\xspace}
\providecommand{\rC}{\ensuremath{\mathrm{C}}\xspace}
\providecommand{\rD}{\ensuremath{\mathrm{D}}\xspace}
\providecommand{\rE}{\ensuremath{\mathrm{E}}\xspace}
\providecommand{\rF}{\ensuremath{\mathrm{F}}\xspace}
\providecommand{\rG}{\ensuremath{\mathrm{G}}\xspace}
\providecommand{\rH}{\ensuremath{\mathrm{H}}\xspace}
\providecommand{\rI}{\ensuremath{\mathrm{I}}\xspace}
\providecommand{\rJ}{\ensuremath{\mathrm{J}}\xspace}
\providecommand{\rK}{\ensuremath{\mathrm{K}}\xspace}
\providecommand{\rL}{\ensuremath{\mathrm{L}}\xspace}
\providecommand{\rM}{\ensuremath{\mathrm{M}}\xspace}
\providecommand{\rN}{\ensuremath{\mathrm{N}}\xspace}
\providecommand{\rO}{\ensuremath{\mathrm{O}}\xspace}
\providecommand{\rP}{\ensuremath{\mathrm{P}}\xspace}
\providecommand{\rQ}{\ensuremath{\mathrm{Q}}\xspace}
\providecommand{\rR}{\ensuremath{\mathrm{R}}\xspace}
\providecommand{\rS}{\ensuremath{\mathrm{S}}\xspace}
\providecommand{\rT}{\ensuremath{\mathrm{T}}\xspace}
\providecommand{\rU}{\ensuremath{\mathrm{U}}\xspace}
\providecommand{\rV}{\ensuremath{\mathrm{V}}\xspace}
\providecommand{\rW}{\ensuremath{\mathrm{W}}\xspace}
\providecommand{\rX}{\ensuremath{\mathrm{X}}\xspace}
\providecommand{\rY}{\ensuremath{\mathrm{Y}}\xspace}
\providecommand{\rZ}{\ensuremath{\mathrm{Z}}\xspace}

\providecommand{\drA}{\ensuremath{\dot{\mathrm{A}}}\xspace}
\providecommand{\drB}{\ensuremath{\dot{\mathrm{B}}}\xspace}
\providecommand{\drC}{\ensuremath{\dot{\mathrm{C}}}\xspace}
\providecommand{\drD}{\ensuremath{\dot{\mathrm{D}}}\xspace}
\providecommand{\drE}{\ensuremath{\dot{\mathrm{E}}}\xspace}
\providecommand{\drF}{\ensuremath{\dot{\mathrm{F}}}\xspace}
\providecommand{\drG}{\ensuremath{\dot{\mathrm{G}}}\xspace}
\providecommand{\drH}{\ensuremath{\dot{\mathrm{H}}}\xspace}
\providecommand{\drI}{\ensuremath{\dot{\mathrm{I}}}\xspace}
\providecommand{\drJ}{\ensuremath{\dot{\mathrm{J}}}\xspace}
\providecommand{\drK}{\ensuremath{\dot{\mathrm{K}}}\xspace}
\providecommand{\drL}{\ensuremath{\dot{\mathrm{L}}}\xspace}
\providecommand{\drM}{\ensuremath{\dot{\mathrm{M}}}\xspace}
\providecommand{\drN}{\ensuremath{\dot{\mathrm{N}}}\xspace}
\providecommand{\drO}{\ensuremath{\dot{\mathrm{O}}}\xspace}
\providecommand{\drP}{\ensuremath{\dot{\mathrm{P}}}\xspace}
\providecommand{\drQ}{\ensuremath{\dot{\mathrm{Q}}}\xspace}
\providecommand{\drR}{\ensuremath{\dot{\mathrm{R}}}\xspace}
\providecommand{\drS}{\ensuremath{\dot{\mathrm{S}}}\xspace}
\providecommand{\drT}{\ensuremath{\dot{\mathrm{T}}}\xspace}
\providecommand{\drU}{\ensuremath{\dot{\mathrm{U}}}\xspace}
\providecommand{\drV}{\ensuremath{\dot{\mathrm{V}}}\xspace}
\providecommand{\drW}{\ensuremath{\dot{\mathrm{W}}}\xspace}
\providecommand{\drX}{\ensuremath{\dot{\mathrm{X}}}\xspace}
\providecommand{\drY}{\ensuremath{\dot{\mathrm{Y}}}\xspace}
\providecommand{\drZ}{\ensuremath{\dot{\mathrm{Z}}}\xspace}

\providecommand{\trA}{\ensuremath{\widetilde{\mathrm{A}}}\xspace}
\providecommand{\trB}{\ensuremath{\widetilde{\mathrm{B}}}\xspace}
\providecommand{\trC}{\ensuremath{\widetilde{\mathrm{C}}}\xspace}
\providecommand{\trD}{\ensuremath{\widetilde{\mathrm{D}}}\xspace}
\providecommand{\trE}{\ensuremath{\widetilde{\mathrm{E}}}\xspace}
\providecommand{\trF}{\ensuremath{\widetilde{\mathrm{F}}}\xspace}
\providecommand{\trG}{\ensuremath{\widetilde{\mathrm{G}}}\xspace}
\providecommand{\trH}{\ensuremath{\widetilde{\mathrm{H}}}\xspace}
\providecommand{\trI}{\ensuremath{\widetilde{\mathrm{I}}}\xspace}
\providecommand{\trJ}{\ensuremath{\widetilde{\mathrm{J}}}\xspace}
\providecommand{\trK}{\ensuremath{\widetilde{\mathrm{K}}}\xspace}
\providecommand{\trL}{\ensuremath{\widetilde{\mathrm{L}}}\xspace}
\providecommand{\trM}{\ensuremath{\widetilde{\mathrm{M}}}\xspace}
\providecommand{\trN}{\ensuremath{\widetilde{\mathrm{N}}}\xspace}
\providecommand{\trO}{\ensuremath{\widetilde{\mathrm{O}}}\xspace}
\providecommand{\trP}{\ensuremath{\widetilde{\mathrm{P}}}\xspace}
\providecommand{\trQ}{\ensuremath{\widetilde{\mathrm{Q}}}\xspace}
\providecommand{\trR}{\ensuremath{\widetilde{\mathrm{R}}}\xspace}
\providecommand{\trS}{\ensuremath{\widetilde{\mathrm{S}}}\xspace}
\providecommand{\trT}{\ensuremath{\widetilde{\mathrm{T}}}\xspace}
\providecommand{\trU}{\ensuremath{\widetilde{\mathrm{U}}}\xspace}
\providecommand{\trV}{\ensuremath{\widetilde{\mathrm{V}}}\xspace}
\providecommand{\trW}{\ensuremath{\widetilde{\mathrm{W}}}\xspace}
\providecommand{\trX}{\ensuremath{\widetilde{\mathrm{X}}}\xspace}
\providecommand{\trY}{\ensuremath{\widetilde{\mathrm{Y}}}\xspace}
\providecommand{\trZ}{\ensuremath{\widetilde{\mathrm{Z}}}\xspace}

\providecommand{\urA}{\ensuremath{\underline{\mathrm{A}}}\xspace}
\providecommand{\urB}{\ensuremath{\underline{\mathrm{B}}}\xspace}
\providecommand{\urC}{\ensuremath{\underline{\mathrm{C}}}\xspace}
\providecommand{\urD}{\ensuremath{\underline{\mathrm{D}}}\xspace}
\providecommand{\urE}{\ensuremath{\underline{\mathrm{E}}}\xspace}
\providecommand{\urF}{\ensuremath{\underline{\mathrm{F}}}\xspace}
\providecommand{\urG}{\ensuremath{\underline{\mathrm{G}}}\xspace}
\providecommand{\urH}{\ensuremath{\underline{\mathrm{H}}}\xspace}
\providecommand{\urI}{\ensuremath{\underline{\mathrm{I}}}\xspace}
\providecommand{\urJ}{\ensuremath{\underline{\mathrm{J}}}\xspace}
\providecommand{\urK}{\ensuremath{\underline{\mathrm{K}}}\xspace}
\providecommand{\urL}{\ensuremath{\underline{\mathrm{L}}}\xspace}
\providecommand{\urM}{\ensuremath{\underline{\mathrm{M}}}\xspace}
\providecommand{\urN}{\ensuremath{\underline{\mathrm{N}}}\xspace}
\providecommand{\urO}{\ensuremath{\underline{\mathrm{O}}}\xspace}
\providecommand{\urP}{\ensuremath{\underline{\mathrm{P}}}\xspace}
\providecommand{\urQ}{\ensuremath{\underline{\mathrm{Q}}}\xspace}
\providecommand{\urR}{\ensuremath{\underline{\mathrm{R}}}\xspace}
\providecommand{\urS}{\ensuremath{\underline{\mathrm{S}}}\xspace}
\providecommand{\urT}{\ensuremath{\underline{\mathrm{T}}}\xspace}
\providecommand{\urU}{\ensuremath{\underline{\mathrm{U}}}\xspace}
\providecommand{\urV}{\ensuremath{\underline{\mathrm{V}}}\xspace}
\providecommand{\urW}{\ensuremath{\underline{\mathrm{W}}}\xspace}
\providecommand{\urX}{\ensuremath{\underline{\mathrm{X}}}\xspace}
\providecommand{\urY}{\ensuremath{\underline{\mathrm{Y}}}\xspace}
\providecommand{\urZ}{\ensuremath{\underline{\mathrm{Z}}}\xspace}

\providecommand{\hrA}{\ensuremath{\widehat{\mathrm{A}}}\xspace}
\providecommand{\hrB}{\ensuremath{\widehat{\mathrm{B}}}\xspace}
\providecommand{\hrC}{\ensuremath{\widehat{\mathrm{C}}}\xspace}
\providecommand{\hrD}{\ensuremath{\widehat{\mathrm{D}}}\xspace}
\providecommand{\hrE}{\ensuremath{\widehat{\mathrm{E}}}\xspace}
\providecommand{\hrF}{\ensuremath{\widehat{\mathrm{F}}}\xspace}
\providecommand{\hrG}{\ensuremath{\widehat{\mathrm{G}}}\xspace}
\providecommand{\hrH}{\ensuremath{\widehat{\mathrm{H}}}\xspace}
\providecommand{\hrI}{\ensuremath{\widehat{\mathrm{I}}}\xspace}
\providecommand{\hrJ}{\ensuremath{\widehat{\mathrm{J}}}\xspace}
\providecommand{\hrK}{\ensuremath{\widehat{\mathrm{K}}}\xspace}
\providecommand{\hrL}{\ensuremath{\widehat{\mathrm{L}}}\xspace}
\providecommand{\hrM}{\ensuremath{\widehat{\mathrm{M}}}\xspace}
\providecommand{\hrN}{\ensuremath{\widehat{\mathrm{N}}}\xspace}
\providecommand{\hrO}{\ensuremath{\widehat{\mathrm{O}}}\xspace}
\providecommand{\hrP}{\ensuremath{\widehat{\mathrm{P}}}\xspace}
\providecommand{\hrQ}{\ensuremath{\widehat{\mathrm{Q}}}\xspace}
\providecommand{\hrR}{\ensuremath{\widehat{\mathrm{R}}}\xspace}
\providecommand{\hrS}{\ensuremath{\widehat{\mathrm{S}}}\xspace}
\providecommand{\hrT}{\ensuremath{\widehat{\mathrm{T}}}\xspace}
\providecommand{\hrU}{\ensuremath{\widehat{\mathrm{U}}}\xspace}
\providecommand{\hrV}{\ensuremath{\widehat{\mathrm{V}}}\xspace}
\providecommand{\hrW}{\ensuremath{\widehat{\mathrm{W}}}\xspace}
\providecommand{\hrX}{\ensuremath{\widehat{\mathrm{X}}}\xspace}
\providecommand{\hrY}{\ensuremath{\widehat{\mathrm{Y}}}\xspace}
\providecommand{\hrZ}{\ensuremath{\widehat{\mathrm{Z}}}\xspace}

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

%---- frak letters

\providecommand{\ffa}{\ensuremath{\mathfrak{a}}\xspace}
\providecommand{\ffb}{\ensuremath{\mathfrak{b}}\xspace}
\providecommand{\ffc}{\ensuremath{\mathfrak{c}}\xspace}
\providecommand{\ffd}{\ensuremath{\mathfrak{d}}\xspace}
\providecommand{\ffe}{\ensuremath{\mathfrak{e}}\xspace}
\providecommand{\fff}{\ensuremath{\mathfrak{f}}\xspace}
\providecommand{\ffg}{\ensuremath{\mathfrak{g}}\xspace}
\providecommand{\ffh}{\ensuremath{\mathfrak{h}}\xspace}
\providecommand{\ffi}{\ensuremath{\mathfrak{i}}\xspace}
\providecommand{\ffj}{\ensuremath{\mathfrak{j}}\xspace}
\providecommand{\ffk}{\ensuremath{\mathfrak{k}}\xspace}
\providecommand{\ffl}{\ensuremath{\mathfrak{l}}\xspace}
\providecommand{\ffm}{\ensuremath{\mathfrak{m}}\xspace}
\providecommand{\ffn}{\ensuremath{\mathfrak{n}}\xspace}
\providecommand{\ffo}{\ensuremath{\mathfrak{o}}\xspace}
\providecommand{\ffp}{\ensuremath{\mathfrak{p}}\xspace}
\providecommand{\ffq}{\ensuremath{\mathfrak{q}}\xspace}
\providecommand{\ffr}{\ensuremath{\mathfrak{r}}\xspace}
\providecommand{\ffs}{\ensuremath{\mathfrak{s}}\xspace}
\providecommand{\fft}{\ensuremath{\mathfrak{t}}\xspace}
\providecommand{\ffu}{\ensuremath{\mathfrak{u}}\xspace}
\providecommand{\ffv}{\ensuremath{\mathfrak{v}}\xspace}
\providecommand{\ffw}{\ensuremath{\mathfrak{w}}\xspace}
\providecommand{\ffx}{\ensuremath{\mathfrak{x}}\xspace}
\providecommand{\ffy}{\ensuremath{\mathfrak{y}}\xspace}
\providecommand{\ffz}{\ensuremath{\mathfrak{z}}\xspace}
\providecommand{\ffA}{\ensuremath{\mathfrak{A}}\xspace}
\providecommand{\ffB}{\ensuremath{\mathfrak{B}}\xspace}
\providecommand{\ffC}{\ensuremath{\mathfrak{C}}\xspace}
\providecommand{\ffD}{\ensuremath{\mathfrak{D}}\xspace}
\providecommand{\ffE}{\ensuremath{\mathfrak{E}}\xspace}
\providecommand{\ffF}{\ensuremath{\mathfrak{F}}\xspace}
\providecommand{\ffG}{\ensuremath{\mathfrak{G}}\xspace}
\providecommand{\ffH}{\ensuremath{\mathfrak{H}}\xspace}
\providecommand{\ffI}{\ensuremath{\mathfrak{I}}\xspace}
\providecommand{\ffJ}{\ensuremath{\mathfrak{J}}\xspace}
\providecommand{\ffK}{\ensuremath{\mathfrak{K}}\xspace}
\providecommand{\ffL}{\ensuremath{\mathfrak{L}}\xspace}
\providecommand{\ffM}{\ensuremath{\mathfrak{M}}\xspace}
\providecommand{\ffN}{\ensuremath{\mathfrak{N}}\xspace}
\providecommand{\ffO}{\ensuremath{\mathfrak{O}}\xspace}
\providecommand{\ffP}{\ensuremath{\mathfrak{P}}\xspace}
\providecommand{\ffQ}{\ensuremath{\mathfrak{Q}}\xspace}
\providecommand{\ffR}{\ensuremath{\mathfrak{R}}\xspace}
\providecommand{\ffS}{\ensuremath{\mathfrak{S}}\xspace}
\providecommand{\ffT}{\ensuremath{\mathfrak{T}}\xspace}
\providecommand{\ffU}{\ensuremath{\mathfrak{U}}\xspace}
\providecommand{\ffV}{\ensuremath{\mathfrak{V}}\xspace}
\providecommand{\ffW}{\ensuremath{\mathfrak{W}}\xspace}
\providecommand{\ffX}{\ensuremath{\mathfrak{X}}\xspace}
\providecommand{\ffY}{\ensuremath{\mathfrak{Y}}\xspace}
\providecommand{\ffZ}{\ensuremath{\mathfrak{Z}}\xspace}

\providecommand{\dffa}{\ensuremath{\dot{\mathfrak{a}}}\xspace}
\providecommand{\dffb}{\ensuremath{\dot{\mathfrak{b}}}\xspace}
\providecommand{\dffc}{\ensuremath{\dot{\mathfrak{c}}}\xspace}
\providecommand{\dffd}{\ensuremath{\dot{\mathfrak{d}}}\xspace}
\providecommand{\dffe}{\ensuremath{\dot{\mathfrak{e}}}\xspace}
\providecommand{\dfff}{\ensuremath{\dot{\mathfrak{f}}}\xspace}
\providecommand{\dffg}{\ensuremath{\dot{\mathfrak{g}}}\xspace}
\providecommand{\dffh}{\ensuremath{\dot{\mathfrak{h}}}\xspace}
\providecommand{\dffi}{\ensuremath{\dot{\mathfrak{i}}}\xspace}
\providecommand{\dffj}{\ensuremath{\dot{\mathfrak{j}}}\xspace}
\providecommand{\dffk}{\ensuremath{\dot{\mathfrak{k}}}\xspace}
\providecommand{\dffl}{\ensuremath{\dot{\mathfrak{l}}}\xspace}
\providecommand{\dffm}{\ensuremath{\dot{\mathfrak{m}}}\xspace}
\providecommand{\dffn}{\ensuremath{\dot{\mathfrak{n}}}\xspace}
\providecommand{\dffo}{\ensuremath{\dot{\mathfrak{o}}}\xspace}
\providecommand{\dffp}{\ensuremath{\dot{\mathfrak{p}}}\xspace}
\providecommand{\dffq}{\ensuremath{\dot{\mathfrak{q}}}\xspace}
\providecommand{\dffr}{\ensuremath{\dot{\mathfrak{r}}}\xspace}
\providecommand{\dffs}{\ensuremath{\dot{\mathfrak{s}}}\xspace}
\providecommand{\dfft}{\ensuremath{\dot{\mathfrak{t}}}\xspace}
\providecommand{\dffu}{\ensuremath{\dot{\mathfrak{u}}}\xspace}
\providecommand{\dffv}{\ensuremath{\dot{\mathfrak{v}}}\xspace}
\providecommand{\dffw}{\ensuremath{\dot{\mathfrak{w}}}\xspace}
\providecommand{\dffx}{\ensuremath{\dot{\mathfrak{x}}}\xspace}
\providecommand{\dffy}{\ensuremath{\dot{\mathfrak{y}}}\xspace}
\providecommand{\dffz}{\ensuremath{\dot{\mathfrak{z}}}\xspace}
\providecommand{\dffA}{\ensuremath{\dot{\mathfrak{A}}}\xspace}
\providecommand{\dffB}{\ensuremath{\dot{\mathfrak{B}}}\xspace}
\providecommand{\dffC}{\ensuremath{\dot{\mathfrak{C}}}\xspace}
\providecommand{\dffD}{\ensuremath{\dot{\mathfrak{D}}}\xspace}
\providecommand{\dffE}{\ensuremath{\dot{\mathfrak{E}}}\xspace}
\providecommand{\dffF}{\ensuremath{\dot{\mathfrak{F}}}\xspace}
\providecommand{\dffG}{\ensuremath{\dot{\mathfrak{G}}}\xspace}
\providecommand{\dffH}{\ensuremath{\dot{\mathfrak{H}}}\xspace}
\providecommand{\dffI}{\ensuremath{\dot{\mathfrak{I}}}\xspace}
\providecommand{\dffJ}{\ensuremath{\dot{\mathfrak{J}}}\xspace}
\providecommand{\dffK}{\ensuremath{\dot{\mathfrak{K}}}\xspace}
\providecommand{\dffL}{\ensuremath{\dot{\mathfrak{L}}}\xspace}
\providecommand{\dffM}{\ensuremath{\dot{\mathfrak{M}}}\xspace}
\providecommand{\dffN}{\ensuremath{\dot{\mathfrak{N}}}\xspace}
\providecommand{\dffO}{\ensuremath{\dot{\mathfrak{O}}}\xspace}
\providecommand{\dffP}{\ensuremath{\dot{\mathfrak{P}}}\xspace}
\providecommand{\dffQ}{\ensuremath{\dot{\mathfrak{Q}}}\xspace}
\providecommand{\dffR}{\ensuremath{\dot{\mathfrak{R}}}\xspace}
\providecommand{\dffS}{\ensuremath{\dot{\mathfrak{S}}}\xspace}
\providecommand{\dffT}{\ensuremath{\dot{\mathfrak{T}}}\xspace}
\providecommand{\dffU}{\ensuremath{\dot{\mathfrak{U}}}\xspace}
\providecommand{\dffV}{\ensuremath{\dot{\mathfrak{V}}}\xspace}
\providecommand{\dffW}{\ensuremath{\dot{\mathfrak{W}}}\xspace}
\providecommand{\dffX}{\ensuremath{\dot{\mathfrak{X}}}\xspace}
\providecommand{\dffY}{\ensuremath{\dot{\mathfrak{Y}}}\xspace}
\providecommand{\dffZ}{\ensuremath{\dot{\mathfrak{Z}}}\xspace}

\providecommand{\tffa}{\ensuremath{\widetilde{\mathfrak{a}}}\xspace}
\providecommand{\tffb}{\ensuremath{\widetilde{\mathfrak{b}}}\xspace}
\providecommand{\tffc}{\ensuremath{\widetilde{\mathfrak{c}}}\xspace}
\providecommand{\tffd}{\ensuremath{\widetilde{\mathfrak{d}}}\xspace}
\providecommand{\tffe}{\ensuremath{\widetilde{\mathfrak{e}}}\xspace}
\providecommand{\tfff}{\ensuremath{\widetilde{\mathfrak{f}}}\xspace}
\providecommand{\tffg}{\ensuremath{\widetilde{\mathfrak{g}}}\xspace}
\providecommand{\tffh}{\ensuremath{\widetilde{\mathfrak{h}}}\xspace}
\providecommand{\tffi}{\ensuremath{\widetilde{\mathfrak{i}}}\xspace}
\providecommand{\tffj}{\ensuremath{\widetilde{\mathfrak{j}}}\xspace}
\providecommand{\tffk}{\ensuremath{\widetilde{\mathfrak{k}}}\xspace}
\providecommand{\tffl}{\ensuremath{\widetilde{\mathfrak{l}}}\xspace}
\providecommand{\tffm}{\ensuremath{\widetilde{\mathfrak{m}}}\xspace}
\providecommand{\tffn}{\ensuremath{\widetilde{\mathfrak{n}}}\xspace}
\providecommand{\tffo}{\ensuremath{\widetilde{\mathfrak{o}}}\xspace}
\providecommand{\tffp}{\ensuremath{\widetilde{\mathfrak{p}}}\xspace}
\providecommand{\tffq}{\ensuremath{\widetilde{\mathfrak{q}}}\xspace}
\providecommand{\tffr}{\ensuremath{\widetilde{\mathfrak{r}}}\xspace}
\providecommand{\tffs}{\ensuremath{\widetilde{\mathfrak{s}}}\xspace}
\providecommand{\tfft}{\ensuremath{\widetilde{\mathfrak{t}}}\xspace}
\providecommand{\tffu}{\ensuremath{\widetilde{\mathfrak{u}}}\xspace}
\providecommand{\tffv}{\ensuremath{\widetilde{\mathfrak{v}}}\xspace}
\providecommand{\tffw}{\ensuremath{\widetilde{\mathfrak{w}}}\xspace}
\providecommand{\tffx}{\ensuremath{\widetilde{\mathfrak{x}}}\xspace}
\providecommand{\tffy}{\ensuremath{\widetilde{\mathfrak{y}}}\xspace}
\providecommand{\tffz}{\ensuremath{\widetilde{\mathfrak{z}}}\xspace}
\providecommand{\tffA}{\ensuremath{\widetilde{\mathfrak{A}}}\xspace}
\providecommand{\tffB}{\ensuremath{\widetilde{\mathfrak{B}}}\xspace}
\providecommand{\tffC}{\ensuremath{\widetilde{\mathfrak{C}}}\xspace}
\providecommand{\tffD}{\ensuremath{\widetilde{\mathfrak{D}}}\xspace}
\providecommand{\tffE}{\ensuremath{\widetilde{\mathfrak{E}}}\xspace}
\providecommand{\tffF}{\ensuremath{\widetilde{\mathfrak{F}}}\xspace}
\providecommand{\tffG}{\ensuremath{\widetilde{\mathfrak{G}}}\xspace}
\providecommand{\tffH}{\ensuremath{\widetilde{\mathfrak{H}}}\xspace}
\providecommand{\tffI}{\ensuremath{\widetilde{\mathfrak{I}}}\xspace}
\providecommand{\tffJ}{\ensuremath{\widetilde{\mathfrak{J}}}\xspace}
\providecommand{\tffK}{\ensuremath{\widetilde{\mathfrak{K}}}\xspace}
\providecommand{\tffL}{\ensuremath{\widetilde{\mathfrak{L}}}\xspace}
\providecommand{\tffM}{\ensuremath{\widetilde{\mathfrak{M}}}\xspace}
\providecommand{\tffN}{\ensuremath{\widetilde{\mathfrak{N}}}\xspace}
\providecommand{\tffO}{\ensuremath{\widetilde{\mathfrak{O}}}\xspace}
\providecommand{\tffP}{\ensuremath{\widetilde{\mathfrak{P}}}\xspace}
\providecommand{\tffQ}{\ensuremath{\widetilde{\mathfrak{Q}}}\xspace}
\providecommand{\tffR}{\ensuremath{\widetilde{\mathfrak{R}}}\xspace}
\providecommand{\tffS}{\ensuremath{\widetilde{\mathfrak{S}}}\xspace}
\providecommand{\tffT}{\ensuremath{\widetilde{\mathfrak{T}}}\xspace}
\providecommand{\tffU}{\ensuremath{\widetilde{\mathfrak{U}}}\xspace}
\providecommand{\tffV}{\ensuremath{\widetilde{\mathfrak{V}}}\xspace}
\providecommand{\tffW}{\ensuremath{\widetilde{\mathfrak{W}}}\xspace}
\providecommand{\tffX}{\ensuremath{\widetilde{\mathfrak{X}}}\xspace}
\providecommand{\tffY}{\ensuremath{\widetilde{\mathfrak{Y}}}\xspace}
\providecommand{\tffZ}{\ensuremath{\widetilde{\mathfrak{Z}}}\xspace}

\providecommand{\hffa}{\ensuremath{\widehat{\mathfrak{a}}}\xspace}
\providecommand{\hffb}{\ensuremath{\widehat{\mathfrak{b}}}\xspace}
\providecommand{\hffc}{\ensuremath{\widehat{\mathfrak{c}}}\xspace}
\providecommand{\hffd}{\ensuremath{\widehat{\mathfrak{d}}}\xspace}
\providecommand{\hffe}{\ensuremath{\widehat{\mathfrak{e}}}\xspace}
\providecommand{\hfff}{\ensuremath{\widehat{\mathfrak{f}}}\xspace}
\providecommand{\hffg}{\ensuremath{\widehat{\mathfrak{g}}}\xspace}
\providecommand{\hffh}{\ensuremath{\widehat{\mathfrak{h}}}\xspace}
\providecommand{\hffi}{\ensuremath{\widehat{\mathfrak{i}}}\xspace}
\providecommand{\hffj}{\ensuremath{\widehat{\mathfrak{j}}}\xspace}
\providecommand{\hffk}{\ensuremath{\widehat{\mathfrak{k}}}\xspace}
\providecommand{\hffl}{\ensuremath{\widehat{\mathfrak{l}}}\xspace}
\providecommand{\hffm}{\ensuremath{\widehat{\mathfrak{m}}}\xspace}
\providecommand{\hffn}{\ensuremath{\widehat{\mathfrak{n}}}\xspace}
\providecommand{\hffo}{\ensuremath{\widehat{\mathfrak{o}}}\xspace}
\providecommand{\hffp}{\ensuremath{\widehat{\mathfrak{p}}}\xspace}
\providecommand{\hffq}{\ensuremath{\widehat{\mathfrak{q}}}\xspace}
\providecommand{\hffr}{\ensuremath{\widehat{\mathfrak{r}}}\xspace}
\providecommand{\hffs}{\ensuremath{\widehat{\mathfrak{s}}}\xspace}
\providecommand{\hfft}{\ensuremath{\widehat{\mathfrak{t}}}\xspace}
\providecommand{\hffu}{\ensuremath{\widehat{\mathfrak{u}}}\xspace}
\providecommand{\hffv}{\ensuremath{\widehat{\mathfrak{v}}}\xspace}
\providecommand{\hffw}{\ensuremath{\widehat{\mathfrak{w}}}\xspace}
\providecommand{\hffx}{\ensuremath{\widehat{\mathfrak{x}}}\xspace}
\providecommand{\hffy}{\ensuremath{\widehat{\mathfrak{y}}}\xspace}
\providecommand{\hffz}{\ensuremath{\widehat{\mathfrak{z}}}\xspace}
\providecommand{\hffA}{\ensuremath{\widehat{\mathfrak{A}}}\xspace}
\providecommand{\hffB}{\ensuremath{\widehat{\mathfrak{B}}}\xspace}
\providecommand{\hffC}{\ensuremath{\widehat{\mathfrak{C}}}\xspace}
\providecommand{\hffD}{\ensuremath{\widehat{\mathfrak{D}}}\xspace}
\providecommand{\hffE}{\ensuremath{\widehat{\mathfrak{E}}}\xspace}
\providecommand{\hffF}{\ensuremath{\widehat{\mathfrak{F}}}\xspace}
\providecommand{\hffG}{\ensuremath{\widehat{\mathfrak{G}}}\xspace}
\providecommand{\hffH}{\ensuremath{\widehat{\mathfrak{H}}}\xspace}
\providecommand{\hffI}{\ensuremath{\widehat{\mathfrak{I}}}\xspace}
\providecommand{\hffJ}{\ensuremath{\widehat{\mathfrak{J}}}\xspace}
\providecommand{\hffK}{\ensuremath{\widehat{\mathfrak{K}}}\xspace}
\providecommand{\hffL}{\ensuremath{\widehat{\mathfrak{L}}}\xspace}
\providecommand{\hffM}{\ensuremath{\widehat{\mathfrak{M}}}\xspace}
\providecommand{\hffN}{\ensuremath{\widehat{\mathfrak{N}}}\xspace}
\providecommand{\hffO}{\ensuremath{\widehat{\mathfrak{O}}}\xspace}
\providecommand{\hffP}{\ensuremath{\widehat{\mathfrak{P}}}\xspace}
\providecommand{\hffQ}{\ensuremath{\widehat{\mathfrak{Q}}}\xspace}
\providecommand{\hffR}{\ensuremath{\widehat{\mathfrak{R}}}\xspace}
\providecommand{\hffS}{\ensuremath{\widehat{\mathfrak{S}}}\xspace}
\providecommand{\hffT}{\ensuremath{\widehat{\mathfrak{T}}}\xspace}
\providecommand{\hffU}{\ensuremath{\widehat{\mathfrak{U}}}\xspace}
\providecommand{\hffV}{\ensuremath{\widehat{\mathfrak{V}}}\xspace}
\providecommand{\hffW}{\ensuremath{\widehat{\mathfrak{W}}}\xspace}
\providecommand{\hffX}{\ensuremath{\widehat{\mathfrak{X}}}\xspace}
\providecommand{\hffY}{\ensuremath{\widehat{\mathfrak{Y}}}\xspace}
\providecommand{\hffZ}{\ensuremath{\widehat{\mathfrak{Z}}}\xspace}

\providecommand{\bffa}{\ensuremath{\overline{\mathfrak{a}}}\xspace}
\providecommand{\bffb}{\ensuremath{\overline{\mathfrak{b}}}\xspace}
\providecommand{\bffc}{\ensuremath{\overline{\mathfrak{c}}}\xspace}
\providecommand{\bffd}{\ensuremath{\overline{\mathfrak{d}}}\xspace}
\providecommand{\bffe}{\ensuremath{\overline{\mathfrak{e}}}\xspace}
\providecommand{\bfff}{\ensuremath{\overline{\mathfrak{f}}}\xspace}
\providecommand{\bffg}{\ensuremath{\overline{\mathfrak{g}}}\xspace}
\providecommand{\bffh}{\ensuremath{\overline{\mathfrak{h}}}\xspace}
\providecommand{\bffi}{\ensuremath{\overline{\mathfrak{i}}}\xspace}
\providecommand{\bffj}{\ensuremath{\overline{\mathfrak{j}}}\xspace}
\providecommand{\bffk}{\ensuremath{\overline{\mathfrak{k}}}\xspace}
\providecommand{\bffl}{\ensuremath{\overline{\mathfrak{l}}}\xspace}
\providecommand{\bffm}{\ensuremath{\overline{\mathfrak{m}}}\xspace}
\providecommand{\bffn}{\ensuremath{\overline{\mathfrak{n}}}\xspace}
\providecommand{\bffo}{\ensuremath{\overline{\mathfrak{o}}}\xspace}
\providecommand{\bffp}{\ensuremath{\overline{\mathfrak{p}}}\xspace}
\providecommand{\bffq}{\ensuremath{\overline{\mathfrak{q}}}\xspace}
\providecommand{\bffr}{\ensuremath{\overline{\mathfrak{r}}}\xspace}
\providecommand{\bffs}{\ensuremath{\overline{\mathfrak{s}}}\xspace}
\providecommand{\bfft}{\ensuremath{\overline{\mathfrak{t}}}\xspace}
\providecommand{\bffu}{\ensuremath{\overline{\mathfrak{u}}}\xspace}
\providecommand{\bffv}{\ensuremath{\overline{\mathfrak{v}}}\xspace}
\providecommand{\bffw}{\ensuremath{\overline{\mathfrak{w}}}\xspace}
\providecommand{\bffx}{\ensuremath{\overline{\mathfrak{x}}}\xspace}
\providecommand{\bffy}{\ensuremath{\overline{\mathfrak{y}}}\xspace}
\providecommand{\bffz}{\ensuremath{\overline{\mathfrak{z}}}\xspace}
\providecommand{\bffA}{\ensuremath{\overline{\mathfrak{A}}}\xspace}
\providecommand{\bffB}{\ensuremath{\overline{\mathfrak{B}}}\xspace}
\providecommand{\bffC}{\ensuremath{\overline{\mathfrak{C}}}\xspace}
\providecommand{\bffD}{\ensuremath{\overline{\mathfrak{D}}}\xspace}
\providecommand{\bffE}{\ensuremath{\overline{\mathfrak{E}}}\xspace}
\providecommand{\bffF}{\ensuremath{\overline{\mathfrak{F}}}\xspace}
\providecommand{\bffG}{\ensuremath{\overline{\mathfrak{G}}}\xspace}
\providecommand{\bffH}{\ensuremath{\overline{\mathfrak{H}}}\xspace}
\providecommand{\bffI}{\ensuremath{\overline{\mathfrak{I}}}\xspace}
\providecommand{\bffJ}{\ensuremath{\overline{\mathfrak{J}}}\xspace}
\providecommand{\bffK}{\ensuremath{\overline{\mathfrak{K}}}\xspace}
\providecommand{\bffL}{\ensuremath{\overline{\mathfrak{L}}}\xspace}
\providecommand{\bffM}{\ensuremath{\overline{\mathfrak{M}}}\xspace}
\providecommand{\bffN}{\ensuremath{\overline{\mathfrak{N}}}\xspace}
\providecommand{\bffO}{\ensuremath{\overline{\mathfrak{O}}}\xspace}
\providecommand{\bffP}{\ensuremath{\overline{\mathfrak{P}}}\xspace}
\providecommand{\bffQ}{\ensuremath{\overline{\mathfrak{Q}}}\xspace}
\providecommand{\bffR}{\ensuremath{\overline{\mathfrak{R}}}\xspace}
\providecommand{\bffS}{\ensuremath{\overline{\mathfrak{S}}}\xspace}
\providecommand{\bffT}{\ensuremath{\overline{\mathfrak{T}}}\xspace}
\providecommand{\bffU}{\ensuremath{\overline{\mathfrak{U}}}\xspace}
\providecommand{\bffV}{\ensuremath{\overline{\mathfrak{V}}}\xspace}
\providecommand{\bffW}{\ensuremath{\overline{\mathfrak{W}}}\xspace}
\providecommand{\bffX}{\ensuremath{\overline{\mathfrak{X}}}\xspace}
\providecommand{\bffY}{\ensuremath{\overline{\mathfrak{Y}}}\xspace}
\providecommand{\bffZ}{\ensuremath{\overline{\mathfrak{Z}}}\xspace}

\providecommand{\uffa}{\ensuremath{\underline{\mathfrak{a}}}\xspace}
\providecommand{\uffb}{\ensuremath{\underline{\mathfrak{b}}}\xspace}
\providecommand{\uffc}{\ensuremath{\underline{\mathfrak{c}}}\xspace}
\providecommand{\uffd}{\ensuremath{\underline{\mathfrak{d}}}\xspace}
\providecommand{\uffe}{\ensuremath{\underline{\mathfrak{e}}}\xspace}
\providecommand{\ufff}{\ensuremath{\underline{\mathfrak{f}}}\xspace}
\providecommand{\uffg}{\ensuremath{\underline{\mathfrak{g}}}\xspace}
\providecommand{\uffh}{\ensuremath{\underline{\mathfrak{h}}}\xspace}
\providecommand{\uffi}{\ensuremath{\underline{\mathfrak{i}}}\xspace}
\providecommand{\uffj}{\ensuremath{\underline{\mathfrak{j}}}\xspace}
\providecommand{\uffk}{\ensuremath{\underline{\mathfrak{k}}}\xspace}
\providecommand{\uffl}{\ensuremath{\underline{\mathfrak{l}}}\xspace}
\providecommand{\uffm}{\ensuremath{\underline{\mathfrak{m}}}\xspace}
\providecommand{\uffn}{\ensuremath{\underline{\mathfrak{n}}}\xspace}
\providecommand{\uffo}{\ensuremath{\underline{\mathfrak{o}}}\xspace}
\providecommand{\uffp}{\ensuremath{\underline{\mathfrak{p}}}\xspace}
\providecommand{\uffq}{\ensuremath{\underline{\mathfrak{q}}}\xspace}
\providecommand{\uffr}{\ensuremath{\underline{\mathfrak{r}}}\xspace}
\providecommand{\uffs}{\ensuremath{\underline{\mathfrak{s}}}\xspace}
\providecommand{\ufft}{\ensuremath{\underline{\mathfrak{t}}}\xspace}
\providecommand{\uffu}{\ensuremath{\underline{\mathfrak{u}}}\xspace}
\providecommand{\uffv}{\ensuremath{\underline{\mathfrak{v}}}\xspace}
\providecommand{\uffw}{\ensuremath{\underline{\mathfrak{w}}}\xspace}
\providecommand{\uffx}{\ensuremath{\underline{\mathfrak{x}}}\xspace}
\providecommand{\uffy}{\ensuremath{\underline{\mathfrak{y}}}\xspace}
\providecommand{\uffz}{\ensuremath{\underline{\mathfrak{z}}}\xspace}
\providecommand{\uffA}{\ensuremath{\underline{\mathfrak{A}}}\xspace}
\providecommand{\uffB}{\ensuremath{\underline{\mathfrak{B}}}\xspace}
\providecommand{\uffC}{\ensuremath{\underline{\mathfrak{C}}}\xspace}
\providecommand{\uffD}{\ensuremath{\underline{\mathfrak{D}}}\xspace}
\providecommand{\uffE}{\ensuremath{\underline{\mathfrak{E}}}\xspace}
\providecommand{\uffF}{\ensuremath{\underline{\mathfrak{F}}}\xspace}
\providecommand{\uffG}{\ensuremath{\underline{\mathfrak{G}}}\xspace}
\providecommand{\uffH}{\ensuremath{\underline{\mathfrak{H}}}\xspace}
\providecommand{\uffI}{\ensuremath{\underline{\mathfrak{I}}}\xspace}
\providecommand{\uffJ}{\ensuremath{\underline{\mathfrak{J}}}\xspace}
\providecommand{\uffK}{\ensuremath{\underline{\mathfrak{K}}}\xspace}
\providecommand{\uffL}{\ensuremath{\underline{\mathfrak{L}}}\xspace}
\providecommand{\uffM}{\ensuremath{\underline{\mathfrak{M}}}\xspace}
\providecommand{\uffN}{\ensuremath{\underline{\mathfrak{N}}}\xspace}
\providecommand{\uffO}{\ensuremath{\underline{\mathfrak{O}}}\xspace}
\providecommand{\uffP}{\ensuremath{\underline{\mathfrak{P}}}\xspace}
\providecommand{\uffQ}{\ensuremath{\underline{\mathfrak{Q}}}\xspace}
\providecommand{\uffR}{\ensuremath{\underline{\mathfrak{R}}}\xspace}
\providecommand{\uffS}{\ensuremath{\underline{\mathfrak{S}}}\xspace}
\providecommand{\uffT}{\ensuremath{\underline{\mathfrak{T}}}\xspace}
\providecommand{\uffU}{\ensuremath{\underline{\mathfrak{U}}}\xspace}
\providecommand{\uffV}{\ensuremath{\underline{\mathfrak{V}}}\xspace}
\providecommand{\uffW}{\ensuremath{\underline{\mathfrak{W}}}\xspace}
\providecommand{\uffX}{\ensuremath{\underline{\mathfrak{X}}}\xspace}
\providecommand{\uffY}{\ensuremath{\underline{\mathfrak{Y}}}\xspace}
\providecommand{\uffZ}{\ensuremath{\underline{\mathfrak{Z}}}\xspace}

%---- functions

\providecommand{\fid}{\mathrm{id}}

%---- groups

\providecommand{\OO}[1]{\ensuremath{\mathrm{O}(#1)}\xspace}
\providecommand{\SO}[1]{\ensuremath{\mathrm{SO}(#1)}\xspace}
\providecommand{\ISO}[1]{\ensuremath{\mathrm{ISO}(#1)}\xspace}
\providecommand{\U}[1]{\ensuremath{\mathrm{U}(#1)}\xspace}
\providecommand{\SU}[1]{\ensuremath{\mathrm{SU}(#1)}\xspace}
\providecommand{\SL}[2]{\ensuremath{\mathrm{SL}_{#1}(#2)}\xspace}
\providecommand{\GL}[2]{\ensuremath{\mathrm{GL}_{#1}(#2)}\xspace}

%---- algebras

\providecommand{\liebraket}[2]{\ensuremath{\left[ #1,\, #2 \right]}}
\providecommand{\no}[1]{\ensuremath{\colon #1 \colon}\xspace}

%---- inline partial derivatives (use $\ipd{s}$ for $\partial_s$)

\providecommand{\ipd}[1]{\partial_{#1}}
\providecommand{\pd}{\ensuremath{\partial}\xspace}
\providecommand{\bpd}{\ensuremath{\overline{\partial}}\xspace}

\providecommand{\lrpd}[2]{\frac{\overset{\leftrightarrow}{\partial} #1}{\partial #2}}
\providecommand{\lpd}[2]{\frac{\overset{\leftarrow}{\partial} #1}{\partial #2}}
\providecommand{\rpd}[2]{\frac{\overset{\rightarrow}{\partial} #1}{\partial #2}}

\providecommand{\lripd}[1]{\overset{\leftrightarrow}{\partial_{#1}}}
\providecommand{\lipd}[1]{\overset{\leftarrow}{\partial_{#1}}}
\providecommand{\ripd}[1]{\overset{\rightarrow}{\partial_{#1}}}

\providecommand{\lrfdv}[2]{\frac{\overset{\leftrightarrow}{\delta} #1}{\delta #2}}
\providecommand{\lfdv}[2]{\frac{\overset{\leftarrow}{\delta} #1}{\delta #2}}
\providecommand{\rfdv}[2]{\frac{\overset{\rightarrow}{\delta} #1}{\delta #2}}

%---- metric (use $\dss[n]{s}$ for $\mathrm{d}s^n$, [n] is optional)

\providecommand{\dss}[2][1]{\ifthenelse{\equal{#1}{1}}
                                       {\dd{#2}}
                                       {\dd{#2^{#1}}}
                           }

%---- integrals, sums and products

\providecommand{\zeroinfint}[1]{\int\limits_0^{+\infty} \dd{#1}}
\providecommand{\infzeroint}[1]{\int\limits_{-\infty}^0 \dd{#1}}
\providecommand{\infinfint}[1]{\int\limits_{-\infty}^{+\infty} \dd{#1}}
\providecommand{\finiteint}[3]{\int\limits_{#2}^{#3} \dd{#1}}

\providecommand{\zeroinfsum}[1]{\sum\limits_{#1 = 0}^{+\infty}}
\providecommand{\infzerosum}[1]{\sum\limits_{#1 = -\infty}^0}
\providecommand{\infinfsum}[1]{\sum\limits_{#1 = -\infty}^{+\infty}}
\providecommand{\finitesum}[3]{\sum\limits_{#1 = #2}^{#3}}

\providecommand{\zeroinfprod}[1]{\prod\limits_{#1 = 0}^{+\infty}}
\providecommand{\infzeroprod}[1]{\prod\limits_{#1 = -\infty}^0}
\providecommand{\infinfprod}[1]{\prod\limits_{#1 = -\infty}^{+\infty}}
\providecommand{\finiteprod}[3]{\prod\limits_{#1 = #2}^{#3}}

% vim: ft=tex