functions.sty

\ProvidesPackage{functions}

%%% AAAA
\newcommand{\abc}[1]{\xrightarrow{#1}} %% Limits with rightarrow condition
\newcommand{\abl}[2]{\xrightarrow{#1\rightarrow#2}} %% Limits with rightarrow and arrow
\newcommand{\angstrom}{\textup{\AA}} % Angstrom mathmode


%%% BBBBB
\renewcommand{\bf}{\textbf}
\newcommand{\cc}[1]{\overline{#1}} %%%% bar overline conjugate
\newcommand{\braN}{\bra{\Pneutron}} %%bra neutron
\newcommand{\braP}{\bra{\Pproton}}   %%bra proton
\newcommand{\bt}[1]{\epsilon_{#1}} %% Bianchi tensor
\newcommand{\bbar}{{\raisebox{3.5px}{$-$}\mkern -9.5mu b}} %% b bar
\newcommand{\bm}{\beta^-} %%decadimento beta meno
\newcommand{\bp}{\beta^+} %%decadimento beta piu
\newcommand{\bv}{Brunt-V\:ais\:al\:a}

%%%%%% CCCCCCCCCCCCCCCCCCCCCCC
\newcommand{\cha}{Chandrasekhar}
\newcommand{\chapref}[2]{\chapter{#1}
\begin{refsection}
#2
\printbibliography[heading=subbibliography]
\end{refsection}}

%%% DDDD
\newcommand{\dal}[1]{\nabla^2-\frac{1}{#1^2}\frac{\partial^2}{\partial t^2}}   %%% operatore di d'alambert: velocita da impostare. compatto
\newcommand{\dalof}[2]{\nabla^2#2-\frac{1}{#1^2}\frac{\partial^2#2}{\partial t^2}}   %%% operatore di d'alambert: velocita da impostare. Esteso
\newcommand{\decay}[2]{\xrightarrow[#1]{#2}} %% Limits with rightarrow condition
\newcommand{\decaya}[1]{\xrightarrow[#1]{\alpha}} %% Limits with rightarrow condition
\newcommand{\decaybp}[1]{\xrightarrow[#1]{\beta^+}} %% Limits with rightarrow condition
\newcommand{\decaybm}[1]{\xrightarrow[#1]{\beta^-}} %% Limits with rightarrow condition
\newcommand*{\ditto}{---\textquotedbl---} %% ditto same as above
\newcommand*\DAlambert{\mathop{}\!\mathbin\Box}

\newcommand{\PDof}[1]{\frac{\partial}{\partial #1}} %%%%Derivative of d/dx()
\newcommand{\TDof}[1]{\frac{d}{d #1}}
\newcommand{\PtwoDof}[1]{\frac{\partial^2}{{\partial #1}^2}}
\newcommand{\TtwoDof}[1]{\frac{d^2}{{d #1}^2}}
\newcommand{\PxDof}[2]{\frac{\partial^{#2}}{{\partial #1}^{#2}}}
\newcommand{\TxDof}[2]{\frac{d^{#2}}{{d #1}^{#2}}}

\newcommand{\PDy}[2]{\frac{\partial #2}{\partial #1}} %%% derivative dy/dx
\newcommand{\TDy}[2]{\frac{d #2}{d #1}}
\newcommand{\PtwoDy}[2]{\frac{\partial^2 #2}{{\partial #1}^2}}
\newcommand{\TtwoDy}[2]{\frac{d^2 #2}{{d #1}^2}}
\newcommand{\PxDy}[3]{\frac{\partial^{#2} #3}{{\partial #1}^{#2}}}
\newcommand{\TxDy}[3]{\frac{d^{#2}#3}{{d #1}^{#2}}}

\newcommand{\PDly}[2]{\frac{\partial \ln{#2}}{\partial \ln{#1}}} %%% derivative dlny/dlnx
\newcommand{\TDly}[2]{\frac{d \ln{#2}}{d \ln{#1}}}

\newcommand{\Dcvar}[2]{(#1)_{#2}}
\newcommand{\Devat}[2]{#1|_{#2}}
%\renewcommand{\div}[1]{\scap{\nabla}{#1}}
\newcommand{\densityscale}{H_{\rho}}


%%%%   EEEEEEEEEE

\newcommand{\ev}[1]{\colorbox{yellow}{$#1$}} %% colorbox
\newcommand{\evt}[1]{\colorbox{yellow}{\noindent\begin{minipage}{\widthof{#1}}#1\end{minipage}}} %%colorbox \text{}
\newcommand{\exv}[1]{\langle #1 \rangle} %%colorbox \text{}
\renewcommand{\exp}[1]{e^{#1}}  %Esponenziale
\newcommand{\ec}{\epsilon} %% cattura elettronica
\newcommand{\ER}{E_{\text{RYD}}} %% E_ryd
\newcommand{\Evar}[1]{#1'} %%% Variazione Euleriana
\newcommand{\expy}[1]{^{#1}} %%  Esponente >1 char

%%% FFFFFFFFF


%%%%%% GGGGGGGGGGGGGGGGGGGGGG

\newcommand{\gsun}{g_{\odot}} %% raggio solare
\newcommand{\gad}{\gamma_{Ad}}
\newcommand{\Gad}{\Gamma_{Ad}}

%%% HHHHHHHHH

\newcommand{\hr}{Hertzsprung-Russel}


%%%%%   IIIIIIIIIIII
\newcommand\irregularcircle[2]{% radius, irregularity		Irregular shape
  \pgfextra {\pgfmathsetmacro\len{(#1)+rand*(#2)}}
  +(0:\len pt)
  \foreach \a in {10,20,...,350}{
    \pgfextra {\pgfmathsetmacro\len{(#1)+rand*(#2)}}
    -- +(\a:\len pt)
  } -- cycle
}
\newcommand{\isw}[2]{\frac{e^{-i#1#2}}{#2}} % Ingoing spherical wave
\newcommand{\intsinf}{\int_{-\infty}^{+\infty}} %% integrale da -infinito a +infinito
\newcommand{\intzi}{\int_{0}^{+\infty}}  %% integrale da 0 a +infinito
\newcommand{\ints}[1]{\int_{-#1}^{+#1}}  %% integrale da -a a +a
\newcommand{\inte}[2]{\int_{#1}^{#2}}  %% integrale da A a B
\newcommand{\Id}[1]{\mathds{1}_{#1}}  %% Matrice unità di dimensione=parametro
\newcommand{\intu}[1]{\intertext{$\uparrow$ #1}} %% intertext freccia sopra
\newcommand{\intd}[1]{\intertext{$\downarrow$ #1}} %% intertext freccia sotto

%%%%%%%%%%%JJJJJJJJJJJJJJJJJJ
\newcommand{\jp}{J^{\Pi}}

%%% KKKKKKK

\newcommand{\kh}{kelvin-Helmholtz}

%%%%%    LLLLLLLL
%\newcommand{\lambdabar}{{\mkern0.75mu\mathchar '26\mkern -9.75mu\lambda}} %%Lambda bar
\newcommand{\lbt}[2]{$\left\{\begin{array}{l}#1\\#2\\ \end{array}\right.$} % parentesi grafa a sinistra 2 linee
\newcommand{\lu}{\mathcal{L}}
\newcommand*\Laplace{\mathop{}\!\mathbin\bigtriangleup}
\newcommand{\LaplaceSC}{\frac{1}{r^2}\PDof{r}(r^2\PDof{r})+\frac{1}{r^2\sin{\phi}^2}\PtwoDof{\theta}+\frac{1}{r^2\sin{\phi}}\PDof{\phi}(\sin{\phi}\PDof{\phi})}
\newcommand{\Lvar}[1]{\delta #1}
\newcommand{\lif}{Lifshitz}

%%% MMMMMMMMMMMMMMM
\newcommand{\msun}{M_{\odot}} %% massa solare
\newcommand{\Mcs}{\frac{MeV}{c^2}} %% massa solare
\newcommand{\Mif}{M_{if}}
\newcommand{\mblock}[1]{ \allowbreak ${#1}$ }


%%%%% NNNNNNNNNNNNNNNN
\newcommand{\nad}{\nabla_{Ad}}
\newcommand{\nTP}{(\PDy{\ln{P}}{\ln{T}})_s}
\newcommand{\nablaTact}{\nabla}
\newcommand{\nablaTacte}{(\TDly{P}{T})_s}
\newcommand{\nel}{\nabla_e}
\newcommand{\nele}{(\TDly{P}{T})_e}
\newcommand{\nmu}{\nabla_{\mu}}
\newcommand{\nmue}{(\TDly{P}{\mu})_s}
\newcommand{\nrad}{\nabla_{rad}}


%%% OOOOOOOOOOOO
\newcommand{\osw}[2]{\frac{e^{i#1#2}}{#2}} %%% Outgoing spherical wave

%%%%PPPPPPPPPPP
\newcommand{\pw}[2]{e^{i\vec{#1}\cdot\vec{#2}}} % Onda piana
\newcommand{\psiN}[1]{\psi_1(\vec{x_1}),\ldots,\psi_{#1}(\vec{x_{#1}})} % Funzione d'onda di un sistema di N particelle
\newcommand{\psiNP}[1]{\psi_1(\vec{-x_1}),\ldots,\psi_{#1}(\vec{-x_{#1}})} % Funzione d'onda di un sistema di N particelle sotto inversione di parità
\newcommand{\PO}{\mathcal{P}}  %%% Operatore parità
\newcommand{\paf}[3]{{#1}^{\frac{#2}{#3}}}  % (a)^(b/c)
\newcommand{\pcsun}{P_{\odot}^c} %% pressione centrale del sole 


%%%%RRRRRRRRRRRRRR
\newcommand{\rbt}[2]{$\left.\begin{array}{l}#1\\#2\\ \end{array}\right\}$} % parentesi grafa a destra 2 linee
\newcommand{\req}[1]{~\ref{eq:#1}} %% ~\ref{eq:ref}
\newcommand{\Ra}{$\alpha$ } %% alpha
\newcommand{\Rb}{$\beta$ } %% beta
\newcommand{\rsun}{R_{\odot}} %% raggio solare
\newcommand{\rhosun}{\overline{\rho}_{\odot}} %% densita media solare
\newcommand{\rhosunc}{\rho_{\odot}^c} %% densita centro solare
\newcommand{\risp}{rispettivamente}

\makeatletter%%Redeclaremathoperator
\newcommand\RedeclareMathOperator{%
  \@ifstar{\def\rmo@s{m}\rmo@redeclare}{\def\rmo@s{o}\rmo@redeclare}%
}
% this is taken from \renew@command
\newcommand\rmo@redeclare[2]{%
  \begingroup \escapechar\m@ne\xdef\@gtempa{{\string#1}}\endgroup
  \expandafter\@ifundefined\@gtempa
     {\@latex@error{\noexpand#1undefined}\@ehc}%
     \relax
  \expandafter\rmo@declmathop\rmo@s{#1}{#2}}
% This is just \@declmathop without \@ifdefinable
\newcommand\rmo@declmathop[3]{%
  \DeclareRobustCommand{#2}{\qopname\newmcodes@#1{#3}}%
}
\@onlypreamble\RedeclareMathOperator
\makeatother %%%Redeclaremathoperator
\newcommand{\gasconstant}{\mathcal{R}}


%%%%% SSSSSSSSSSSSS
%% Matrici di Pauli
\newcommand{\sigmax}{$\begin{pmatrix}0&1\\1&0\\\end{pmatrix}$}   % matrice pauli x
\newcommand{\sigmay}{$\begin{pmatrix}0&i\\-i&0\\\end{pmatrix}$}   % matrice pauli x
\newcommand{\sigmaz}{$\begin{pmatrix}1&0\\0&-1\\\end{pmatrix}$}   % matrice pauli x

\newcommand{\singleti}{\ket{\frac{1}{2},\frac{1}{2};S=0,S_z=0}} 
\newcommand{\singlete}[2]{\frac{\ket{+}_{#1}\ket{-}_{#2}-\ket{-}_{#1}\ket{+}–{#2}}{\sqrt{2}}}
\newcommand{\vpm}[1]{\vec{\sigma_{#1}}} %%% Vector pauli matrix

\newcommand{\scap}[2]{\vec{#1}\cdot\vec{#2}}  %%% prodotto scalare
\newcommand{\scapflex}[4]{#1{\vec{#2}}\cdot#3{\vec{#4}}}  %%% prodotto scalare comandi applicati ai vettori

\newcommand{\scapq}[2]{{#1}_{\mu}{#2}^{\mu}}  %%% prodotto scalare quadrivettori
\newcommand{\sphag}{Y_{lm}(\theta,\phi)}  %%% Sperical Harmonics argument l m
\newcommand{\spha}[4]{Y_{#1,#2}(#3,#4)}  %%% Sperical Harmonics argument l m
\newcommand{\sumzi}[1]{\sum_{#1=0}^{\infty}}  %%% Sum da 0 a infty con argomento
\newcommand{\sumft}[2]{\sum_{#1}^{#2}}  %%% Sum da 1 a 2 

\newcommand{\sci}[1]{\ 10^{#1}\ }  %%% 10^{arg1}
\newcommand{\sch}{Schwarzschild}
\newcommand{\subsecref}[2]{\subsection{#1}\begin{refsection}
#2
\printbibliography[heading=subbibliography]
\end{refsection}}


%%% TTTTT
%\renewcommand\thesection{\arabic{chapter}.\arabic{section}}  %%% subsection refernece
%\renewcommand\thesubsection{\Roman{subsection}}
%\makeatletter
%\renewcommand\p@subsection{\thesection.}
%\makeatother         										%%%%%

\newcommand{\PartialToc}{
\vspace*{1pc}\hrule\vspace*{0.5pc}% toc at beginning chapter
\startcontents[chapters]\vbox{\bf\Large 
\hypertarget{outline\thechapter}{\noindent Outline Cap. \thechapter}}
\printcontents[chapters]{}{1}{\setcounter{tocdepth}{3}}\vspace*{0.5pc}\hrule


\lfoot{\begingroup
\hypersetup{allcolors=blue}
\hyperlink{outline\thechapter}{Toc.\thechapter} Pg: \thepage (\thepart)Sec.\thesection,\hyperlink{toc}{Main Toc}\endgroup
}

}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}

\newcommand{\thalf}{t_{\frac{1}{2}}}
%\newcommand{\tref}[1]{~\ref{eq:#1}}  %%% Operatore inversione temporale
\newcommand{\tbf}[1]{\textbf{#1}\index{#1}}  %%% Operatore inversione temporale
\newcommand{\TO}{\mathcal{T}}  %%% Operatore inversione temporale
\newcommand{\tsv}[2]{\begin{pmatrix}#1\\#2\\\end{pmatrix}}  % vettore stato sistema 2 stati
\newcommand{\threesv}[3]{\begin{pmatrix}#1\\#2\\#3\end{pmatrix}}  % vettore stato sistema 3 stati
\newcommand{\txtrm}[1]{\begin{pmatrix}\cos{#1}&\sin{#1}\\-\sin{#1}&\cos{#1}\\\end{pmatrix}} % matrice rotazione 2x2

\newcommand{\tripleti}[1]{\ket{\frac{1}{2},\frac{1}{2};S=1,S_z=#1}}
\newcommand{\triplet}[2]{\left\{\begin{array}{c}\ket{+}_{#1}\ket{+}_{#2}\\\frac{\ket{+}_{#1}\ket{-}_{#2}+\ket{-}_{#1}\ket{+}_{#2}}{\sqrt{2}}\\\ket{-}_{#1}\ket{-}_{#2}\end{array}\right.}

\newcommand{\tripletz}[3]{\ifnum#1=-1 \ket{-}_{#2}\ket{-}_{#3} \else\ifnum#1=0 \frac{\ket{+}_{#2}\ket{-}_{#3}+\ket{-}_{#2}\ket{+}_{#3}}{\sqrt{2}} \else \ket{+}_{#2}\ket{+}_{#3}\fi\fi}

\newcommand{\tpc}[5]{%%%           Tikz plot caption
\captionsetup[figure]{format=plain,skip=0pt,indention=0pt}
{
\begin{figure}[#1]
\centering
\begin{tikzpicture}{#2}
\node at #3 {\parbox{#4}{\captionof{figure}{#5}}};   %\label{fig:myfig}\label{fig:~\ref{fig:myfig}}}};
\end{tikzpicture}
\end{figure}
}\clearpage
}                   %%%%%% 

\newcommand{\tsun}{\overline{T}_{\odot}}  %% T solare media
\newcommand{\tsunc}{T_{\odot}^c} %% T centro sole
\newcommand{\tsuns}{T^S_{\odot}} % temperatura superficie sole
\newcommand{\lsun}{\mathcal{L}_{\odot}} % Luminosita sole}
\newcommand{\tkh}{\tau_{KH}} % tempo di Kelvin Helmholtz
\newcommand{\thydro}{\tau_{Hyd}} % tempo di idrodinamic
\newcommand{\tff}{\tau_{FF}} % tempo di Free Fall
\newcommand{\ten}[1]{\tensor{#1}{_\cdot_\cdot}}
%\def\shrinkage{2.1mu}  %% ten
%\def\vecsign{\mathchar"017E}
%\def\dvecsign{\smash{\stackon[-1.95pt]{\mkern-\shrinkage\vecsign}{\rotatebox{180}{$\mkern-\shrinkage\vecsign$}}}}
%\def\ten#1{\def\useanchorwidth{T}\stackon[-4.2pt]{#1}{\,\dvecsign}}
%\stackMath

%%%%%%%%%%%%%%UUUUUUUUUUUUUUUUUUUU
%%%Units
% Astronomy
\DeclareSIUnit\parsec{pc}
\DeclareSIUnit\lightyear{ly}
\DeclareSIUnit\year{yr}
% Energy
\DeclareSIUnit\erg{erg}
\DeclareSIUnit\ev{ev}

% Momentum
\DeclareSIUnit\momentum{p}
%% Forces
\DeclareSIUnit\dyn{Dyne}
%% Maasss
\DeclareSIUnit\mass{mass}
\DeclareSIUnit\volume{volume}
%%%% Time
\DeclareSIUnit\minute{min}


%%%%    VVVVVVVVVVV
\newcommand{\vecp}[2]{\vec{#1}\wedge\vec{#2}} %%%Prodotto vettore
\newcommand{\vai}{V\"ais\"al\"a}

% --- Macro \xvec-------------------------------------
\makeatletter
\newlength\xvec@height%
\newlength\xvec@depth%
\newlength\xvec@width%
\newcommand{\xvec}[2][]{%
  \ifmmode%
    \settoheight{\xvec@height}{$#2$}%
    \settodepth{\xvec@depth}{$#2$}%
    \settowidth{\xvec@width}{$#2$}%
  \else%
    \settoheight{\xvec@height}{#2}%
    \settodepth{\xvec@depth}{#2}%
    \settowidth{\xvec@width}{#2}%
  \fi%
  \def\xvec@arg{#1}%
  \def\xvec@dd{:}%
  \def\xvec@d{.}%
  \raisebox{.2ex}{\raisebox{\xvec@height}{\rlap{%
    \kern.05em%  (Because left edge of drawing is at .05em)
    \begin{tikzpicture}[scale=1]
    \pgfsetroundcap
    \draw (.05em,0)--(\xvec@width-.05em,0);
    \draw (\xvec@width-.05em,0)--(\xvec@width-.15em, .075em);
    \draw (\xvec@width-.05em,0)--(\xvec@width-.15em,-.075em);
    \ifx\xvec@arg\xvec@d%
      \fill(\xvec@width*.45,.5ex) circle (.5pt);%
    \else\ifx\xvec@arg\xvec@dd%
      \fill(\xvec@width*.30,.5ex) circle (.5pt);%
      \fill(\xvec@width*.65,.5ex) circle (.5pt);%
    \fi\fi%
    \end{tikzpicture}%
  }}}%
  #2%
}
\makeatother

% --- Override \vec with an invocation of \xvec.
\let\stdvec\vec
\renewcommand{\vec}[1]{\xvec[]{#1}}
% --- Define \dvec and \ddvec for dotted and double-dotted vectors.
\newcommand{\dvec}[1]{\xvec[.]{#1}}
\newcommand{\ddvec}[1]{\xvec[:]{#1}}
%---------------------------------------------------------