557 lines
17 KiB
TeX
557 lines
17 KiB
TeX
%%%%%%%%%% Oriented LR RM splitting %%%%%%%%%%%%
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\newcommand\PICorientLRsplitRM{\setlength{\unitlength}{0.5mm}
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\begin{picture}(10,8)(-1.5,2)
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%under:
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\qbezier(0,0)(1,0.7)(1.5,1.1)
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\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
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\qbezier(1.5,6.9)(1,7.3)(0,8)
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%over:
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\qbezier(6,0)(-3,4)(6,8)
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%%%%%%%%%%%%%%%%%%%
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\put(-1,9){\vector(-3.5,3){0.2}}%
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\put(7,9){\vector(3.3,3){0.2}}
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\end{picture}}
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\newcommand\PICorientpluscrossRMup{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,2)(-1.4,-0.6)
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\put(-1,-1){\vector(1,1){2.3}}%
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%%%%%%%%%%%%%%
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\put(-1,1){\vector(-1,1){0.3}}%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%
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%%%
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\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
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\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
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\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
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\put(1.5,0.2){\vector(1,0){0.3}}%
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\end{picture}}
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\newcommand\PICorientpluscrossRMdown{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,2)(-1.4,-0.6)
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\put(-1,-1){\vector(1,1){2.3}}%
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%%%%%%%%%%%%%%
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\put(-1,1){\vector(-1,1){0.3}}%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%
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\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
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\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
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\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
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\put(1.5,0.2){\vector(1,0){0.3}}%
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\end{picture}}
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%%%%%%%%%%%%%%
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%%%%%% mine %%%%%
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%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
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\newcommand\PICunorientpluscrossRMsolveDOWN{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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%\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%%
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%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%left
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\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2)
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\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
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%%%%%%%%%%%%
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\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
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\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
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\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
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\end{picture}}
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%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
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\newcommand\PICunorientpluscrossRMsolveUP{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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%\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%%
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%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%left
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\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2)
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%rigth
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\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
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%%%%%%%%%%%%
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\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
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\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
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\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
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\end{picture}}
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%%%%%%%%%
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\newcommand\PICunorientpluscrossRMsolveHorizontalDown{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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%\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%%
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%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%left
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\qbezier(1.2,1.2)(0,-1)(-1.2,1.2)
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%rigth
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\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
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%%%%%%%%%%%%
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\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
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\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
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\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
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\end{picture}}
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%%%%%%%%%%%%%%
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\newcommand\PICunorientpluscrossRMsolveHorizontal{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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%\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%%
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%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%left
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\qbezier(1.2,1.2)(0,-1)(-1.2,1.2)
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%rigth
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\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
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%%%%%%%%%%%%
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\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
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\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
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\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
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\end{picture}}
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\newcommand\PICunorientLRsplitSolve{\setlength{\unitlength}{0.6mm}
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\begin{picture}(9,6)(-1,2)
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\qbezier(0,0)(1,0.7)(1.5,1.1)
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%\qbezier(3.4, 2.8)(6,4)(3.6, 5)
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\qbezier(6,8)(3,4)(0,8)
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\qbezier(6,0)(-3,6)(4,4)
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\qbezier(4,4)(4,2)(4,2)
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%\qbezier(6,4)(-3,6)(4,3)
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\end{picture}}
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%%%%%%%%%%%%%%
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%%%%%% mine %%%%%
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%%% Unoriented LR splitting RM move II %%%%%%%%%%%%
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\newcommand\PICunorientLRsplitRM{\setlength{\unitlength}{0.6mm}
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\begin{picture}(9,6)(-1,2)
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\qbezier(0,0)(1,0.7)(1.5,1.1)
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\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
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\qbezier(1.5,6.9)(1,7.3)(0,8)
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\qbezier(6,0)(-3,4)(6,8)
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\end{picture}}
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\newcommand\PICunorientpluscrossRMup{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%
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\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
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\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
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\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
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\end{picture}}
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\newcommand\PICunorientpluscrossRMdown{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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%%%
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\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
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\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
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\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
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\end{picture}}
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%%%%%% Symbol-Pictures %%%%%%%%%%%%%%%
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% thickness of lines in symbol-pictures
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\linethickness{0.3pt}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%% UNORIENTED %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED
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%%% Unoriented trivial line
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\newcommand\PICline{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2,1)
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\put(0.9,-0.5){\line(0,1){2}}
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\end{picture}}
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%%% Trivial circle
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\newcommand\PICcircle{\setlength{\unitlength}{3mm}
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\begin{picture}(1.8,1)(0.2,0.5)
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\put(1,1){\circle{1.2}}
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\end{picture}}
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%%% Union of unoriented vertical line and circle
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\newcommand\PIClinecircle{\setlength{\unitlength}{2.5mm}
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\begin{picture}(4.5,1.2)(0.5,0.5)
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\put(1,0){\line(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
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\put(3.8,1){\circle{1.2}}
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\end{picture}}
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%%% Unoriented LR splitting %%%%%%%%%%%%
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\newcommand\PICunorientLRsplit{\setlength{\unitlength}{0.6mm}
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\begin{picture}(9,6)(-1,2)
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\qbezier(0,0)(4,4)(0,8) \qbezier(6,0)(2,4)(6,8)
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\end{picture}}
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%%% Unoriented UD splitting %%%%%%%%%%%%
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\newcommand\PICunorientUDsplit{\setlength{\unitlength}{0.6mm}
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\begin{picture}(11,6)(-1,1)
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\qbezier(0,6)(4,2)(8,6) \qbezier(0,0)(4,4)(8,0)
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\end{picture}}
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%%%%%%%%%% Unoriented line + crossing %%%%%%%%%%%%
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\newcommand\PICunorientpluscross{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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\qbezier(-1,-1)(0.0,0.0)(1,1)
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%%%%%%%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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\end{picture}}
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%%%%%%%%%% Unoriented line - crossing %%%%%%%%%%%%
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\newcommand\PICunorientminuscross{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,1.9)(-1.3,-0.6)
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\qbezier(1,-1)(0.0,0.0)(-1,1)
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%%%%%%%
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\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
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\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
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\end{picture}}
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%%%%%%%%%% Unoriented open writhes gamma_{+} %%%%%%%%%%%%
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\newcommand\PICopengammaplus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(11,8)(-2,-6)
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%top-left Bezier
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\qbezier(1.4,-5.2)(2.0,-6.2)(3.2,-6.1)
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%top-right Bezier
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\qbezier(3.2,-6.2)(6.0,-6.2)(6.2,-3.1)
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%bottom-right Bezier
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\qbezier(6.2,-3.1)(5.9,-0.3)(3.1,-0)
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%bottom-left Bezier
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\qbezier(3.1,-0)(0.3,-0.3)(0.0,-2.9)
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%line
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\put(0.0,-3.1){\line(0,-1){7}} \put(0,0.8){\line(0,1){4}}
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\end{picture}}
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%%%%%%%%%% Unoriented open writhes gamma_{-} %%%%%%%%%%%%
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\newcommand\PICopengammaminus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(11,8)(-2,0)
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%top-left Bezier
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\qbezier(1.4,5.2)(2.0,6.2)(3.2,6.1)
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%top-right Bezier
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\qbezier(3.2,6.2)(6.0,6.2)(6.2,3.1)
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%bottom-right Bezier
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\qbezier(6.2,3.1)(5.9,0.3)(3.1,0)
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%bottom-left Bezier
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\qbezier(3.1,0)(0.3,0.3)(0.0,2.9)
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%line
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\put(0.0,3.1){\line(0,1){7}} \put(0,-0.8){\line(0,-1){4}}
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\end{picture}}
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%%%%%%%%%% Unoriented closed writhes gamma_{+} %%%%%%%%%%%%
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\newcommand\PICclosedgammaplus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(12,7)(-6,-2)
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%%%% Right Branch %%%%%%%%%
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%Right-bottom-left Bezier
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\qbezier(1.4,-2.3)(2.0,-3.3)(3.2,-3.2)
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%Right-bottom-right Bezier
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\qbezier(3.2,-3.3)(6.0,-3.3)(6.2,-0.3)
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%Right-top-right Bezier
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\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
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%Right-top-left Bezier
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\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)
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%%%% Left Branch %%%%%%%%%
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%Left-bottom-right Bezier
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\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
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%Left-bottom-left Bezier
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\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
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%Left-top-left Bezier
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\qbezier(-3.2,3.3)(-6.0,3.3)(-6.2,0.3)
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%Left-top-right Bezier
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\qbezier(-1.4,2.3)(-2.0,3.3)(-3.2,3.2)
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\end{picture}}
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%%%%%%%%%% Unoriented closed writhes gamma_{-} %%%%%%%%%%%%
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\newcommand\PICclosedgammaminus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(12,7)(-6,-2)
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%%%% Right Branch %%%%%%%%%
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%Right-top-left Bezier
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\qbezier(1.4,2.3)(2.0,3.3)(3.2,3.2)
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%Right-top-right Bezier
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\qbezier(3.2,3.3)(6.0,3.3)(6.2,0.3)
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%Right-bottom-right Bezier
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\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
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%Right-bottom-left Bezier
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\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
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%%%% Left Branch %%%%%%%%%
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%Left-top-right Bezier
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\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
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%Left-top-left Bezier
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\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
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%Left-bottom-left Bezier
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\qbezier(-3.2,-3.3)(-6.0,-3.3)(-6.2,-0.3)
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%Left-bottom-right Bezier
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\qbezier(-1.4,-2.3)(-2.0,-3.3)(-3.2,-3.2)
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\end{picture}}
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%%%%%%%%%% Unoriented close writhes gamma_{+} %%%%%%%%%%%%
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\newcommand\PICclosegammaplus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(16,8)(-8,-2)
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%RIGHT-top-left Bezier
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\qbezier(1.4,-1.8)(2.0,-2.7)(3.2,-2.9)
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%RIGHT-top-right Bezier
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\qbezier(3.2,-2.9)(6.0,-2.7)(6.2,-0.2)
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%RIGHT-bottom-right Bezier
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\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
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%RIGHT-bottom-left Bezier
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\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)
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%%%%%%
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%%%%%%
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%LEFT-top-right Bezier
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\qbezier(-1.4,1.8)(-2.0,2.7)(-3.2,2.9)
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%LEFT-top-left Bezier
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\qbezier(-3.2,2.9)(-6.0,2.7)(-6.2,0.2)
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%LEFT-bottom-left Bezier
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\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
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%LEFT-bottom-right Bezier
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\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
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\end{picture}}
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%%%%%%%%%% Unoriented close writhes gamma_{-} %%%%%%%%%%%%
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\newcommand\PICclosegammaminus{\setlength{\unitlength}{0.5mm}
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\begin{picture}(16,8)(-8,-2)
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%RIGHT-top-left Bezier
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\qbezier(-1.4,-1.8)(-2.0,-2.7)(-3.2,-2.9)
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%RIGHT-top-right Bezier
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\qbezier(-3.2,-2.9)(-6.0,-2.7)(-6.2,-0.2)
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%RIGHT-bottom-right Bezier
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\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
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%RIGHT-bottom-left Bezier
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\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
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%%%%%%
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%%%%%%
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%LEFT-top-right Bezier
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\qbezier(1.4,1.8)(2.0,2.7)(3.2,2.9)
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%LEFT-top-left Bezier
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\qbezier(3.2,2.9)(6.0,2.7)(6.2,0.2)
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%LEFT-bottom-left Bezier
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\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
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%LEFT-bottom-right Bezier
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\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
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\end{picture}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED
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%%%%%%%%%% Oriented trivial line %%%%%%%%%%%%
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\newcommand\PICorientline{\setlength{\unitlength}{2.5mm}
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\begin{picture}(2,1)
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\put(0.9,-0.5){\vector(0,1){2}}
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\end{picture}}
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%%%%%%%%%% Oriented trivial circle -- right %%%%%%%%%%
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\newcommand\PICorientcircleright{\setlength{\unitlength}{3mm}
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\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
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\put(1.3,1.55){\vector(1,0){0.01}} %%% Put arrow to the circle
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\end{picture}}
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%%%%%%%%%% Oriented trivial circle -- left %%%%%%%%%%
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\newcommand\PICorientcircleleft{\setlength{\unitlength}{3mm}
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\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
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\put(0.7,1.55){\vector(-1,0){0.01}} %%% Put arrow to the circle
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\end{picture}}
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%%% Union of oriented vertical line and circle
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\newcommand\PICorientlinecircle{\setlength{\unitlength}{2.5mm}
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%\begin{picture}(3.5,1.2)(0.5,0.5)
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%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
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%\put(2.6,1){\circle{1.2}}
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%\end{picture}}
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\begin{picture}(3.2,1.2)(0.5,0.5)
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\put(1,0){\vector(0,1){2}}
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\put(2.6,1){\circle{1.2}}
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\end{picture}}
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|
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%%% Union of oriented vertical line and oriented circle right
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\newcommand\PICorientlinecircler{\setlength{\unitlength}{2.5mm}
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%\begin{picture}(3.5,1.2)(0.5,0.5)
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%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
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%\put(2.6,1){\circle{1.2}}
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%\end{picture}}
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\begin{picture}(3.2,1.2)(0.5,0.5)
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\put(1,0){\vector(0,1){2}}
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\put(2.6,1){\circle{1.2}}
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\put(2.9,1.6){\vector(1,0){0.01}}
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\end{picture}}
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|
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%%%%%%%%%% Oriented line + crossing %%%%%%%%%%%%
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\newcommand\PICorientpluscross{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,2)(-1.4,-0.6)
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\put(-1,-1){\vector(1,1){2.3}}%
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%%%%%%%%%%%%%%
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\put(-1,1){\vector(-1,1){0.3}}%
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\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
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\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
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\end{picture}}
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|
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%%%%%%%%%% Oriented line - crossing %%%%%%%%%%%%
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\newcommand\PICorientminuscross{\setlength{\unitlength}{2mm}
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\begin{picture}(2.9,2)(-1.4,-0.6)
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\put(1,-1){\vector(-1,1){2.3}}%
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|
%%%
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|
\put(1,1){\vector(1,1){0.3}}%
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\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
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\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
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\end{picture}}
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|
|
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%%%%%%%%%% Oriented LR splitting %%%%%%%%%%%%
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\newcommand\PICorientLRsplit{\setlength{\unitlength}{0.5mm}
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\begin{picture}(10,8)(-1.5,2)
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|
%\arc
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|
\qbezier(0,0)(4,4)(0,8)
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|
%%%%%%%%%%%%%%%%%%%
|
|
\qbezier(6,0)(2,4)(6,8)
|
|
%%%%%%%%%%%%%%%%%%%
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|
\put(-0.2,9){\vector(-2,3){0.2}}%
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\put(7,9){\vector(2,3){0.2}}
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\end{picture}}
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|
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%%% Oriented UD splitting %%%%%%%%%%%%
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|
\newcommand\PICorientUDsplit{\setlength{\unitlength}{0.6mm}
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|
\begin{picture}(11,6)(-1,1)
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|
\qbezier(0,6)(4,2)(8,6)
|
|
\qbezier(0,0)(4,4)(8,0)
|
|
%%%%%%%%%%%%%%%%%%%
|
|
\put(-0.4,6.2){\vector(-3,2){0.2}}%
|
|
\put(8.4,6.2){\vector(3,2){0.2}}
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|
\put(-0.4,-0.2){\vector(-3,-2){0.2}}%
|
|
\put(8.4,-0.2){\vector(3,-2){0.2}}
|
|
\end{picture}}
|
|
|
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%%%%%%%%%% Oriented open writhes gamma_{+} %%%%%%%%%%%%
|
|
\newcommand\PICorientopengammaplus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,-6)
|
|
%top-left Bezier
|
|
\qbezier(1.4,-5.2)(2.0,-6.2)(3.2,-6.1)
|
|
%top-right Bezier
|
|
\qbezier(3.2,-6.2)(6.0,-6.2)(6.2,-3.1)
|
|
%bottom-right Bezier
|
|
\qbezier(6.2,-3.1)(5.9,-0.3)(3.1,-0)
|
|
%bottom-left Bezier
|
|
\qbezier(3.1,-0)(0.3,-0.3)(0.0,-2.9)
|
|
%line
|
|
\put(0.0,-3.1){\line(0,-1){7}} \put(0,0.8){\vector(0,1){4}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented open writhes gamma_{-} %%%%%%%%%%%%
|
|
\newcommand\PICorientopengammaminus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,0)
|
|
%top-left Bezier
|
|
\qbezier(1.4,5.2)(2.0,6.2)(3.2,6.1)
|
|
%top-right Bezier
|
|
\qbezier(3.2,6.2)(6.0,6.2)(6.2,3.1)
|
|
%bottom-right Bezier
|
|
\qbezier(6.2,3.1)(5.9,0.3)(3.1,0)
|
|
%bottom-left Bezier
|
|
\qbezier(3.1,0)(0.3,0.3)(0.0,2.9)
|
|
%line
|
|
\put(0.0,3.1){\vector(0,1){7}} \put(0,-0.8){\line(0,-1){4}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented clockwise overcurve %%%%%%%%%%%%
|
|
\newcommand\PICorientclockwise{\setlength{\unitlength}{0.6mm}
|
|
\begin{picture}(11,6)(-1,1)
|
|
\qbezier(0,3)(4,7)(8,3) \put(8,3){\vector(3,-2){0.1}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented anti-clockwise undercurve %%%%%%%%%%%%
|
|
\newcommand\PICorientanticlockwise{\setlength{\unitlength}{0.6mm}
|
|
\begin{picture}(11,6)(-1,1)
|
|
\qbezier(0,3)(4,-1)(8,3) \put(8,3){\vector(3,2){0.1}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented anti-clockwise overcurve %%%%%%%%%%%%
|
|
\newcommand\PICorientanticlockwiseover{\setlength{\unitlength}{0.6mm}
|
|
\begin{picture}(11,6)(-1,1)
|
|
\qbezier(0,3)(4,7)(8,3) \put(0,3){\vector(-3,-2){0.1}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented closed writhes gamma_{+} %%%%%%%%%%%%
|
|
\newcommand\PICorientclosedgammaplus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,7)(-6,-2)
|
|
|
|
%%%% Right Branch %%%%%%%%%
|
|
%Right-bottom-left Bezier
|
|
\qbezier(1.4,-2.3)(2.0,-3.3)(3.2,-3.2)
|
|
%Right-bottom-right Bezier
|
|
\qbezier(3.2,-3.3)(6.0,-3.3)(6.2,-0.3)
|
|
%Right-top-right Bezier
|
|
\qbezier(6.2,-0.2)(5.9,2.6)(3.1,2.9)
|
|
%Right-top-left Bezier
|
|
\qbezier(3.1,2.9)(0.3,2.6)(0.0,0.0)
|
|
\put(4.7,2.7){\vector(3,0){0.05}} %%% Putting arrow to \gamma+
|
|
% \put(-4.9,3.2){\vector(-3,0){0.04}}
|
|
|
|
%%%% Left Branch %%%%%%%%%
|
|
%Left-bottom-right Bezier
|
|
\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
|
|
%Left-bottom-left Bezier
|
|
\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
|
|
%Left-top-left Bezier
|
|
\qbezier(-3.2,3.3)(-6.0,3.3)(-6.2,0.3)
|
|
%Left-top-right Bezier
|
|
\qbezier(-1.4,2.3)(-2.0,3.3)(-3.2,3.2)
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Oriented closed writhes gamma_{-} %%%%%%%%%%%%
|
|
\newcommand\PICorientclosedgammaminus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,7)(-6,-2)
|
|
|
|
%%%% Right Branch %%%%%%%%%
|
|
%Right-top-left Bezier
|
|
\qbezier(1.4,2.3)(2.0,3.3)(3.2,3.2)
|
|
%Right-top-right Bezier
|
|
\qbezier(3.2,3.3)(6.0,3.3)(6.2,0.3)
|
|
%Right-bottom-right Bezier
|
|
\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
|
|
%Right-bottom-left Bezier
|
|
\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
|
|
% \put(4.9,3.2){\vector(3,0){0.04}} %%% Putting arrow to \gamma-
|
|
\put(-4.7,2.7){\vector(-3,0){0.05}}
|
|
|
|
%%%% Left Branch %%%%%%%%%
|
|
%Left-top-right Bezier
|
|
\qbezier(-3.1,2.9)(-0.3,2.6)(0.0,0.0)
|
|
%Left-top-left Bezier
|
|
\qbezier(-6.2,-0.2)(-5.9,2.6)(-3.1,2.9)
|
|
%Left-bottom-left Bezier
|
|
\qbezier(-3.2,-3.3)(-6.0,-3.3)(-6.2,-0.3)
|
|
%Left-bottom-right Bezier
|
|
\qbezier(-1.4,-2.3)(-2.0,-3.3)(-3.2,-3.2)
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% RibbonUnknot %%%%%%%%%%%%
|
|
\newcommand\PICRibbonUnknot{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,0)
|
|
\put(-2,-2.4){\includegraphics[width=0.035\textwidth]{RibbonUnknot}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% TwistedUnknot %%%%%%%%%%%%
|
|
\newcommand\PICTwistedUnknot{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,0)
|
|
\put(-2,-2.4){\includegraphics[width=0.035\textwidth]{TwistedUnknot}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Dehn surgery_{+} %%%%%%%%%%%%
|
|
\newcommand\PICDehnplus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,0)
|
|
\put(-2,-2.4){\includegraphics[width=0.1\textwidth]{Twplus}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%% Dehn surgery_{-} %%%%%%%%%%%%
|
|
\newcommand\PICDehnminus{\setlength{\unitlength}{0.5mm}
|
|
\begin{picture}(12,8)(-2.5,0)
|
|
\put(-3,-2){\includegraphics[width=0.1\textwidth]{Twminus}}
|
|
\end{picture}}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|