diff options
Diffstat (limited to 'Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty | 265 |
1 files changed, 138 insertions, 127 deletions
diff --git a/Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty b/Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty index bc492919e48..5bc64f18841 100644 --- a/Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty +++ b/Master/texmf-dist/tex/latex/rank-2-roots/rank-2-roots.sty @@ -2,7 +2,7 @@ % % The Rank 2 Roots package. % -% Version 1.1 +% Version 1.2 % % % This package draws root and weight lattices for rank 2 root systems in LaTeX documents, @@ -19,7 +19,7 @@ % % \NeedsTeXFormat{LaTeX2e}[1994/06/01] -\ProvidesPackage{rank-2-roots}[2023/08/31 Rank 2 roots] +\ProvidesPackage{rank-2-roots}[2023/09/03 Rank 2 roots] \RequirePackage{tikz} \RequirePackage{xstring} \RequirePackage{xparse} @@ -47,16 +47,31 @@ fadings \setlength\weightLength{.5cm} \newlength\gradingDot \setlength\gradingDot{2pt} -\tikzstyle{weight lattice}=[gray!40] -\tikzstyle{root}=[gray] -\tikzstyle{root polygon}=[gray!40,opacity=.5] -\tikzstyle{hyperplane}=[gray!50,fill opacity=.5] -\tikzstyle{Weyl chamber}=[gray!60,fill opacity=.5] -\tikzstyle{grading}=[line width=3pt,gray,opacity=0.5,line cap=round] - \def\defaultWeightLatticeSize{0} +\newlength\simple@root@radius +\setlength\simple@root@radius{1.2pt} +\def\weight@multiplicity{1} \newif\ifAutoSizeWeightLattice \AutoSizeWeightLatticetrue +\pgfkeys{/root system/.is family, +/root system, +weight lattice/.style={draw=gray!40}, +root polygon/.style={gray!40,opacity=.5}, +hyperplane/.style={gray!50,fill opacity=.5}, +Weyl chamber/.style={gray!60,fill opacity=.5}, +grading/.style={line width=3pt,gray,opacity=0.5,line cap=round}, +weight radius/.code={\pgfmathsetlength\weightRadius{#1}}, +weight length/.code={\pgfmathsetlength\weightLength{#1}}, +grading dot radius/.code={\pgfmathsetlength\gradingDot{#1}}, +simple root radius/.code={\pgfmathsetlength\simple@root@radius{#1}}, +weight/.style={fill=gray,draw=white}, +root/.style={fill=gray,draw=white}, +simple root/.style={fill=white,draw=gray}, +fundamental weight/.style={fill=black,draw=gray}, +multiplicity/.estore in = \weight@multiplicity, +multiplicity/.default = 1, +.search also={/tikz}, +} \makeatletter \def\root@system{?} @@ -93,14 +108,15 @@ fadings \pgf@y=\pgfmathresult pt% } -\NewDocumentEnvironment{rootSystem}{m}% +\NewDocumentEnvironment{rootSystem}{O{}m}% {% \xdef\weight@lattice@size{\defaultWeightLatticeSize}% -\IfSubStr{ABCG}{#1}{}{\unrecognized@root@system{#1}}% -\xdef\root@system{#1}% +\IfSubStr{ABCG}{#2}{}{\unrecognized@root@system{#2}}% +\xdef\root@system{#2}% \check@root@system{}% \choose@weight@lattice{}% \choose@root@lattice{}% +\pgfkeys{/root system,#1}% }% {% \IfStrEq{\weight@lattice@size}{0}%% @@ -116,7 +132,10 @@ fadings }% \NewDocumentCommand\simpleroots{}% -{\rt[black]{1}{0}\rt[black]{0}{1}} +{\rt[simple root]{1}{0}\rt[simple root]{0}{1}} + +\NewDocumentCommand\fundamentalweights{}% +{\wt[fundamental weight]{1}{0}\wt[fundamental weight]{0}{1}} \NewDocumentCommand\choose@root@lattice{} {% @@ -132,17 +151,17 @@ fadings \NewDocumentCommand\A@root{mm}% x,y in units of simple roots {% -(hex cs:x={(2*(#1)-(#2))},y={(-(#1)+2*(#2))})% +(hex cs:x={(-(#1)+2*(#2))},y={(2*(#1)-(#2))})% }% \NewDocumentCommand\B@root{mm}% x,y in units of simple roots {% -(square cs:x={((#1)-(#2))},y=#2)% +(square cs:x={((#1))},y={(-(#1)+(#2))})% }% \NewDocumentCommand\C@root{mm}% x,y in units of simple roots {% -(square cs:x={(2*(#1)-(#2))},y={#2})% +(square cs:x={(2*(#2)-(#1))},y={#1})% }% \NewDocumentCommand\G@root{mm}% x,y in units of simple roots @@ -150,21 +169,6 @@ fadings (hex cs:x={(-(#1)+(#2))},y={(2*(#1)-(#2))})% }% -\NewDocumentCommand\rt{O{}mm}%[tikz options,multiplicity=???]{x}{y} -{% -\check@root@system% -\pgfkeys{/weight, default, #1}% -\IfStrEq{\weight@multiplicity}{1}{}% -{%%% -\foreach \i in {2,...,\weight@multiplicity}% -{% -\draw[/weight,weight,#1,fill=none] \Root{#2}{#3} circle ({\i*\weightRadius});% -}% -}%%% -\fill[/weight,weight,#1] \Root{#2}{#3} circle (\weightRadius);% -%}%% -}% - \NewDocumentCommand\unrecognized@root@system{m}% {% \ClassError{Rank 2 roots}{Unrecognized root system: ``#1''. Allowed values are A,B,C,G}{}% @@ -196,19 +200,19 @@ fadings {% \check@root@system% \begin{scope}[on background layer]% -\draw[weight lattice,step=\weightLength,#1] +\draw[/root system/weight lattice,step=\weightLength,#1] ({-\weight@lattice@size*\weightLength},{-\weight@lattice@size*\weightLength}) grid ({\weight@lattice@size*\weightLength},{\weight@lattice@size*\weightLength});% \foreach \i in {-\weight@lattice@size,...,\weight@lattice@size}% {% -\draw[weight lattice,#1] ({\weightLength*\i},{\weightLength*\weight@lattice@size}) +\draw[/root system/weight lattice,#1] ({\weightLength*\i},{\weightLength*\weight@lattice@size}) -- ({\weightLength*\weight@lattice@size},{\weightLength*\i});% -\draw[weight lattice,#1] ({-\weightLength*\weight@lattice@size},{\weightLength*\i}) +\draw[/root system/weight lattice,#1] ({-\weightLength*\weight@lattice@size},{\weightLength*\i}) -- ({\weightLength*\i},{-\weightLength*\weight@lattice@size});% -\draw[weight lattice,#1] ({-\weightLength*\i},{\weightLength*\weight@lattice@size}) +\draw[/root system/weight lattice,#1] ({-\weightLength*\i},{\weightLength*\weight@lattice@size}) -- ({-\weightLength*\weight@lattice@size},{\weightLength*\i});% -\draw[weight lattice,#1] ({\weightLength*\weight@lattice@size},{\weightLength*\i}) +\draw[/root system/weight lattice,#1] ({\weightLength*\weight@lattice@size},{\weightLength*\i}) -- ({-\weightLength*\i},{-\weightLength*\weight@lattice@size});% }% \end{scope}% @@ -219,7 +223,6 @@ fadings \B@weight@lattice[#1]% }% - \NewDocumentCommand\weightLattice{O{}m}% {% \check@root@system% @@ -238,29 +241,63 @@ fadings \NewDocumentCommand\hexwt{O{}mm}% {% \check@root@system% -\pgfkeys{/weight, default, #1}% +\pgfkeys{/root system,#1}% \IfStrEq{\weight@multiplicity}{1}{}% {%%% \foreach \i in {2,...,\weight@multiplicity}% {% -\draw[/weight,weight,#1,fill=none] (hex cs:x=#2,y=#3) circle ({\i*\weightRadius});% +\draw[/root system,weight,#1,fill=none] (hex cs:x=#2,y=#3) circle ({\i*\weightRadius});% }% +\gdef\weight@multiplicity{1}% }%%% -\fill[/weight,weight,#1] (hex cs:x=#2,y=#3) circle (\weightRadius);% +\fill[/root system,weight,#1] (hex cs:x=#2,y=#3) circle (\weightRadius);% }% \NewDocumentCommand\squarewt{O{}mm}% {% \check@root@system% -\pgfkeys{/weight, default, #1}% +\pgfkeys{/root system,weight,#1}% +\IfStrEq{\weight@multiplicity}{1}{}% +{%%% +\foreach \i in {2,...,\weight@multiplicity}% +{% +\draw[/root system,weight,#1,fill=none] (square cs:x=#2,y=#3) circle ({\i*\weightRadius});% +}% +\gdef\weight@multiplicity{1}% +}%%% +\fill[/root system,weight,#1] (square cs:x=#2,y=#3) circle (\weightRadius);% +}% + +\NewDocumentCommand\rt{O{}mm}%[tikz options,multiplicity=???]{x}{y} +{% +\check@root@system% +\pgfkeys{/root system,weight,#1}% +\IfStrEq{\weight@multiplicity}{1}{}% +{%%% +\foreach \i in {2,...,\weight@multiplicity}% +{% +\draw[/root system,weight,#1,fill=none] \Root{#2}{#3} circle ({\i*\weightRadius});% +}% +\gdef\weight@multiplicity{1}% +}%%% +\fill[/root system,weight,#1] \Root{#2}{#3} circle (\weightRadius);% +%}%% +}% + +\NewDocumentCommand\wt{O{}mm}%[tikz options,multiplicity=???]{x}{y} +{% +\check@root@system% +\pgfkeys{/root system,weight,#1}% \IfStrEq{\weight@multiplicity}{1}{}% {%%% \foreach \i in {2,...,\weight@multiplicity}% {% -\draw[/weight,weight,#1,fill=none] (square cs:x=#2,y=#3) circle ({\i*\weightRadius});% +\draw[/root system,weight,#1,fill=none] \weight{#2}{#3} circle ({\i*\weightRadius});% }% +\gdef\weight@multiplicity{1}% }%%% -\fill[/weight,weight,#1] (square cs:x=#2,y=#3) circle (\weightRadius);% +\fill[/root system,weight,#1] \weight{#2}{#3} circle (\weightRadius);% +%}%% }% \newif\if@decimals @@ -322,38 +359,10 @@ fadings }%% }% - -\def\weight@multiplicity{1} -\pgfkeys{ -/weight/.is family, -/weight, -weight/.style = {fill=gray,draw=gray}, - default/.style = { - multiplicity/.estore in = \weight@multiplicity, - multiplicity = 1, - }, - .search also={/tikz}, -} - -\NewDocumentCommand\wt{O{}mm}%[tikz options,multiplicity=???]{x}{y} -{% -\check@root@system% -\pgfkeys{/weight, default, #1}% -\IfStrEq{\weight@multiplicity}{1}{}% -{%%% -\foreach \i in {2,...,\weight@multiplicity}% -{% -\draw[/weight,weight,#1,fill=none] \weight{#2}{#3} circle ({\i*\weightRadius});% -}% -}%%% -\fill[/weight,weight,#1] \weight{#2}{#3} circle (\weightRadius);% -%}%% -}% - \NewDocumentCommand\A@roots{O{}}% {% \begin{scope}[on background layer]% -\fill[root polygon] +\fill[/root system/root polygon] (hex cs:x=1,y=1) -- (hex cs:x=-1,y=2) -- (hex cs:x=-2,y=1) -- @@ -373,7 +382,7 @@ cycle;% \NewDocumentCommand\B@roots{O{}}% {% \begin{scope}[on background layer]% -\fill[root polygon] +\fill[/root system/root polygon] (square cs:x=-1,y=-1) -- (square cs:x=-1,y=1) -- (square cs:x=1,y=1) -- @@ -401,7 +410,7 @@ cycle;% \NewDocumentCommand\C@roots{O{}}% {% \begin{scope}[on background layer]% -\fill[root polygon] +\fill[/root system/root polygon] (square cs:x=2,y=0) -- (square cs:x=0,y=2) -- (square cs:x=-2,y=0) -- @@ -421,7 +430,7 @@ cycle;% \NewDocumentCommand\G@roots{O{}}% {% \begin{scope}[on background layer]% -\fill[root polygon] +\fill[/root system/root polygon] (hex cs:x=1,y=0) -- (hex cs:x=1,y=1) -- (hex cs:x=0,y=1) -- @@ -488,10 +497,10 @@ cycle;% \begin{scope}[on background layer] \IfStrEqCase{\root@system}% {%% -{A}{\fill[Weyl chamber,#1] \weight{0}{#2} -- \weight{0}{0} -- \weight{#2}{0} --cycle;}% -{B}{\fill[Weyl chamber,#1] (square cs:x=#2,y=#2) -- (square cs:x=0,y=0) --(square cs:x=#2,y=0) --cycle;}% -{C}{\fill[Weyl chamber,#1] (square cs:x=#2,y=#2) -- (square cs:x=0,y=0) --(square cs:x=#2,y=0) --cycle;}% -{G}{\fill[Weyl chamber,#1] (hex cs:x={(.5*#2)},y={(.5*#2)}) -- (hex cs:x=0,y=0) --(hex cs:x=#2,y=0) --cycle;}% +{A}{\fill[/root system/Weyl chamber,#1] \weight{0}{#2} -- \weight{0}{0} -- \weight{#2}{0} --cycle;}% +{B}{\fill[/root system/Weyl chamber,#1] (square cs:x=#2,y=#2) -- (square cs:x=0,y=0) --(square cs:x=#2,y=0) --cycle;}% +{C}{\fill[/root system/Weyl chamber,#1] (square cs:x=#2,y=#2) -- (square cs:x=0,y=0) --(square cs:x=0,y=#2) --cycle;}% +{G}{\fill[/root system/Weyl chamber,#1] (hex cs:x={(.5*#2)},y={(.5*#2)}) -- (hex cs:x=0,y=0) --(hex cs:x=#2,y=0) --cycle;}% }%% [\check@root@system]% \end{scope} @@ -502,16 +511,15 @@ cycle;% \begin{scope}[on background layer] \IfStrEqCase{\root@system}% {%% -{A}{\fill[Weyl chamber,#1] (hex cs:x=0,y=1.5) -- (hex cs:x=0,y=0) -- (hex cs:x=1.5,y=0) -- (hex cs:x=1,y=1) -- cycle;}% -{B}{\fill[Weyl chamber,#1] (square cs:x=1,y=1) -- (square cs:x=0,y=0) --(square cs:x=1,y=0) --cycle;}% -{C}{\fill[Weyl chamber,#1] (square cs:x=1,y=1) -- (square cs:x=0,y=0) --(square cs:x=2,y=0) --cycle;}% -{G}{\fill[Weyl chamber,#1] (hex cs:x=1,y=1) -- (hex cs:x=0,y=0) --(hex cs:x=1,y=0) --cycle;}% +{A}{\fill[/root system/Weyl chamber,#1] (hex cs:x=0,y=1.5) -- (hex cs:x=0,y=0) -- (hex cs:x=1.5,y=0) -- (hex cs:x=1,y=1) -- cycle;}% +{B}{\fill[/root system/Weyl chamber,#1] (square cs:x=1,y=1) -- (square cs:x=0,y=0) --(square cs:x=1,y=0) --cycle;}% +{C}{\fill[/root system/Weyl chamber,#1] (square cs:x=1,y=1) -- (square cs:x=0,y=0) --(square cs:x=2,y=0) --cycle;}% +{G}{\fill[/root system/Weyl chamber,#1] (hex cs:x=1,y=1) -- (hex cs:x=0,y=0) --(hex cs:x=1,y=0) --cycle;}% }%% [\check@root@system]% \end{scope} }% - \NewDocumentCommand\WeylChamber{O{}}% {% \check@root@system% @@ -539,10 +547,10 @@ cycle;% \tikzdeclarecoordinatesystem{B weight}% {% \setkeys{Bkeys}{#1}% -\ifAutoSizeWeightLattice\auto@stretch@square{(\myx+.5*(\myy))}{(.5*(\myy))}\fi% -\pgfmathparse{((\myx)+.5*(\myy))*\weightLength}% +\ifAutoSizeWeightLattice\auto@stretch@square{(\myy+.5*(\myx))}{(.5*(\myx))}\fi% +\pgfmathparse{((\myy)+.5*(\myx))*\weightLength}% \pgf@x=\pgfmathresult pt% -\pgfmathparse{.5*(\myy)*\weightLength}% +\pgfmathparse{.5*(\myx)*\weightLength}% \pgf@y=\pgfmathresult pt% } @@ -557,10 +565,10 @@ cycle;% \tikzdeclarecoordinatesystem{C weight}% {% \setkeys{Ckeys}{#1}% -\ifAutoSizeWeightLattice\auto@stretch@square{(\myx+\myy)}{(\myy)}\fi% -\pgfmathparse{(\myx+\myy)*\weightLength}% +\ifAutoSizeWeightLattice\auto@stretch@square{(\myx+\myy)}{(\myx)}\fi% +\pgfmathparse{\myx*\weightLength}% \pgf@x=\pgfmathresult pt% -\pgfmathparse{\myy*\weightLength}% +\pgfmathparse{(\myx+\myy)*\weightLength}% \pgf@y=\pgfmathresult pt% } @@ -576,7 +584,7 @@ cycle;% \NewDocumentCommand\draw@hex@grid@line{O{}mmmm}% {% -\draw[weight lattice,#1] (hex cs:x=#2,y=#3) -- (hex cs:x=#4,y=#5);% +\draw[/root system/weight lattice,#1] (hex cs:x=#2,y=#3) -- (hex cs:x=#4,y=#5);% }% \NewDocumentCommand\hexgrid{O{}m}% @@ -624,23 +632,23 @@ cycle;% \NewDocumentCommand\A@positive@root@hyperplane{O{}}% {% \begin{scope}[on background layer] -\fill[hyperplane,#1] (hex cs:x=-1.5,y=1.5) --(hex cs:x=-1,y=2) --(hex cs:x=1,y=1) --(hex cs:x=2,y=-1) --(hex cs:x=1.5,y=-1.5) --cycle;% +\fill[/root system/hyperplane,#1] (hex cs:x=-1.5,y=1.5) --(hex cs:x=-1,y=2) --(hex cs:x=1,y=1) --(hex cs:x=2,y=-1) --(hex cs:x=1.5,y=-1.5) --cycle;% \end{scope} }% - \NewDocumentCommand\B@positive@root@hyperplane{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-1,y=.5) -- (square cs:x=-1,y=1) -- (square cs:x=1,y=1) -- (square cs:x=1,y=-.5) -- cycle;% +\fill[/root system/hyperplane,#1] +(square cs:x=-.5,y=1) -- (square cs:x=1,y=1) -- (square cs:x=1,y=-1) -- (square cs:x=.5,y=-1) -- cycle;% +%(square cs:x=-1,y=.5) -- (square cs:x=-1,y=1) -- (square cs:x=1,y=1) -- (square cs:x=1,y=-.5) -- cycle;% \end{scope}% }% - \NewDocumentCommand\C@positive@root@hyperplane{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-1.5,y=.5) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- (square cs:x=1.5,y=-.5) -- cycle;% +\fill[/root system/hyperplane,#1] (square cs:x=-1.5,y=.5) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- (square cs:x=1.5,y=-.5) -- cycle;% \end{scope}% }% @@ -648,7 +656,7 @@ cycle;% \NewDocumentCommand\G@positive@root@hyperplane{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] +\fill[/root system/hyperplane,#1] (hex cs:x=-1,y=1.5) -- (hex cs:x=-1,y=2) -- (hex cs:x=0,y=1) -- @@ -675,28 +683,28 @@ cycle;% \NewDocumentCommand\A@parabolic@one{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (hex cs:x=-2,y=1) -- (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1) -- cycle;% +\fill[/root system/hyperplane,#1] (hex cs:x=-2,y=1) -- (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1) -- cycle;% \end{scope}% }% \NewDocumentCommand\A@parabolic@two{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1) -- (hex cs:x=1,y=-2) -- cycle;% +\fill[/root system/hyperplane,#1] (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1) -- (hex cs:x=1,y=-2) -- cycle;% \end{scope}% }% \NewDocumentCommand\B@parabolic@one{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-1,y=0) --(square cs:x=-1,y=1) --(square cs:x=1,y=1) --(square cs:x=1,y=0) --cycle;% +\fill[/root system/hyperplane,#1] (square cs:x=0,y=-1) --(square cs:x=1,y=-1) --(square cs:x=1,y=1) --(square cs:x=0,y=1) --cycle;% \end{scope}% }% \NewDocumentCommand\B@parabolic@two{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-1,y=1) --(square cs:x=1,y=-1) --(square cs:x=1,y=1) --cycle;% +\fill[/root system/hyperplane,#1] (square cs:x=-1,y=1) --(square cs:x=1,y=-1) --(square cs:x=1,y=1) --cycle;% \end{scope}% }% @@ -704,7 +712,7 @@ cycle;% \NewDocumentCommand\C@parabolic@one{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-2,y=0) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- cycle;% +\fill[/root system/hyperplane,#1] (square cs:x=-2,y=0) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- cycle;% \end{scope}% }% @@ -712,7 +720,7 @@ cycle;% \NewDocumentCommand\C@parabolic@two{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (square cs:x=-1,y=1) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- (square cs:x=1,y=-1) -- cycle;% +\fill[/root system/hyperplane,#1] (square cs:x=-1,y=1) -- (square cs:x=0,y=2) -- (square cs:x=2,y=0) -- (square cs:x=1,y=-1) -- cycle;% \end{scope}% }% @@ -720,7 +728,7 @@ cycle;% \NewDocumentCommand\G@parabolic@one{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (hex cs:x=-1,y=1) -- (hex cs:x=-1,y=2) -- (hex cs:x=0,y=1) -- (hex cs:x=1,y=1) -- (hex cs:x=1,y=0) -- (hex cs:x=2,y=-1) -- (hex cs:x=1,y=-1) -- cycle;% +\fill[/root system/hyperplane,#1] (hex cs:x=-1,y=1) -- (hex cs:x=-1,y=2) -- (hex cs:x=0,y=1) -- (hex cs:x=1,y=1) -- (hex cs:x=1,y=0) -- (hex cs:x=2,y=-1) -- (hex cs:x=1,y=-1) -- cycle;% \end{scope}% }% @@ -728,7 +736,7 @@ cycle;% \NewDocumentCommand\G@parabolic@two{O{}}% {% \begin{scope}[on background layer]% -\fill[hyperplane,#1] (hex cs:x=-1,y=2) --(hex cs:x=0,y=1) --(hex cs:x=1,y=1) --(hex cs:x=1,y=0) --(hex cs:x=2,y=-1) --(hex cs:x=1,y=-1) --(hex cs:x=1,y=-2) --cycle;% +\fill[/root system/hyperplane,#1] (hex cs:x=-1,y=2) --(hex cs:x=0,y=1) --(hex cs:x=1,y=1) --(hex cs:x=1,y=0) --(hex cs:x=2,y=-1) --(hex cs:x=1,y=-1) --(hex cs:x=1,y=-2) --cycle;% \end{scope}% }% @@ -757,17 +765,19 @@ cycle;% {% \IfStrEqCase{\root@system\parabolic@subalgebra}% {%% -{A1}{\draw[grading] (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1);}% -{A2}{\draw[grading] (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1);}% -{A3}{\draw[grading] (hex cs:x=-1,y=2) -- (hex cs:x=2,y=-1);\draw[grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=0);}% -{B1}{\draw[grading] (square cs:x=-1,y=1) -- (square cs:x=1,y=1);}% -{B2}{\draw[grading] (square cs:x=0,y=1) -- (square cs:x=1,y=0);\draw[grading] (square cs:x=1,y=1) circle (\gradingDot);}% -{B3}{\draw[grading] (square cs:x=-1,y=1) -- (square cs:x=1,y=0);% -\draw[grading] (square cs:x=0,y=1) -- (square cs:x=1,y=.5);% -\draw[grading] (square cs:x=1,y=1) circle (\gradingDot);}% -{C1}{\draw[grading] (square cs:x=-2,y=1) -- (square cs:x=2,y=1);% -\draw[grading] (square cs:x=-2,y=2) -- (square cs:x=2,y=2);}% -{C2}{\draw[grading] (square cs:x=0,y=2) -- (square cs:x=2,y=0);}% +{A1}{\draw[/root system/grading] (hex cs:x=-1,y=2) -- (hex cs:x=1,y=1);}% +{A2}{\draw[/root system/grading] (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1);}% +{A3}{\draw[/root system/grading] (hex cs:x=-1,y=2) -- (hex cs:x=2,y=-1);% +\draw[/root system/grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=0);}% +{B1}{\draw[/root system/grading] (square cs:x=1,y=-1) -- (square cs:x=1,y=1);}% +{B2}{\draw[/root system/grading] (square cs:x=0,y=1) -- (square cs:x=1,y=0);% +\draw[/root system/grading] (square cs:x=1,y=1) circle (\gradingDot);}% +{B3}{\draw[/root system/grading] (square cs:x=1,y=-1) -- (square cs:x=0,y=1);% +\draw[/root system/grading] (square cs:x=1,y=0) -- (square cs:x=.5,y=1);% +\draw[/root system/grading] (square cs:x=1,y=1) circle (\gradingDot);}% +{C1}{\draw[/root system/grading] (square cs:x=-2,y=1) -- (square cs:x=2,y=1);% +\draw[/root system/grading] (square cs:x=-2,y=2) -- (square cs:x=2,y=2);}% +{C2}{\draw[/root system/grading] (square cs:x=0,y=2) -- (square cs:x=2,y=0);}% {C3}{ \begin{scope} \clip @@ -776,31 +786,32 @@ cycle;% (square cs:x=2,y=-2) -- (square cs:x=-2,y=-2) -- cycle; -\draw[grading] (square cs:x=0,y=2) -- (square cs:x=2,y=1.333333); -\draw[grading] (square cs:x=-2,y=1.3333333) -- (square cs:x=2,y=0); -\draw[grading] (square cs:x=-2,y=2) -- (square cs:x=2,y=.666666); +\draw[/root system/grading] (square cs:x=0,y=2) -- (square cs:x=2,y=1.333333); +\draw[/root system/grading] (square cs:x=-2,y=1.3333333) -- (square cs:x=2,y=0); +\draw[/root system/grading] (square cs:x=-2,y=2) -- (square cs:x=2,y=.666666); \end{scope} }% -{G1}{\draw[grading] (hex cs:x=-1,y=2) -- (hex cs:x=2,y=-1);\draw[grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=0);}% +{G1}{\draw[/root system/grading] (hex cs:x=-1,y=2) -- (hex cs:x=2,y=-1);% +\draw[/root system/grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=0);}% {G2}{\begin{scope}[on background layer] \IfStrEq{\weight@lattice@size}{0}% {% -\draw[grading] (square cs:x=1.5,y=\sqrt@three) -- (square cs:x=1.5,y=-\sqrt@three); -\draw[grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=-2); -\draw[grading] (hex cs:x=-.5,y=2) -- (hex cs:x=1.5,y=-2); +\draw[/root system/grading] (square cs:x=1.5,y=\sqrt@three) -- (square cs:x=1.5,y=-\sqrt@three); +\draw[/root system/grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=-2); +\draw[/root system/grading] (hex cs:x=-.5,y=2) -- (hex cs:x=1.5,y=-2); }% {% \hexclip -\draw[grading] (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1); -\draw[grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=-2); -\draw[grading] (hex cs:x=-.5,y=2) -- (hex cs:x=1.5,y=-2); +\draw[/root system/grading] (hex cs:x=1,y=1) -- (hex cs:x=2,y=-1); +\draw[/root system/grading] (hex cs:x=0,y=2) -- (hex cs:x=2,y=-2); +\draw[/root system/grading] (hex cs:x=-.5,y=2) -- (hex cs:x=1.5,y=-2); }% \end{scope}}% {G3}{\begin{scope}[on background layer] \IfStrEq{\weight@lattice@size}{0}{}{\hexclip}% \foreach \i in {1,...,5}% {% -\draw[grading] +\draw[/root system/grading] (square cs:x={.333333333*(\i-1)},y=\sqrt@three) -- (square cs:x={.333333333*(\i+1)},y=-\sqrt@three); }% |