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Diffstat (limited to 'macros/latex/contrib/nchairx/source/chairxmathDiffgeo.dtx')
-rw-r--r-- | macros/latex/contrib/nchairx/source/chairxmathDiffgeo.dtx | 574 |
1 files changed, 574 insertions, 0 deletions
diff --git a/macros/latex/contrib/nchairx/source/chairxmathDiffgeo.dtx b/macros/latex/contrib/nchairx/source/chairxmathDiffgeo.dtx new file mode 100644 index 0000000000..1acce1e09f --- /dev/null +++ b/macros/latex/contrib/nchairx/source/chairxmathDiffgeo.dtx @@ -0,0 +1,574 @@ +% \iffalse meta-comment +% +% Copyright (C) 2018 - 2021 by ChairX +% +% This file may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either +% version 1.3 of this license or (at your option) any later +% version. The latest version of this license is in: +% +% http://www.latex-project.org/lppl.txt +% +% and version 1.3 or later is part of all distributions of +% LaTeX version 2005/12/01 or later. +% +% This file contains the implementation of all differential geometry related macros . +% +% Macros have to be described by (delete the first %) +% %\begin{macro}{\macro} +% % Description of the implementation. +% % \begin{macrocode} +%\newcommand{\macro}[] {} +% % \end{macrocode} +% %\end{macro} +% +% The implementation and description will appear in the implementation +% part of the documentation. Use \subsubsection{} etc. for structuring. +% +% The documentation of the macros defined here has to be written in +% chairxmathDiffgeoDoc.dtx +%\fi +% +% First we check of macros should be included: +% \begin{macrocode} +\if@loadmath +% \end{macrocode} +% +% \subsubsection{General Differential Geometry} \label{sec:GeneralMacrosDiffGeo} +% +%\begin{macro}{\Lie} +% \begin{macrocode} +\newcommand{\Lie}{\mathscr{L}} +% \end{macrocode} +%\end{macro} +% +% A generic bracket as paired delimiter, used in several other macros +% +%\begin{macro}{\ch@irxbbracket} +% \begin{macrocode} +\DeclarePairedDelimiter{\ch@irxbracket}{[}{]} +% \end{macrocode} +% \end{macro} +% +% A generic double bracket as paired delimiter, used in several other macros +% +%\begin{macro}{\ch@irxbbracket} +% \begin{macrocode} +\DeclareMathDelimiter\ch@irxllbbracket{\mathopen}{stmry}{"4A}{stmry}{"71} +\DeclareMathDelimiter\ch@irxrrbbracket{\mathclose}{stmry}{"4B}{stmry}{"79} +\DeclarePairedDelimiter{\ch@irxbbracket}{\ch@irxllbbracket}{\ch@irxrrbbracket} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Schouten} +% \begin{macrocode} +\newcommand{\@schoutenstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{S}}} +\newcommand{\@schoutennostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{S}}} +\newcommand{\Schouten}{\@ifstar\@schoutenstar\@schoutennostar} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Forms} +% \begin{macrocode} +\newcommand{\Forms}{\Omega} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\ZdR} +% \begin{macrocode} +\newcommand{\ZdR}{\ch@irxoperatorfont{Z}_{\scriptscriptstyle\mathrm{dR}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\BdR} +% \begin{macrocode} +\newcommand{\BdR}{\ch@irxoperatorfont{B}_{\scriptscriptstyle\ch@irxscriptfont{dR}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\HdR} +% \begin{macrocode} +\newcommand{\HdR}{\ch@irxoperatorfont{H}_{\scriptscriptstyle\ch@irxscriptfont{dR}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Diffeo} +% \begin{macrocode} +\newcommand{\Diffeo}{\operatorname{\ch@irxoperatorfont{Diffeo}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Diffop} +% \begin{macrocode} +\newcommand{\Diffop}{\operatorname{\ch@irxoperatorfont{DiffOp}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\loc} +% \begin{macrocode} +\newcommand{\loc}{\ch@irxscriptfont{loc}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\germ} +% \begin{macrocode} +\newcommand{\germ}{\operatorname{\ch@irxoperatorfont{germ}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\prol} +% \begin{macrocode} +\newcommand{\prol}{\ch@irxoperatorfont{prol}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\NRbracket} +% \begin{macrocode} +\newcommand{\@nrbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{NR}}} +\newcommand{\@nrbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{NR}}} +\newcommand{\NRbracket}{\@ifstar\@nrbracketstar\@nrbracketnostar} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\FNbracket} +% \begin{macrocode} +\newcommand{\@fnbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{FN}}} +\newcommand{\@fnbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{FN}}} +\newcommand{\FNbracket}{\@ifstar\@fnbracketstar\@fnbracketnostar} +% \end{macrocode} +%\end{macro} +% +% \begin{macro}{\Manifold} +% \begin{macrocode} +\newcommand{\Manifolds}{\categoryname{\categoryname{Manifold}}} +% \end{macrocode} +% \end{macro} +% +%\subsubsection{Lie Groups and Principal Fiber Bundles} +% +%\begin{macro}{\lefttriv} +% \begin{macrocode} +\newcommand{\lefttriv}{\ch@irxoperatorfont{left}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\righttriv} +% \begin{macrocode} +\newcommand{\righttriv}{\ch@irxoperatorfont{right}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Gau} +% \begin{macrocode} +\newcommand{\Gau}{\operatorname{\ch@irxoperatorfont{Gau}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Conn} +% \begin{macrocode} +\newcommand{\Conn}{\operatorname{\ch@irxoperatorfont{Conn}}} +% \end{macrocode} +% \end{macro} +% +%\begin{macro}{\ratio} +% \begin{macrocode} +\newcommand{\ratio}{\ch@irxoperatorfont{r}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Parallel} +% \begin{macrocode} +\newcommand{\Parallel}{\operatorname{\ch@irxoperatorfont{P}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\CE} +% \begin{macrocode} +\newcommand{\CE}{{\scriptscriptstyle{\ch@irxscriptfont{CE}}}} +% \end{macrocode} +%\end{macro} +% +% \begin{macro}{\HCE} +% \begin{macrocode} +\newcommand{\HCE}{\ch@irxoperatorfont{H}_\CE} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\fund} +% \begin{macrocode} +\newcommand{\fund}{\ch@irxoperatorfont{fund}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Universal} +% \begin{macrocode} +\newcommand{\Universal}{\operatorname{\ch@irxoperatorfont{U}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\BCH} +% \begin{macrocode} +\newcommand{\BCH}{\ch@irxscriptfont{\scriptscriptstyle{BCH}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\LieGroups} +% \begin{macrocode} +\newcommand{\LieGroups}{\categoryname{\categoryname{LieGroup}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Principal} +% \begin{macrocode} +\newcommand{\Principal}{\categoryname{\categoryname{Principal}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\GPrincipal} +% \begin{macrocode} +\newcommand{\GPrincipal}[1][G]{#1\categoryname{\textrm{-}\categoryname{Principal}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Fiber} +% \begin{macrocode} +\newcommand{\Fiber}{\categoryname{Fiber}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\FFiber} +% \begin{macrocode} +\newcommand{\FFiber}[1][F]{#1\categoryname{\textrm{-}\categoryname{Fiber}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Pin} +% \begin{macrocode} +\newcommand{\Pin}{\group{Pin}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\Spin} +% \begin{macrocode} +\newcommand{\Spin}{\group{Spin}} +% \end{macrocode} +% \end{macro} + +% +%\subsubsection{(Pseudo) Riemannian Geometry } +% +%\begin{macro}{\nablaLC} +% \begin{macrocode} +\newcommand{\nablaLC}{\nabla^{\scriptscriptstyle\ch@irxscriptfont{LC}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Laplace} +% \begin{macrocode} +\newcommand{\Laplace}{\Delta} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\dAlembert} +% \begin{macrocode} +\DeclareMathSymbol\dAlembert{\mathord}{AMSa}{"03} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\feynman} +% \begin{macrocode} +\newcommand{\feynman}[1]{\ooalign{$#1$\cr\hidewidth$\raise0.19ex\hbox{/}$\hidewidth\cr}} +% \end{macrocode} +%\end{macro} + +%\begin{macro}{\Dirac} +% \begin{macrocode} +\newcommand{\Dirac}{\feynman{D}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\rotation} +% \begin{macrocode} +\newcommand{\rotation}{\operatorname{\ch@irxoperatorfont{rot}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\curl} +% \begin{macrocode} +\newcommand{\curl}{\operatorname{\ch@irxoperatorfont{curl}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\divergence} +% \begin{macrocode} +\newcommand{\divergence}{\operatorname{\ch@irxoperatorfont{div}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\gradient} +% \begin{macrocode} +\newcommand{\gradient}{\operatorname{\ch@irxoperatorfont{grad}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Tor} +% \begin{macrocode} +\newcommand{\Tor}{\operatorname{\ch@irxoperatorfont{Tor}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Ric} +% \begin{macrocode} +\newcommand{\Ric}{\operatorname{\ch@irxoperatorfont{Ric}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\scal} +% \begin{macrocode} +\newcommand{\scal}{\operatorname{\ch@irxoperatorfont{scal}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Riem} +% \begin{macrocode} +\newcommand{\Riem}{\operatorname{\ch@irxoperatorfont{Riem}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Hessian} +% \begin{macrocode} +\newcommand{\Hessian}{\ch@irxoperatorfont{Hessian}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\hodge} +% \begin{macrocode} +\newcommand{\hodge}{\operatorname{\star}} +% \end{macrocode} +%\end{macro} +% +%\subsubsection{Complex Geometry} +% +%\begin{macro}{\Nijenhuis} +% \begin{macrocode} +\newcommand{\Nijenhuis}{\operatorname{\ch@irxoperatorfont{Nij}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\del} +% \begin{macrocode} +\newcommand{\del}{\mathop{}\!\partial} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\delbar} +% \begin{macrocode} +\newcommand{\delbar}{\mathop{}\!\cc{\partial}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\FS} +% \begin{macrocode} +\newcommand{\FS}{{\scriptscriptstyle{\ch@irxscriptfont{FS}}}} +% \end{macrocode} +%\end{macro} +% +% +%\subsubsection{Vector Bundles} +% +% \begin{macro}{\Lift} +% \begin{macrocode} +\newcommand{\Lift}{{\scriptscriptstyle{\ch@irxscriptfont{Lift}}}} +% \end{macrocode} +% \end{macro} +% +%\begin{macro}{\ver} +% \begin{macrocode} +\newcommand{\ver}{\ch@irxscriptfont{ver}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\hor} +% \begin{macrocode} +\newcommand{\hor}{\ch@irxscriptfont{hor}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Ver} +% \begin{macrocode} +\newcommand{\Ver}{\operatorname{\ch@irxoperatorfont{Ver}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Hor} +% \begin{macrocode} +\newcommand{\Hor}{\operatorname{\ch@irxoperatorfont{Hor}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Sec} +% \begin{macrocode} +\newcommand{\Sec}[1][k]{\Gamma^{#1}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Secinfty} +% \begin{macrocode} +\newcommand{\Secinfty}{\Sec[\infty]} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\HolSec} +% \begin{macrocode} +\newcommand{\HolSec}{\Sec[]_{\ch@irxscriptfont{hol}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\SymD} +% \begin{macrocode} +\newcommand{\SymD}{\mathop{}\!\ch@irxoperatorfont{D}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Densities} +% \begin{macrocode} +\newcommand{\Densities}[1][n]{\abs{\Lambda^{#1}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\MeasurableSections} +% \begin{macrocode} +\newcommand{\MeasurableSections}{\ch@irxspacefont{M}\Sec[]} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\IntpSections} +% \begin{macrocode} +\newcommand{\IntpSections}[1][p]{\Intp[#1]\Sec[]} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\IntegrableSections} +% \begin{macrocode} +\newcommand{\IntegrableSections}{\IntpSections[1]} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Translation} +% \begin{macrocode} +\newcommand{\Translation}{\ch@irxoperatorfont{T}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\frames} +% \begin{macrocode} +\newcommand{\frames}[1]{\ch@irxoperatorfont{#1}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Frames} +% \begin{macrocode} +\newcommand{\Frames}{\operatorname{\ch@irxoperatorfont{Frames}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\FDiff} +% \begin{macrocode} +\newcommand{\FDiff}{\ch@irxoperatorfont{F}} +% \end{macrocode} +%\end{macro} +% +% +%\subsubsection{Symplectic and Poisson Geometry} +% +%\begin{macro}{\Sympl} +% \begin{macrocode} +\newcommand{\Sympl}{\operatorname{\ch@irxgroupfont{Sympl}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Jacobiator} +% \begin{macrocode} +\newcommand{\Jacobiator}[1][\pi]{\operatorname{\ch@irxoperatorfont{Jac}}_{#1}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\red} +% \begin{macrocode} +\newcommand{\red}{\ch@irxscriptfont{red}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Hess} +% \begin{macrocode} +\newcommand{\Hess}{\ch@irxoperatorfont{Hess}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\KKS} +% \begin{macrocode} +\newcommand{\KKS}{{\scriptscriptstyle\ch@irxscriptfont{KKS}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Courant} +% \begin{macrocode} +\newcommand{\@courantstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{C}}} +\newcommand{\@courantnostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{C}}} +\newcommand{\Courant}{\@ifstar\@courantstar\@courantnostar} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Dorfman} +% \begin{macrocode} +\newcommand{\@dorfmanstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{D}}} +\newcommand{\@dorfmannostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{D}}} +\newcommand{\Dorfman}{\@ifstar\@dorfmanstar\@dorfmannostar} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Dir} +% \begin{macrocode} +\newcommand{\Dir}{\operatorname{\ch@irxoperatorfont{Dir}}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Forward} +% \begin{macrocode} +\newcommand{\Forward}{\mathcal{F}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Backward} +% \begin{macrocode} +\newcommand{\Backward}{\mathcal{B}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Tangent} +% \begin{macrocode} +\newcommand{\Tangent}{\mathbb{T}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\MWreduction} +% \begin{macrocode} +\newcommand{\MWreduction}{\big/\!\!\big/} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Mon} +% \begin{macrocode} +\newcommand{\Mon}{\ch@irxoperatorfont{Mon}} +% \end{macrocode} +%\end{macro} +% +%\begin{macro}{\Hol} +% \begin{macrocode} +\newcommand{\Hol}{\ch@irxoperatorfont{Hol}} +% \end{macrocode} +%\end{macro} +% +% \begin{macrocode} +\fi +% \end{macrocode}
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