table.tex

%! TEX root = cheat_sheet.tex

$\vect{u}$ & 1 & \verb|\vect{u}| & \verb|\underline{#1}| \\
$ \tensor{A} $ & 1 & \verb|\tensor{A}| & \verb|\underline{\underline{#1}}| \\
$ \mesure{c} $ & 1 & \verb|\mesure{c}| & \verb|\lvert #1 \rvert| \\
$ \tange{e} $ & 1 & \verb|\tange{e}| & \verb|\vect{\tau}_{#1}| \\
$ \norm $ & 0 & \verb|\norm| & \verb|\vect{n}| \\
$ \norma{f} $ & 1 & \verb|\norma{f}| & \verb|\norm_{#1}| \\
$ \incid{f}{c} $ & 2 & \verb|\incid{f}{c}| & \verb|\iota{#1,#2}| \\
$ \mean{g} $ & 1 & \verb|\mean{g}| & \verb|\overline{#1}| \\
$ \zmean $ & 0 & \verb|\zmean| & \verb|\perp\mathbf{1}| \\
$ \integ{c} $ & 1 & \verb|\integ{c}| & \verb|\int\limits_{#1}| \\
$ \twistm{E} $ & 1 & \verb|\twistm{E}| & \verb|\tilde{#1}| \\
$ \twist{E} $ & 1 & \verb|\twist{E}| & \verb|\widetilde{E}| \\
$ \transpose{M} $ & 1 & \verb|\transpose{M}| & \verb|{#1}^{\textsc{t}}| \\
$ \dif $ & 0 & \verb|\dif| & \verb|\,\mathrm{d}| \\
$ \Leq $ & 0 & \verb|\Leq| & \verb|\lesssim| \\
$ \pond{c} $ & 1 & \verb|\pond{c}| & \verb|\varphi_{#1}| \\
$ a\usc{Be} $  & 1 & \verb|a\usc{Bc}| & \verb|^{\textsc{#1}}| \\
$ \EB $ & 0 & \verb|\EB| & \verb|\mathrm{EB}| \\
\multicolumn{4}{c}{\bfseries Sets}\\
\hline
$ \tq $ & 0 & \verb|\tq| & \verb!\,|\,! \\
$ \Set{u_n} $ & 1 & \verb|\Set{u_n}| & \verb|\lbrace #1 \rbrace| \\
$ \Factor{v_n} $ & 1 & \verb|\Factor{u_n}| & \verb|\left( #1 \right)| \\
$ \Factorb{w_n} $ & 1 & \verb|\Factorb{w_n}| & \verb|\left[ #1 \right]| \\
$ \ar{u}{v}{w} $ & 3 & \verb|\ar{u}{v}{w}| & \verb|\begin{bmatrix} #1 \\ #2 \\ #3 \end{bmatrix}| \\
\hline
$ \Ddi $ & 0 & \verb|\Ddi| & \verb|\boldsymbol{\delta}| \\
$ \In $ & 0 & \verb|\In| & \verb|\mathrm{\textsc{i}}| \\
$ \Bd $ & 0 & \verb|\Bd| & \verb|\mathrm{\textsc{b}}| \\
$ \pb $ & 0 & \verb|\pb| & \verb|\mathrm{pb}| \\
$ \bc $ & 0 & \verb|\bc| & \verb|\mathrm{bc}| \\
$ \harm $ & 0 & \verb|\harm| & \verb|\mathsf{h}| \\
$ \vb $ & 0 & \verb|\vb| & \verb|\mathsf{vb}| \\
$ \cb $ & 0 & \verb|\cb| & \verb|\mathsf{cb}| \\
$ \bnd $ & 0 & \verb|\bnd| & \verb|\partial| \\
$ \Dom $ & 0 & \verb|\Dom| & \verb|\Omega| \\
$ \pOm $ & 0 & \verb|\pOm| & \verb|\bnd\Dom| \\
$ \closure $ & 0 & \verb|\closure| & \verb|\overline{\bnd}| \\
\hline
$ \rhs $ & 0 & \verb|\rhs| & \verb|\mathsf{RHS}| \\
$ \mom $ & 0 & \verb|\mom| & \verb|\mathsf{mom}| \\
$ \mas $ & 0 & \verb|\mas| & \verb|\mathsf{mas}| \\
$ \vor $ & 0 & \verb|\vor| & \verb|\mathsf{vor}| \\
$ \BC $ & 0 & \verb|\BC| & \verb|\mathsf{B \! C}| \\
$ \Src $ & 0 & \verb|\Src| & \verb|\mathsf{S}| \\
$ \SrcP $ & 0 & \verb|\SrcP| & \verb|\Src_{\mathsf{p}}| \\
$ \SrcD $ & 0 & \verb|\SrcD| & \verb|\Src_{\mathsf{d}}| \\
\multicolumn{4}{c}{\bfseries Variables}\\
\multicolumn{4}{l}{Continuous Setting}\\
\hline
$\Oex$ & 0 & \verb|\Oex| & \verb|\mathrm{1}| \\
$\Vit$ & 0 & \verb|\Vit| & \verb|u| \\
$\Vex$ & 0 & \verb|\Vex| & \verb|\vect{\Vit}| \\
$\Vort$ & 0 & \verb|\Vort| & \verb|\omega| \\
$\Wex$ & 0 & \verb|\Wex| & \verb|\vect{\Vort}| \\
$\Pex$ & 0 & \verb|\Pex| & \verb|p| \\
$\Gex$ & 0 & \verb|\Gex| & \verb|\vect{g}| \\
$\Gdual$ & 0 & \verb|\Gdual| & \verb|\Gex^\zeta| \\
$\Fex$ & 0 & \verb|\Fex| & \verb|\vect{\phi}| \\
$\Fdual$ & 0 & \verb|\Fdual| & \verb|\vect{\phi}^\zeta| \\
$\Sex$ & 0 & \verb|\Sex| & \verb|s| \\
$\Wsex$ & 0 & \verb|\Wsex| & \verb|\vect{\Vort}^{\ast}| \\
$\Wsdi$ & 0 & \verb|\Wsdi| & \verb|\Wdi^{\ast}| \\
$\Psex$ & 0 & \verb|\Psex| & \verb|\Pex^{\ast}| \\
$\Foex$ & 0 & \verb|\Foex| & \verb|\vect{f}| \\
$\Fosex$ & 0 & \verb|\Fosex| & \verb|\vect{f}^{\ast}| \\
$\Posex$ & 0 & \verb|\Posex| & \verb|\theta| \\
$\Povex$ & 0 & \verb|\Povex| & \verb|\vect{\psi}| \\
$\Vtest $ & 0 & \verb|\Vtest| & \verb|\vect{v}| \\ %
$\Vttest $ & 0 & \verb|\Vttest| & \verb|\vect{w}| \\ %
$\Ptest $ & 0 & \verb|\Ptest| & \verb|q| \\ %
$\Pttest $ & 0 & \verb|\Pttest| & \verb|r| \\ %
\multicolumn{4}{l}{Discrete Setting}\\
\hline
$\Odi$ & 0 & \verb|\Odi| & \verb|\boldsymbol{1}| \\
$\Vdi$ & 0 & \verb|\Vdi| & \verb|\mathbf{\Vit}| \\
$\Wdi$ & 0 & \verb|\Wdi| & \verb|\boldsymbol{\Vort}| \\
$\Pdi$ & 0 & \verb|\Pdi| & \verb|\mathbf{\Pex}| \\
$\Psdi$ & 0 & \verb|\Psdi| & \verb|\Pdi^{\ast}| \\
$\Gdi$ & 0 & \verb|\Gdi| & \verb|\mathbf{g}| \\
$\Fdi$ & 0 & \verb|\Fdi| & \verb|\boldsymbol{\phi}| \\
$\Sdi$ & 0 & \verb|\Sdi| & \verb|\mathbf{\Sex}| \\
$\Sgdi$ & 0 & \verb|\Sgdi| & \verb|\boldsymbol{\sigma}| \\
$\Fodi$ & 0 & \verb|\Fodi| & \verb|\mathbf{f}| \\
$\Posdi$ & 0 & \verb|\Posdi| & \verb|\boldsymbol{\theta}| \\
$\Povdi$ & 0 & \verb|\Povdi| & \verb|\boldsymbol{\psi}| \\
$\Taudi$ & 0 & \verb|\Taudi| & \verb|\boldsymbol{\tau}| \\
$\Xdi$ & 0 & \verb|\Xdi| & \verb|\mathbf{x}| \\
$\Ydi$ & 0 & \verb|\Ydi| & \verb|\mathbf{y}| \\
\multicolumn{4}{l}{Auxiliary Variables}\\
\hline
$\Adi$ & 0 & \verb|\Adi| & \verb|\mathbf{a}| \\
$\Bdi$ & 0 & \verb|\Bdi| & \verb|\mathbf{b}| \\
$\Qdi$ & 0 & \verb|\Qdi| & \verb|\mathbf{q}| \\
$\Vvdi$ & 0 & \verb|\Vvdi| & \verb|\mathbf{w}| \\
$\Zdi$ & 0 & \verb|\Zdi| & \verb|\boldsymbol{\zeta}| \\
\multicolumn{4}{l}{Phenomenological parameters}\\
\hline
$\rhop$ & 0 & \verb|\rhop| & \verb|(\rho)| \\
$\rhom$ & 0 & \verb|\rhom| & \verb|\rho^{{\scriptscriptstyle -1}}| \\
$\rhomp$ & 0 & \verb|\rhomp| & \verb|(\rho)^{{\scriptscriptstyle -1}}| \\
$\Visc$ & 0 & \verb|\Visc| & \verb|\nu| \\
$\Viscp$ & 0 & \verb|\Viscp| & \verb|(\Visc)| \\
$\Viscm$ & 0 & \verb|\Viscm| & \verb|\Visc^{{\scriptscriptstyle -1}}| \\
$\Viscpm$ & 0 & \verb|\Viscpm| & \verb|(\Visc)^{{\scriptscriptstyle -1}}| \\
$\CondTh$ & 0 & \verb|\CondTh| & \verb|\kappa| \\
$\CondThp$ & 0 & \verb|\CondThp| & \verb|(\CondTh)| \\
$\CondThm$ & 0 & \verb|\CondThm| & \verb|\CondTh^{{\scriptscriptstyle -1}}| \\
$\CondThpm$ & 0 & \verb|\CondThpm| & \verb|(\CondTh)^{{\scriptscriptstyle -1}}| \\
$\TeTh$ & 0 & \verb|\TeTh| & \verb|\tensor{\CondTh}| \\
$\TeThav$ & 0 & \verb|\TeThav| & \verb|\tensor{\widehat \CondTh}| \\
$\alpham$ & 0 & \verb|\alpham| & \verb|\alpha^{{\scriptscriptstyle -1}}| \\
$\alphap$ & 0 & \verb|\alphap| & \verb|(\alpha)| \\
$\alphapm$ & 0 & \verb|\alphapm| & \verb|(\alpha)^{{\scriptscriptstyle -1}}| \\
%=======================
% Mesh entities (also called chain spaces)
%=======================
\multicolumn{4}{c}{\bfseries Mesh-related}\\
\multicolumn{4}{l}{Mesh entities (aka chain spaces)}\\
\hline
$\vtx$ & 0 & \verb|\vtx| & \verb|\mathrm{v}| \\
$\edge$ & 0 & \verb|\edge| & \verb|\mathrm{e}|\\%
$\face$ & 0 & \verb|\face| & \verb|\mathrm{f}|\\%
$\cell$ & 0 & \verb|\cell| & \verb|\mathrm{c}|\\%
$\x$ & 0 & \verb|\x| & \verb|\mathrm{x}|\\%
\hline
$\vtxd$ & 0 & \verb|\vtxd| & \verb|\twistm{\vtx}|\\%
$\edged$ & 0 & \verb|\edged| & \verb|\twistm{\edge}|\\%
$\faced$ & 0 & \verb|\faced| & \verb|\twistm{\face}|\\%
$\celld$ & 0 & \verb|\celld| & \verb|\twistm{\cell}|\\%
$\yd$ & 0 & \verb|\yd| & \verb|\twistm{\mathrm{y}}|\\%
$\Kd$ & 0 & \verb|\Kd| & \verb|\twist{K}|\\%
\hline
$\pt$ & 0 & \verb|\pt| & \verb|\vect{x}|\\%
$\nent{f}{c}$ & 2 & \verb|\nent{f,c}| & \verb|\mathrm{n}_{#1,#2}}|\\%
$\edgev$ & 0 & \verb|\edgev| & \verb|\vect{\edge}|\\%
$\edgedv$ & 0 & \verb|\edgedv| & \verb|\vect{\edged}|\\%
$\facev$ & 0 & \verb|\facev| & \verb|\vect{\face}|\\%
$\facedv$ & 0 & \verb|\facedv| & \verb|\vect{\faced}|\\%
% Set of mesh entities
\multicolumn{4}{l}{Sets of mesh entities}\\
\hline
$\Mesh$ & 0 & \verb|\Mesh| & \verb|\mathrm{M}|\\%
$\xh$ & 0 & \verb|\xh| & \verb|\mathrm{X}|\\%
$\vtxh$ & 0 & \verb|\vtxh| & \verb|\mathrm{V}|\\%
$\edgeh$ & 0 & \verb|\edgeh| & \verb|\mathrm{E}|\\%
$\faceh$ & 0 & \verb|\faceh| & \verb|\mathrm{F}|\\%
$\cellh$ & 0 & \verb|\cellh| & \verb|\mathrm{C}|\\%
\hline
$\Meshd$ & 0 & \verb|\Meshd| & \verb|\twist{\Mesh}|\\%
$\yhd$ & 0 & \verb|\yhd| & \verb|\twist{\mathrm{Y}}|\\%
$\vtxhd$ & 0 & \verb|\vtxhd| & \verb|\twist{\vtxh}|\\%
$\edgehd$ & 0 & \verb|\edgehd| & \verb|\twist{\edgeh}|\\%
$\facehd$ & 0 & \verb|\facehd| & \verb|\twist{\faceh}|\\%
$\cellhd$ & 0 & \verb|\cellhd| & \verb|\twist{\cellh}|\\%
\multicolumn{4}{l}{Sub-meshes}\\
\hline
$\svol$ & 0 & \verb|\svol| & \verb|\mathfrak{s}|\\%
$ \Svol{f} $ & 1 & \verb|\Svol{f}| & \verb|\svol^{\textsc{#1}}| \\
$\Smesh$ & 0 & \verb|\Smesh| & \verb|\mathfrak{S}|\\%
$\pvol$ & 0 & \verb|\pvol| & \verb|\mathfrak{p}|\\%
$\Pvol$ & 0 & \verb|\Pvol| & \verb|\mathfrak{P}|\\%
$ \Part{f} $ & 1 & \verb|\Part{f}| & \verb|\Pvol_{#1}| \\
$\tef$ & 0 & \verb|\tef| & \verb|\mathfrak{t}_{\edge\face}|\\%
$\pef$ & 0 & \verb|\pef| & \verb|\pvol_{\edge\face,\cell}|\\%
$\pfc$ & 0 & \verb|\pfc| & \verb|\pvol_{\face,\cell}|\\%
\hline
%
$\frakc$ & 0 & \verb|\frakc| & \verb|\mathfrak{c}|\\%
$\frakt$ & 0 & \verb|\frakt| & \verb|\mathfrak{t}|\\%
$\frake$ & 0 & \verb|\frake| & \verb|\mathfrak{e}|\\%
$\frakv$ & 0 & \verb|\frakv| & \verb|\mathfrak{v}|\\%
$\frakC$ & 0 & \verb|\frakC| & \verb|\mathfrak{C}|\\%
$\frakT$ & 0 & \verb|\frakT| & \verb|\mathfrak{T}|\\%
$\frakE$ & 0 & \verb|\frakE| & \verb|\mathfrak{E}|\\%
$\frakV$ & 0 & \verb|\frakV| & \verb|\mathfrak{V}|\\%
\hline
%
$\Step$ & 0 & \verb|\Step| & \verb|h|\\%
$\StepMesh$ & 0 & \verb|\StepMesh| & \verb|\Step_{\scriptscriptstyle{\Mesh}}|\\%
$\Stepc$ & 0 & \verb|\Stepc| & \verb|\Step_{\cell}|\\%
\multicolumn{4}{c}{\bfseries DoF spaces (aka cochain spaces)}\\
\hline
$ \vtxsp $ & 0 & \verb|\vtxsp| & \verb|\mathcal{V}| \\
$ \edgesp $ & 0 & \verb|\edgesp| & \verb|\mathcal{E}| \\
$ \facesp $ & 0 & \verb|\facesp| & \verb|\mathcal{F}| \\
$ \cellsp $ & 0 & \verb|\cellsp| & \verb|\mathcal{C}| \\
\hline
$ \vtxspd $ & 0 & \verb|\vtxspd| & \verb|\twist{\vtxsp}| \\
$ \edgespd $ & 0 & \verb|\edgespd| & \verb|\twist{\edgesp}| \\
$ \facespd $ & 0 & \verb|\facespd| & \verb|\twist{\facesp}| \\
$ \cellspd $ & 0 & \verb|\cellspd| & \verb|\twist{\cellsp}| \\
$ \xsp $ & 0 & \verb|\xsp| & \verb|\mathcal{X}| \\
$ \ysp $ & 0 & \verb|\ysp| & \verb|\mathcal{Y}| \\
$ \yspd $ & 0 & \verb|\yspd| & \verb|\twist{\mathcal{Y}}| \\
\hline
$ H^{\PrimalDual{A}{B}} $ & 2 & \begin{tabular}{@{}l} \verb|H^| [\dots]\\ \verb|{\PrimalDual{A}{B}}| \end{tabular}& \begin{tabular}{@{}l}
  \verb|{\scriptscriptstyle{#1}}{\textstyle| [\dots]\\ \verb|\twistm{{\scriptscriptstyle{#2}}}}|
\end{tabular}  \\
$H^{\EpFd} $ & 0 & \verb|H^{\EpFd}| & \verb|\PrimalDual{\edgesp}{\facesp}|\\%
$H^{\VpCd} $ & 0 & \verb|H^{\VpCd}| & \verb|\PrimalDual{\vtxsp}{\cellsp}|\\%
$H^{\FpEd} $ & 0 & \verb|H^{\FpEd}| & \verb|\PrimalDual{\facesp}{\edgesp}|\\%
$H^{\CpVd} $ & 0 & \verb|H^{\CpVd}| & \verb|\PrimalDual{\cellsp}{\vtxsp}|\\%
$H^{\XpYd} $ & 0 & \verb|H^{\XpYd}| & \verb|\PrimalDual{\xsp}{\ysp}|\\%
\hline
$ H^{\DualPrimal{A}{B}} $ & 2 & \begin{tabular}{@{}l} \verb|H^| [\dots]\\ \verb|{\DualPrimal{A}{B}}| \end{tabular} & \begin{tabular}{@{}l}
  \verb|{\textstyle\twistm{{\scriptscriptstyle{#1}}}}| [\dots]\\ \verb|{\scriptscriptstyle{#2}}|
\end{tabular}  \\
$H^{\VdCp} $ & 0 & \verb|H^{\VdCp}| & \verb|\DualPrimal{\vtxsp}{\cellsp}|\\%
$H^{\EdFp} $ & 0 & \verb|H^{\EdFp}| & \verb|\DualPrimal{\edgesp}{\facesp}|\\%
$H^{\FdEp} $ & 0 & \verb|H^{\FdEp}| & \verb|\DualPrimal{\facesp}{\edgesp}|\\%
$H^{\CdVp} $ & 0 & \verb|H^{\CdVp}| & \verb|\DualPrimal{\cellsp}{\vtxsp}|\\%
$H^{\YdXp} $ & 0 & \verb|H^{\YdXp}| & \verb|\DualPrimal{\ysp}{\xsp}|\\%
\hline
$ H^{\PrimalDualSub{A}{B}{c}} $ & 3 & \begin{tabular}{@{}l} \verb|H^{\PrimalDualSub| [\dots]\\ \verb|{A}{B}{c}}| \end{tabular} & \begin{tabular}{@{}l}
  \verb|{\scriptscriptstyle{#1_{#3}}}{\textstyle| [\dots]\\ \verb|\twistm{{\scriptscriptstyle{#2}}}}|
\end{tabular}  \\
$H^{\EpFdc} $ & 0 & \verb|H^{\EpFdc}| & \verb|\PrimalDualSub{\edgesp}{\facesp}{\cell}|\\%
$H^{\VpCdc} $ & 0 & \verb|H^{\VpCdc}| & \verb|\PrimalDualSub{\vtxsp}{\cellsp}{\cell}|\\%
$H^{\FpEdc} $ & 0 & \verb|H^{\FpEdc}| & \verb|\PrimalDualSub{\facesp}{\edgesp}{\cell}|\\%
$H^{\CpVdc} $ & 0 & \verb|H^{\CpVdc}| & \verb|\PrimalDualSub{\cellsp}{\vtxsp}{\cell}|\\%
$H^{\XpYdc} $ & 0 & \verb|H^{\XpYdc}| & \verb|\PrimalDualSub{\xsp}{\ysp}{\cell}|\\%
\hline
$ H^{\DualPrimalSub{A}{B}{c}} $ & 3 & \begin{tabular}{@{}l} \verb|H^{\DualPrimalSub| [\dots]\\ \verb|{A}{B}{c}}| \end{tabular} & \begin{tabular}{@{}l}
  \verb|{\textstyle\twistm{{\scriptscriptstyle{#1}}}| [\dots]\\ \verb|_{\scriptscriptstyle{#3}}{\scriptscriptstyle{#2}}|
\end{tabular}  \\
$H^{\FdEpc} $ & 0 & \verb|H^{\FdEpc}| & \verb|\DualPrimalSub{\facesp}{\edgesp}{\cell}|\\%
$H^{\EdFpc} $ & 0 & \verb|H^{\EdFpc}| & \verb|\DualPrimalSub{\edgesp}{\facesp}{\cell}|\\%
$H^{\YdXpc} $ & 0 & \verb|H^{\YdXpc}| & \verb|\DualPrimalSub{\ysp}{\xsp}{\cell}|\\%
\multicolumn{4}{c}{\bfseries Operators}\\
\hline
$ \Ker $ & 0 & \verb|\Ker| & \verb|\operatorname{Ker}| \\
$ \Ran $ & 0 & \verb|\Ran| & \verb|\operatorname{Im}| \\
$ \Harm{u} $ & 1 & \verb|\Harm{u}| & \verb|\operatorname{Harm}#1| \\
$ \ima $ & 0 & \verb|\ima| & \verb|\DeclareMathOperator{\ima}{im}|\\
$ \trace $ & 0 & \verb|\trace| & \verb|\DeclareMathOperator{\trace}{tr}|\\
$ \card $ & 0 & \verb|\card| & \verb|\DeclareMathOperator{\card}{card}|\\
$ \domain $ & 0 & \verb|\domain| & \verb|\DeclareMathOperator{\domain}{domain}|\\
$ \diag $ & 0 & \verb|\diag| & \verb|\DeclareMathOperator{\diag}{diag}|\\
$ \grd $ & 0 & \verb|\grd| & \verb|\DeclareMathOperator{\grd}{\vect{grad}}|\\
$ \divm $ & 0 & \verb|\divm| & \verb|\DeclareMathOperator{\divm}{div}|\\
$ \curl $ & 0 & \verb|\curl| & \verb|\DeclareMathOperator{\curl}{\vect{curl}}|\\
$ \grdt $ & 0 & \verb|\grdt| & \begin{tabular}{@{}l} \verb|\DeclareMathOperator{\grdt}| [\dots]\\ \verb|{\tensor{\mathrm{grad}}}| \end{tabular}\\
$ \divv $ & 0 & \verb|\divv| & \verb|\DeclareMathOperator{\divv}{\vect{div}}|\\
$ \lapvec $ & 0 & \verb|\lapvec| & \verb|\DeclareMathOperator{\lapvec}{\vect{\Delta}}|\\
\multicolumn{4}{l}{Discrete Operators}\\
\hline
$ \opid $ & 0 & \verb|\opid| & \verb|\mathsf{Id}| \\
$ \TeId $ & 0 & \verb|\TeId| & \verb|\tensor{\opid}| \\
\multicolumn{4}{l}{Discrete Differential Operators}\\
\hline
$ \opgrad $ & 0 & \verb|\opgrad| & \verb|\mathsf{GRAD}| \\
$ \opdiv $ & 0 & \verb|\opdiv| & \verb|\mathsf{DIV}| \\
$ \opcurl $ & 0 & \verb|\opcurl| & \verb|\mathsf{CURL}| \\
$ \opgradd $ & 0 & \verb|\opgradd| & \verb|\twist{\opgrad}| \\
$ \opdivd $ & 0 & \verb|\opdivd| & \verb|\twist{\opdiv}| \\
$ \opcurld $ & 0 & \verb|\opcurld| & \verb|\twist{\opcurl}| \\
\multicolumn{4}{l}{Reductions aka deRham maps}\\
\hline
$ \opred $ & 0 & \verb|\opred| & \verb|\mathsf{R}| \\
$ \opRed{F} $ & 1 & \verb|\opRed{F}| & \verb|\opred_{#1}| \\
\multicolumn{4}{l}{Projection maps}\\
\hline
$ \opproj $ & 0 & \verb|\opproj| & \verb|\mathsf{T}| \\
$ \opProj{F} $ & 1 & \verb|\opProj{F}| & \verb|\opproj_{#1}| \\
$ \PVc $ & 0 & \verb|\PVc| & \verb|\opProj{\vtxsp,\cell}| \\
$ \PEc $ & 0 & \verb|\PEc| & \verb|\opProj{\edgesp,\cell}| \\
$ \PFc $ & 0 & \verb|\PFc| & \verb|\opProj{\facesp,\cell}| \\
\hline
$ \optrans $ & 0 & \verb|\optrans| & \verb|\mathsf{T}| \\
$ \opT{u} $ & 1 & \verb|\opT{u}| & \verb|\optrans_{#1}| \\
\multicolumn{4}{l}{Hodge operators}\\
\hline
$ \opHodge $ & 0 & \verb|\opHodge| & \verb|\mathsf{H}| \\
$ \opHodgec $ & 0 & \verb|\opHodgec| & \verb|\hat{\opHodge}| \\
$ \opHodgeFull{A}{E}{F} $ & 3 & \begin{tabular}{@{}l} \verb|\opHodgeFull| [\dots]\\ \verb|{A}{E}{F}| \end{tabular}& \verb|\opHodge_{#1}^{\scriptscriptstyle{#2 #3}}| \\
$ \Hperp $ & 0 & \verb|\Hperp| & \verb|\perp\opHodge| \\
\multicolumn{4}{l}{Reconstruction operators}\\
\hline
$ \conf $ & 0 & \verb|\conf| & \verb|{\rm conf}| \\
\hline
$ \oprec $ & 0 & \verb|\oprec| & \verb|\mathtt{L}| \\
$ \opcrec $ & 0 & \verb|\opcrec| & \verb|\mathtt{C}| \\
$ \opsrec $ & 0 & \verb|\opsrec| & \verb|\mathtt{S}| \\
$ \opRec{E} $ & 1 & \verb|\opRec{E}| & \verb|\oprec_{#1}| \\
$ \opReco{E} $ & 1 & \verb|\opReco{E}| & \verb|\oprec_{#1}| \\
$ \opCRec{E} $ & 1 & \verb|\opCRec{E}| & \verb|\opcrec_{#1}| \\
$ \opSRec{E} $ & 1 & \verb|\opSRec{E}| & \verb|\opsrec_{#1}| \\
$ \opShRec{E} $ & 1 & \verb|\opShRec{E}| & \verb|\hat{\opsrec}_{#1}| \\
$ \opRecv{E} $ & 1 & \verb|\opRecv{E}| & \verb|\vect{\oprec}_{#1}| \\
$ \opCRecv{E} $ & 1 & \verb|\opCRecv{E}| & \verb|\vect{\opcrec}_{#1}| \\
$ \opSRecv{E} $ & 1 & \verb|\opSRecv{E}| & \verb|\vect{\opsrec}_{#1}| \\
$ \opShRecv{E} $ & 1 & \verb|\opShRecv{E}| & \verb|\hat{\vect{\opsrec}}_{#1}| \\
\multicolumn{4}{l}{Reconstruction functions}\\
\hline
$ \freco $ & 0 & \verb|\freco| & \verb|\ell| \\
$ \frecov $ & 0 & \verb|\frecov| & \verb|\vect{\freco}| \\
$ \Freco{a}{b} $ & 2 & \verb|\Freco{a}{b}| & \verb|\freco_{#1}^{\textsc{#2}}| \\
$ \Frecov{a}{b} $ & 2 & \verb|\Frecov{a}{b}| & \verb|\frecov_{#1}^{\textsc{#2}}| \\
$ \frecoc $ & 0 & \verb|\frecoc| & \verb|\freco^\conf| \\
$ \frecovc $ & 0 & \verb|\frecovc| & \verb|\frecov^\conf| \\
$ \fform $ & 0 & \verb|\fform| & \verb|\varphi| \\
$ \Fform{E} $ & 1 & \verb|\Fform{E}| & \verb|\fform^{\textsc{#1}}| \\
$ \Fformv{E} $ & 1 & \verb|\Fformv{E}| & \verb|\vect{\fform}^{\textsc{#1}}| \\
\multicolumn{4}{l}{Approximation maps}\\
\hline
$ \opapx $ & 0 & \verb|\opapx| & \verb|\mathtt{A}| \\
$ \opapxv $ & 0 & \verb|\opapxv| & \verb|\vect{\opapx}| \\
$ \opApx{E} $ & 1 & \verb|\opApx{E}| & \verb|\opapx_{#1}| \\
$ \opApxv{E} $ & 1 & \verb|\opApxv{E}| & \verb|\opapxv_{#1}| \\
\hline
$ \Commut{A}{B} $ & 2 & \verb|\Commut{A}{B}| & \verb|\lfloor #1, \, #2 \rceil| \\
\multicolumn{4}{l}{Generic operators}\\
\hline
$ \opA $ & 0 & \verb|\opA| & \verb|\mathsf{A}| \\
$ \opB $ & 0 & \verb|\opB| & \verb|\mathsf{B}| \\
$ \opC $ & 0 & \verb|\opC| & \verb|\mathsf{C}| \\
$ \opD $ & 0 & \verb|\opD| & \verb|\mathsf{D}| \\
$ \opBt $ & 0 & \verb|\opBt| & \verb|\transpose{\opB}| \\
$ \opCt $ & 0 & \verb|\opCt| & \verb|\transpose{\opC}| \\
$ \opDt $ & 0 & \verb|\opDt| & \verb|\transpose{\opD}| \\
\multicolumn{4}{c}{\bfseries Stokes}\\
\hline
$ \Wt $ & 0 & \verb|\Wt| & \verb|\Wex_{\tau}^{\bc}| \\
$ \Un $ & 0 & \verb|\Un| & \verb|\Vit_\nu^{\bc}| \\
$ \Ut $ & 0 & \verb|\Ut| & \verb|\Vex_\tau^{\bc}| \\
$ \Pbc $ & 0 & \verb|\Pbc| & \verb|\Pex^{\bc}| \\
 \UnWt  & 0 & \verb|\UnWt| & \verb|\textbf{(UnWt)}\@\xspace| \\
 \UtPr  & 0 & \verb|\UtPr| & \verb|\textbf{(UtPr)}\@\xspace| \\
 %\PL  & 0 & \verb|\PL| & \verb|\cblue{(PL)}\@\xspace| \\
 %\DL  & 0 & \verb|\DL| & \verb|\cred{(DL)}\@\xspace| \\
\multicolumn{4}{c}{\bfseries Functional Analysis}\\
\hline
$ \Hcurl{p} $ & 1 & \verb|\Hcurl{p}| & \verb|H(\vect{\rm curl};#1)| \\
$ \Hdiv{p} $ & 1 & \verb|\Hdiv{p}| & \verb|H({\rm div};#1)| \\
$ \Hilbert{p} $ & 1 & \verb|\Hilbert{p}| & \verb|H^{#1}| \\
$ \Sobolev{p}{q} $ & 2 & \verb|\Sobolev{p}{q}| & \verb|W^{#1,#2}| \\
$ \Lebesgue{p} $ & 1 & \verb|\Lebesgue{p}| & \verb|L^{#1}| \\
$ \Hilbertv{p} $ & 1 & \verb|\Hilbertv{p}| & \verb|\vect{H}^{#1}| \\
$ \Sobolevv{p}{q} $ & 2 & \verb|\Sobolevv{p}{q}| & \verb|\vect{W}^{#1,#2}| \\
$ \Lebesguev{p} $ & 1 & \verb|\Lebesguev{p}| & \verb|\vect{L}^{#1}| \\
\hline
$ \Ldisc{A}{B} $ & 2 & \verb|\Ldisc{A}{B}| & \verb|#1,#2| \\
$ \Real $ & 0 & \verb|\Real| & \verb|{\mathbb{R}}| \\
$ \Poly $ & 0 & \verb|\Poly| & \verb|{\mathbb{P}}| \\
$ \Polyv{k}{C} $ & 2 & \verb|\Polyv{k}{C}| & \verb|[\Poly_{#1}(#2)]^{3}| \\
\hline
$ \CSo{A}{B} $ & 2 & \verb|\CSo{A}{B}| & \verb|C_{#2}^{_{(#1)}}| \\
$ \CPo{u} $ & 1 & \verb|\CPo{u}| & \verb|C_{\textsc{p}}^{_{(#1)}}| \\
$ \CPW{u} $ & 1 & \verb|\CPW{u}| & \verb|C_{\textsc{pw}}^{_{(#1)}}| \\
$ \CPoO{u} $ & 1 & \verb|\CPoO{u}| & \verb|C_{\textsc{p},\Omega}^{_{(#1)}}| \\
$ \PoC $ & 0 & \verb|\PoC| & \verb|[ \Poly_0(\cellh) ]^3| \\
$ \HiC $ & 0 & \verb|\HiC| & \verb|[H^1(\cellh)]^3| \\
$ \LeO $ & 0 & \verb|\LeO| & \verb|[L^4(\Omega)]^3| \\
\hline
$ \normBV{u} $ & 1 & \verb|\normBV{u}| & \verb|\normc{#1}_{\textsc{bv}}| \\
\multicolumn{4}{l}{Domaine et co-domaine}\\
\hline
$ \Space{E} $ & 1 & \verb|\Space{E}| & \verb|S_{#1}| \\
$ \SpaceGrd $ & 0 & \verb|\SpaceGrd| & \verb|\Space{\vtxsp}^{\mathrm{g}}(\Omega)| \\
$ \SpaceCurl $ & 0 & \verb|\SpaceCurl| & \verb|\Space{\edgesp}^{\mathrm{c}}(\Omega)| \\
$ \SpaceDiv $ & 0 & \verb|\SpaceDiv| & \verb|\Space{\facesp}^{\mathrm{d}}(\Omega)| \\
$ \Spacev{E} $ & 1 & \verb|\Spacev{E}| & \verb|\vect{S}_{#1}| \\
$ \SPol{E} $ & 1 & \verb|\SPol{E}| & \verb|P_{#1}| \\
$ \SPolv{E} $ & 1 & \verb|\SPolv{E}| & \verb|\vect{P}_{#1}| \\
\multicolumn{4}{l}{Norms, scalar products}\\
\hline
$ \pscont{A}{B} $ & 2 & \verb|\pscont{A}{B}| & \verb|\left[ #1,#2 \right]| \\
$ \psdico{A}{B} $ & 2 & \verb|\psdico{A}{B}| & \verb|\left[ #1,#2 \right]}%{\left(#1 , #2 \right)| \\
$ \psdisc{A}{B} $ & 2 & \verb|\psdisc{A}{B}| & \verb| \llbracket #1,#2 \rrbracket | \\
$ \proddual{A}{B} $ & 2 & \verb|\proddual{A}{B}| & \verb|\left\langle #1,\, #2 \right\rangle| \\
$ \normc{u} $ & 1 & \verb|\normc{u}| & \verb|\lvert\!\lvert #1 \rvert\!\rvert| \\
$ \normd{u} $ & 1 & \verb|\normd{u}| & \verb|\lvert\!\lvert\!\vert #1 \rvert\!\rvert\!\rvert| \\
$ \jump{u} $ & 1 & \verb|\jump{u}| & \verb| \llbracket #1 \rrbracket | \\
\multicolumn{4}{l}{Analysis of numerical results}\\
\hline
$ \rate $ & 0 & \verb|\rate| & \verb|\mathrm{\textsc{r}}| \\
$ \Errd{u} $ & 1 & \verb|\Errd{u}| & \verb|\mathbf{Er}_{#1}| \\
$ \Errc{u} $ & 1 & \verb|\Errc{u}| & \verb|Er_{#1}| \\
$ \nsys $ & 0 & \verb|\nsys| & \verb|\mathrm{n_{\textsc{s}ys}}| \\
$ \nite $ & 0 & \verb|\nite| & \verb|\mathrm{n_{\textsc{i}te}}| \\
$ \nnz $ & 0 & \verb|\nnz| & \verb|\mathrm{\textsc{nnz}}| \\
$ \CompCo $ & 0 & \verb|\CompCo| & \verb|\boldsymbol{\chi}| \\
$ \CompCoR $ & 0 & \verb|\CompCoR| & \verb|\boldsymbol{\chi}_{\mathrm{\textsc{r}el}}| \\
$ \stencil $ & 0 & \verb|\stencil| & \verb|\mathrm{St}| \\
 \Hex  & 0 & \verb|\Hex| & \verb|\texttt{Hex}\@\xspace| \\
 \PrT  & 0 & \verb|\PrT| & \verb|\texttt{PrT}\@\xspace| \\
 \PrG  & 0 & \verb|\PrG| & \verb|\texttt{PrG}\@\xspace| \\
 \CB  & 0 & \verb|\CB| & \verb|\texttt{CB}\@\xspace| \\
 \K  & 0 & \verb|\K| & \verb|\texttt{Ker}\@\xspace| \\
\multicolumn{4}{c}{\bfseries Macros for environments}\\
\multicolumn{4}{l}{Equations}\\
\hline
$  $ & 1 & \verb|\eq{...}| & \verb|\begin{equation} #1 \end{equation}| \\
$  $ & 1 & \verb|\eqn{...}| & \verb|\begin{equation*} #1 \end{equation*}| \\
$  $ & 1 & \verb|\eqb{...}| & \verb|\begin{equation}\boxed{ #1 }\end{equation}| \\
$  $ & 1 & \verb|\eqnb{...}| & \verb|\begin{equation*}\boxed{ #1 }\end{equation*}| \\
\multicolumn{4}{l}{Figures}\\
\hline
 & 4 & \begin{tabular}{@{}l} \verb|\Figure{h}| [\dots]\\ \verb|{0.9}{pic}{Cap}| \end{tabular} & \begin{tabular}{@{}l}
   \verb|\begin{figure}[#1] \centering| [\dots]\\
   \verb|\includegraphics[width=#2\textwidth]{#3}| [\dots]\\
   \verb|\caption{#4} \end{figure}| \end{tabular}\\
\hhline{====}
\multicolumn{4}{c}{\Large \bfseries {\scshape MR}'s {\scshape Macros}}\\
\hhline{====}
\multicolumn{4}{c}{\bfseries Miscellaneous}\\
\hline
$ \bO{h} $ & 1 & \verb|\bO{u}| & \verb|\mathcal{O}\left(#1\right)| \\
$ \abs{p} $ & 1 & \verb|\abs{p}| & \verb|\left\lvert #1\right\rvert| \\
$ \nrm{u} $ & 1 & \verb|\nrm{u}| & \verb|\left\lVert #1\right\rVert| \\
$ \dsb{A}{B} $ & 2 & \verb|\dsb{A}{B}| & \verb|\llbracket #1,\,#2 \rrbracket| \\
\multicolumn{4}{c}{\bfseries Variable modifiers}\\
\multicolumn{4}{l}{Dual, hybrid, vectorial, discrete, \dots}\\
\hline
$ \dual{u} $ & 1 & \verb|\dual{u}| & \verb|\widetilde{#1}| \\
$ \hyb{u} $ & 1 & \verb|\hyb{u}| & \verb|\widehat{#1}| \\
$ \vct{u} $ & 1 & \verb|\vct{u}| & \verb|\underline{#1}| \\
$ \tens{u} $ & 1 & \verb|\tens{u}| & \verb|\underline{\underline{#1}}| \\
$ \hybv{u} $ & 1 & \verb|\hybv{u}| & \verb|\widehat{\vct{#1}}| \\
$ \dsc $ & 0 & \verb|\dsc| & \verb|\mathrm{h}| \\
\hline
$ \hVex $ & 0 & \verb|\hVex| & \verb|\hyb{\Vex}| \\
$ \hVtest $ & 0 & \verb|\hVtest| & \verb|\hyb{\Vtest}| \\
$ \hVttest $ & 0 & \verb|\hVttest| & \verb|\hyb{\Vttest}| \\
\multicolumn{4}{c}{\bfseries Time discretization \& Iterations}\\
\hline
$ u\np[1] $ & 1[1] & \verb|u\np[1]| & \verb|^{n+#1}| \\
$ u\nm[1] $ & 1[1] & \verb|u\nm[1]| & \verb|^{n-#1}| \\
$ \deltat $ & 0 & \verb|\deltat| & \verb|\Delta t| \\
$ u\kp[1] $ & 1[1] & \verb|u\kp[1]| & \verb|_{k+#1}| \\
$ u\km[1] $ & 1[1] & \verb|u\km[1]| & \verb|_{k-#1}| \\
\multicolumn{4}{c}{\bfseries Geometry}\\
\hline
$ \meas{f} $ & 1 & \verb|\meas{f}| & \verb|\left\lvert #1\right\rvert| \\
$\ifc$ & 0 & \verb|\ifc| & \verb|\incid{\face}{\cell}|\\%
$ \nf $ & 0 & \verb|\nf| & \verb|\norma{\face}| \\
$ \nfc $ & 0 & \verb|\nfc| & \verb|\norma{\face\cell}| \\
$ \restr{f} $ & 1 & \verb|\restr{f}| & \verb|{}_{\lvert #1}| \\
\multicolumn{4}{c}{\bfseries Sets shortcuts}\\
\hline
$ \Fc $ & 0 & \verb|\Fc| & \verb|\faceh_{\cell}| \\
$ \finf $ & 0 & \verb|\finf| & \verb|\face \in \Fc| \\
$ \finh $ & 0 & \verb|\finh| & \verb|\face \in \faceh| \\
$ \cinc $ & 0 & \verb|\cinc| & \verb|\cell \in \cellh| \\
$ \cinf $ & 0 & \verb|\cinf| & \verb|\cell \in \cellh_{\face}| \\
$ \Vex\uc $ & 0 & \verb|\uc| & \verb|_{\cell}| \\ %
$ \Vex\uf $ & 0 & \verb|\uf| & \verb|_{\face}| \\ %
$ \Vex\ud $ & 0 & \verb|\ud| & \verb|_{\dsc}| \\ %
$ \Vex\uh $ & 0 & \verb|\ud| & \verb|\ud| \\ %
\multicolumn{4}{c}{\bfseries Discrete setting}\\
\hline
$ \R $ & 0 & \verb|\R| & \verb|\mathbb{R}| \\
$ \Pk[d] $ & 1 [k] & \verb|\Pk[d]| & \verb|\mathbb{P}^{#1}| \\
\multicolumn{4}{c}{\bfseries Spaces}\\
\multicolumn{4}{l}{Hybrid, pressure/velocity}\\
\hline
$ \vsp $ & 0 & \verb|\vsp| & \verb|\mathcal{U}| \\
$ \vvsp $ & 0 & \verb|\vvsp| & \verb|\vct{\vsp}| \\
$ \hvsp $ & 0 & \verb|\hvsp| & \verb|\hybv{\vsp}| \\
$ \spsp $ & 0 & \verb|\spsp| & \verb|\mathcal{P}| \\
\multicolumn{4}{l}{Original CDO spaces}\\
\hline
$ \psp{u} $ & 1 & \verb|\psp{u}| & \verb|\mathcal{#1}| \\
$ \dsp{u} $ & 1 & \verb|\dsp{u}| & \verb|\dual{\mathcal{#1}}| \\
\multicolumn{4}{c}{\bfseries Reductions and deRham maps}\\
\multicolumn{4}{l}{Hybrid, velocity}\\
\hline
$ \prj $ & 0 & \verb|\prj| & \verb|\pi| \\
$ \red $ & 0 & \verb|\red| & \verb|\prj| \\
$ \Red{u} $ & 1 & \verb|\Red{u}| & \verb|\red_{#1}| \\
$ \vRed{u} $ & 1 & \verb|\vRed{u}| & \verb|\vct{\red}_{#1}| \\
$ \Redc $ & 0 & \verb|\Redc| & \verb|\vRed{\cell}\,| \\
$ \Redf $ & 0 & \verb|\Redf| & \verb|\vRed{\face}\,| \\
$ \Redh $ & 0 & \verb|\Redh| & \verb|\hv{\red}_{\cell}\,| \\
$ \Redg $ & 0 & \verb|\Redg| & \verb|\hv{\red}_{\cellh}\,| \\
\multicolumn{4}{l}{Pressure}\\
\hline
$ \Redp $ & 0 & \verb|\Redp| & \verb|\Red{\cell}\,| \\
$ \Redph $ & 0 & \verb|\Redph| & \verb|\Red{\cellh}\,| \\
\multicolumn{4}{c}{\bfseries Differential operators}\\
\multicolumn{4}{l}{Continuous}\\
\hline
$ \pd{f}{x} $ & 2 & \verb|\pd{f}{x}| & \verb|\frac{\partial{#1}}{\partial{#2}}| \\
$ \ddt{u} $ & 1 & \verb|\ddt{u}| & \verb|\pd{#1}{t}| \\
$ \dive $ & 0 & \verb|\dive| & \verb|\vct{\nabla}\cdot| \\
$ \grad $ & 0 & \verb|\grad| & \verb|\vct{\nabla}\,| \\
$ \rot $ & 0 & \verb|\rot| & \verb|\vct{\nabla}\times| \\
$ \graddiv $ & 0 & \verb|\graddiv| & \verb|\grad\dive| \\
$ \lapl $ & 0 & \verb|\lapl| & \verb|\vct{\Delta}\,| \\
\multicolumn{4}{l}{Discrete}\\
\hline
$ \dddt{u} $ & 1 & \verb|\dddt{u}| & \verb|\frac{{#1}^{n+1}-{#1}^{n}}{\deltat}| \\
$ \dddtp{u} $ & 1 & \verb|\dddtp{u}| & \verb|\frac{{#1}^{n+1}-{#1}^{n}}{\deltat}| \\
$ \dddtm{u} $ & 1 & \verb|\dddtm{u}| & \verb|\frac{{#1}^{n}-{#1}^{n-1}}{\deltat}| \\
\multicolumn{4}{l}{Orignial CDO}\\
\hline
$ \Gh $ & 0 & \verb|\Gh| & \verb|\mathrm{G}| \\
$ \vGh $ & 0 & \verb|\vGh| & \verb|\vct{\Gh}| \\
$ \tGh $ & 0 & \verb|\tGh| & \verb|\tens{\Gh}| \\
$ \Dh $ & 0 & \verb|\Dh| & \verb|\mathrm{D}| \\
$ \Dhh $ & 0 & \verb|\Dhh| & \verb|\mathrm{D}^{H}_{\cellh}| \\