From bc5ff8b4f042de58fe26b00ce9fcc2c733572a94 Mon Sep 17 00:00:00 2001
From: Maria Marchwicka <maria.marchwicka@gmx.net>
Date: Sat, 4 May 2019 18:30:26 +0200
Subject: [PATCH] Macros

---
 knots_macros.tex | 556 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 556 insertions(+)
 create mode 100644 knots_macros.tex

diff --git a/knots_macros.tex b/knots_macros.tex
new file mode 100644
index 0000000..eb70782
--- /dev/null
+++ b/knots_macros.tex
@@ -0,0 +1,556 @@
+%%%%%%%%%% Oriented LR RM splitting %%%%%%%%%%%%
+\newcommand\PICorientLRsplitRM{\setlength{\unitlength}{0.5mm}
+\begin{picture}(10,8)(-1.5,2)
+%under:
+\qbezier(0,0)(1,0.7)(1.5,1.1)
+\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
+\qbezier(1.5,6.9)(1,7.3)(0,8)
+%over:
+\qbezier(6,0)(-3,4)(6,8)
+%%%%%%%%%%%%%%%%%%%
+\put(-1,9){\vector(-3.5,3){0.2}}%
+\put(7,9){\vector(3.3,3){0.2}}
+\end{picture}}
+
+
+\newcommand\PICorientpluscrossRMup{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,2)(-1.4,-0.6)
+\put(-1,-1){\vector(1,1){2.3}}%
+%%%%%%%%%%%%%%
+\put(-1,1){\vector(-1,1){0.3}}%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%
+%%%
+\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
+\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
+\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
+\put(1.5,0.2){\vector(1,0){0.3}}%
+\end{picture}}
+\newcommand\PICorientpluscrossRMdown{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,2)(-1.4,-0.6)
+\put(-1,-1){\vector(1,1){2.3}}%
+%%%%%%%%%%%%%%
+\put(-1,1){\vector(-1,1){0.3}}%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%
+\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
+\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
+\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
+\put(1.5,0.2){\vector(1,0){0.3}}%
+\end{picture}}
+
+%%%%%%%%%%%%%%
+%%%%%% mine %%%%%
+%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
+\newcommand\PICunorientpluscrossRMsolveDOWN{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+%\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%%
+%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%left
+\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2) 
+
+\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
+%%%%%%%%%%%%
+\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
+\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
+\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
+\end{picture}}
+%%% Unoriented LR splitting RM move III II solve %%%%%%%%%%%%
+\newcommand\PICunorientpluscrossRMsolveUP{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+%\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%%
+%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%left
+\qbezier(-1.2,-1.2)(0.5,0)(-1.2,1.2) 
+%rigth
+\qbezier(1.2,-1.2)(-0.5,0)(1.2,1.2)
+%%%%%%%%%%%%
+\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
+\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
+\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
+\end{picture}}
+%%%%%%%%%
+\newcommand\PICunorientpluscrossRMsolveHorizontalDown{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+%\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%%
+%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%left
+\qbezier(1.2,1.2)(0,-1)(-1.2,1.2) 
+%rigth
+\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
+%%%%%%%%%%%%
+\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
+\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
+\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
+\end{picture}}
+%%%%%%%%%%%%%%
+\newcommand\PICunorientpluscrossRMsolveHorizontal{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+%\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%%
+%\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+%\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%left
+\qbezier(1.2,1.2)(0,-1)(-1.2,1.2) 
+%rigth
+\qbezier(-1.2,-1.2)(0,0)(1.2,-1.2)
+%%%%%%%%%%%%
+\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
+\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
+\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
+\end{picture}}
+\newcommand\PICunorientLRsplitSolve{\setlength{\unitlength}{0.6mm}
+\begin{picture}(9,6)(-1,2)
+\qbezier(0,0)(1,0.7)(1.5,1.1)
+%\qbezier(3.4, 2.8)(6,4)(3.6, 5)
+\qbezier(6,8)(3,4)(0,8)
+\qbezier(6,0)(-3,6)(4,4)
+\qbezier(4,4)(4,2)(4,2)
+%\qbezier(6,4)(-3,6)(4,3)
+\end{picture}}
+%%%%%%%%%%%%%%
+%%%%%% mine %%%%%
+%%% Unoriented LR splitting RM move II %%%%%%%%%%%%
+\newcommand\PICunorientLRsplitRM{\setlength{\unitlength}{0.6mm}
+\begin{picture}(9,6)(-1,2)
+\qbezier(0,0)(1,0.7)(1.5,1.1)
+\qbezier(3.4, 2.8)(6,4)(3.4, 5.2)
+\qbezier(1.5,6.9)(1,7.3)(0,8)
+\qbezier(6,0)(-3,4)(6,8)
+\end{picture}}
+
+\newcommand\PICunorientpluscrossRMup{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%
+\qbezier(-1.5, 0.2)(-0.8, 0.2)(-0.8,0.3)
+\qbezier(-0.35, 0.7)(0, 1.3)(0.35,0.7)
+\qbezier(0.8, 0.3)(0.8, 0.2)(1.5,0.2)
+\end{picture}}
+
+\newcommand\PICunorientpluscrossRMdown{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+%%%
+\qbezier(-1.5, 0.2)(-0.7, 0.2)(-0.6,-0.3)
+\qbezier(-0.4, -0.7)(0, -1.3)(0.4,-0.7)
+\qbezier(0.6, -0.3)(0.7, 0.2)(1.5,0.2)
+\end{picture}}
+
+
+%%%%%% Symbol-Pictures  %%%%%%%%%%%%%%%
+
+% thickness of lines in symbol-pictures
+\linethickness{0.3pt}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%% UNORIENTED  %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED %%% UNORIENTED  
+
+%%% Unoriented trivial line
+\newcommand\PICline{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2,1)
+\put(0.9,-0.5){\line(0,1){2}}
+\end{picture}}
+
+%%% Trivial circle
+\newcommand\PICcircle{\setlength{\unitlength}{3mm}
+\begin{picture}(1.8,1)(0.2,0.5) 
+\put(1,1){\circle{1.2}}
+\end{picture}}
+
+%%% Union of unoriented vertical line and circle
+\newcommand\PIClinecircle{\setlength{\unitlength}{2.5mm}
+\begin{picture}(4.5,1.2)(0.5,0.5)
+\put(1,0){\line(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
+\put(3.8,1){\circle{1.2}}
+\end{picture}}
+
+%%% Unoriented LR splitting %%%%%%%%%%%%
+\newcommand\PICunorientLRsplit{\setlength{\unitlength}{0.6mm}
+\begin{picture}(9,6)(-1,2)
+\qbezier(0,0)(4,4)(0,8) \qbezier(6,0)(2,4)(6,8)
+\end{picture}}
+
+
+
+%%% Unoriented UD splitting %%%%%%%%%%%%
+\newcommand\PICunorientUDsplit{\setlength{\unitlength}{0.6mm}
+\begin{picture}(11,6)(-1,1)
+\qbezier(0,6)(4,2)(8,6) \qbezier(0,0)(4,4)(8,0)
+\end{picture}}
+
+%%%%%%%%%% Unoriented line + crossing %%%%%%%%%%%%
+\newcommand\PICunorientpluscross{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+\qbezier(-1,-1)(0.0,0.0)(1,1)
+%%%%%%%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+\end{picture}}
+
+%%%%%%%%%% Unoriented line - crossing %%%%%%%%%%%%
+\newcommand\PICunorientminuscross{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,1.9)(-1.3,-0.6)
+\qbezier(1,-1)(0.0,0.0)(-1,1)
+%%%%%%%
+\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
+\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
+\end{picture}}
+
+%%%%%%%%%% Unoriented open writhes gamma_{+} %%%%%%%%%%%%
+\newcommand\PICopengammaplus{\setlength{\unitlength}{0.5mm}
+\begin{picture}(11,8)(-2,-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){\line(0,1){4}}
+\end{picture}}
+
+%%%%%%%%%% Unoriented open writhes gamma_{-} %%%%%%%%%%%%
+\newcommand\PICopengammaminus{\setlength{\unitlength}{0.5mm}
+\begin{picture}(11,8)(-2,0)
+%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){\line(0,1){7}} \put(0,-0.8){\line(0,-1){4}}
+\end{picture}}
+
+%%%%%%%%%% Unoriented closed writhes gamma_{+} %%%%%%%%%%%%
+\newcommand\PICclosedgammaplus{\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)
+
+%%%% 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}}
+
+%%%%%%%%%% Unoriented closed writhes gamma_{-} %%%%%%%%%%%%
+\newcommand\PICclosedgammaminus{\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)
+
+%%%% 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}}
+
+%%%%%%%%%% Unoriented close writhes gamma_{+} %%%%%%%%%%%%
+\newcommand\PICclosegammaplus{\setlength{\unitlength}{0.5mm}
+\begin{picture}(16,8)(-8,-2)
+%RIGHT-top-left Bezier
+\qbezier(1.4,-1.8)(2.0,-2.7)(3.2,-2.9)
+%RIGHT-top-right Bezier
+\qbezier(3.2,-2.9)(6.0,-2.7)(6.2,-0.2)
+%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)
+%%%%%%
+%%%%%%
+%LEFT-top-right Bezier
+\qbezier(-1.4,1.8)(-2.0,2.7)(-3.2,2.9)
+%LEFT-top-left Bezier
+\qbezier(-3.2,2.9)(-6.0,2.7)(-6.2,0.2)
+%LEFT-bottom-left Bezier
+\qbezier(-6.2,0.2)(-5.9,-2.6)(-3.1,-2.9)
+%LEFT-bottom-right Bezier
+\qbezier(-3.1,-2.9)(-0.3,-2.6)(0.0,0.0)
+\end{picture}}
+
+%%%%%%%%%% Unoriented close writhes gamma_{-} %%%%%%%%%%%%
+\newcommand\PICclosegammaminus{\setlength{\unitlength}{0.5mm}
+\begin{picture}(16,8)(-8,-2)
+%RIGHT-top-left Bezier
+\qbezier(-1.4,-1.8)(-2.0,-2.7)(-3.2,-2.9)
+%RIGHT-top-right Bezier
+\qbezier(-3.2,-2.9)(-6.0,-2.7)(-6.2,-0.2)
+%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)
+%%%%%%
+%%%%%%
+%LEFT-top-right Bezier
+\qbezier(1.4,1.8)(2.0,2.7)(3.2,2.9)
+%LEFT-top-left Bezier
+\qbezier(3.2,2.9)(6.0,2.7)(6.2,0.2)
+%LEFT-bottom-left Bezier
+\qbezier(6.2,0.2)(5.9,-2.6)(3.1,-2.9)
+%LEFT-bottom-right Bezier
+\qbezier(3.1,-2.9)(0.3,-2.6)(0.0,0.0)
+\end{picture}}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%% ORIENTED  %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED %%% ORIENTED 
+
+%%%%%%%%%% Oriented trivial line %%%%%%%%%%%%
+\newcommand\PICorientline{\setlength{\unitlength}{2.5mm}
+\begin{picture}(2,1)
+\put(0.9,-0.5){\vector(0,1){2}}
+\end{picture}}
+
+%%%%%%%%%% Oriented trivial circle -- right  %%%%%%%%%%
+\newcommand\PICorientcircleright{\setlength{\unitlength}{3mm}
+\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
+\put(1.3,1.55){\vector(1,0){0.01}}   %%% Put arrow to the circle
+\end{picture}}
+
+%%%%%%%%%% Oriented trivial circle -- left  %%%%%%%%%%
+\newcommand\PICorientcircleleft{\setlength{\unitlength}{3mm}
+\begin{picture}(1.8,1)(0.2,0.5) \put(1,1){\circle{1.2}}
+ \put(0.7,1.55){\vector(-1,0){0.01}}   %%% Put arrow to the circle
+\end{picture}}
+
+%%% Union of oriented vertical line and circle
+\newcommand\PICorientlinecircle{\setlength{\unitlength}{2.5mm}
+%\begin{picture}(3.5,1.2)(0.5,0.5)
+%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
+%\put(2.6,1){\circle{1.2}}
+%\end{picture}}
+\begin{picture}(3.2,1.2)(0.5,0.5)
+\put(1,0){\vector(0,1){2}}
+\put(2.6,1){\circle{1.2}}
+\end{picture}}
+
+%%% Union of oriented vertical line and oriented circle right
+\newcommand\PICorientlinecircler{\setlength{\unitlength}{2.5mm}
+%\begin{picture}(3.5,1.2)(0.5,0.5)
+%\put(1,0){\vector(0,1){2}} \put(1.7,0.4){\small$\sqcup$}
+%\put(2.6,1){\circle{1.2}}
+%\end{picture}}
+\begin{picture}(3.2,1.2)(0.5,0.5)
+\put(1,0){\vector(0,1){2}}
+\put(2.6,1){\circle{1.2}}
+\put(2.9,1.6){\vector(1,0){0.01}}
+\end{picture}}
+
+%%%%%%%%%% Oriented line + crossing %%%%%%%%%%%%
+\newcommand\PICorientpluscross{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,2)(-1.4,-0.6)
+\put(-1,-1){\vector(1,1){2.3}}%
+%%%%%%%%%%%%%%
+\put(-1,1){\vector(-1,1){0.3}}%
+\qbezier(-0.3,0.3)(-0.8,0.8)(-1.0,1.0)
+\qbezier(0.3,-0.3)(0.8,-0.8)(1.0,-1.0)
+\end{picture}}
+
+%%%%%%%%%% Oriented line - crossing %%%%%%%%%%%%
+\newcommand\PICorientminuscross{\setlength{\unitlength}{2mm}
+\begin{picture}(2.9,2)(-1.4,-0.6)
+\put(1,-1){\vector(-1,1){2.3}}%
+%%%
+\put(1,1){\vector(1,1){0.3}}%
+\qbezier(0.3,0.3)(0.8,0.8)(1.0,1.0)
+\qbezier(-0.3,-0.3)(-0.8,-0.8)(-1.0,-1.0)
+\end{picture}}
+
+%%%%%%%%%% Oriented LR splitting %%%%%%%%%%%%
+\newcommand\PICorientLRsplit{\setlength{\unitlength}{0.5mm}
+\begin{picture}(10,8)(-1.5,2)
+%\arc
+\qbezier(0,0)(4,4)(0,8)
+%%%%%%%%%%%%%%%%%%%
+\qbezier(6,0)(2,4)(6,8)
+%%%%%%%%%%%%%%%%%%%
+\put(-0.2,9){\vector(-2,3){0.2}}%
+\put(7,9){\vector(2,3){0.2}}
+\end{picture}}
+
+%%% Oriented UD splitting %%%%%%%%%%%%
+\newcommand\PICorientUDsplit{\setlength{\unitlength}{0.6mm}
+\begin{picture}(11,6)(-1,1)
+\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}}
+\put(-0.4,-0.2){\vector(-3,-2){0.2}}%
+\put(8.4,-0.2){\vector(3,-2){0.2}}
+\end{picture}}
+
+%%%%%%%%%% 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}}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%