CTAN sync 202311110303

31 files changed, 760 insertions, 317 deletions

diff --git a/macros/latex/contrib/tkz/tkz-elements/README.md b/macros/latex/contrib/tkz/tkz-elements/README.md
index 49f16ad785..96f3746c6e 100644
--- a/macros/latex/contrib/tkz/tkz-elements/README.md
+++ b/macros/latex/contrib/tkz/tkz-elements/README.md
@@ -1,6 +1,6 @@
 # tkz-elements — for euclidean geometry
 
-Release 1.00b 2023/10/25
+Release 1.20b 2023/11/10
 
 ## Description
 
@@ -66,7 +66,27 @@ Other examples, in French, are on my site.
 
 ## History
 
-- First version 1.00b 
+   - Version 1.20 Memory management: tables are emptied when the tkzelements environment is opened.
+
+   
+   `set_lua_to_tex` has been replaced by `tkzUseLua` to transfer data between the `tkzelements` and `tikzpicture` environments.
+   
+   New version of `inversion` with respect to a circle method. It selects the correct algorithm based on the object passed as a parameter.
+   
+   Added an `in_out_disk` method for the `circle` object, which indicates whether or not a point is in the disk. `in_out` is for the circle.
+   
+   Added two methods: `radical_center (C1,C2,C3)`  radical center of three circles.
+   `radical_circle (C1,C2,C3)` orthogonal circle of three circles.
+   
+   Added function `circle : radius` to define a circle with a centre and a radius.
+   
+   Added methods `normalize` and  `normalize_inv`  for `line`. 
+   
+   Added methods `translation` and `set_translation` to the `line` object. 
+   
+   Added  an example to illustrate combinations of methods and attributes.
+     
+   - First version 1.00b 
 
 ## Author
 
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
index a86fe1230b..7c8c94aec4 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
@@ -31,7 +31,7 @@ This class is also defined by two points, on the one hand the center and on the
 \subsubsection{Example: circle attributes} % (fold)
 \label{ssub:example_circle_attributes}
 
-Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\_lua\_to\_tex} (see \ref{ssub:transfer_from_lua_to_tex}) creates global macros. The |\r| macro must not already be defined.
+Three attributes are used (south, west, radius).  
 
 \begin{minipage}{0.5\textwidth}
 \begin{tkzexample}[latex=0cm,small,code only]
@@ -43,7 +43,6 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
    z.s   = C.ab.south
    z.w   = C.ab.west
    r     = C.ab.radius
-   set_lua_to_tex{"r"}
 \end{tkzelements}
 \begin{tikzpicture}
     \tkzGetNodes
@@ -51,7 +50,7 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
     \tkzLabelPoints(a,b,s,w)
     \tkzDrawCircle(a,b)
     \tkzDrawSegment(a,b)
-    \tkzLabelSegment[sloped](a,b){ab = \r}
+    \tkzLabelSegment[sloped](a,b){ab = \tkzUseLua{r}}
 \end{tikzpicture}
 \end{tkzexample}
 \end{minipage}
@@ -64,7 +63,6 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
    z.s = C.ab.south
    z.w = C.ab.west
    r   = C.ab.radius
-   set_lua_to_tex{"r"}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -74,7 +72,7 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
 \tkzLabelPoints(a,b,s,w)
 \tkzDrawCircle(a,b)
 \tkzDrawSegment(a,b)
-\tkzLabelSegment[sloped](a,b){ab = \r}
+\tkzLabelSegment[sloped](a,b){ab = \tkzUseLua{r}}
 \end{tikzpicture}
 \hspace*{\fill}
 \end{minipage}
@@ -95,6 +93,7 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
 \textbf{Methods} & \textbf{Comments}    \\
 \midrule   \\
 \Imeth{circle}{new(O,A)} & |C.OA = circle : new (z.O,z.A)| \tkzar circle  center $O$ through $A$\\
+\Imeth{circle}{radius(O,r)} & |C.OA = circle : radius (z.O,2)| \tkzar circle  center $O$ radius =2 cm\\
 \midrule 
  \textbf{Points} &\\
 \midrule 
@@ -112,22 +111,29 @@ Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\
 \Imeth{circle}{radical\_axis (C)} &   \\
 \Imeth{circle}{tangent\_at (pt)} & |z.P = C.OA: tangent_at (z.M)|  $((PM) \perp (OM))$\\
 \Imeth{circle}{tangent\_from (pt)}& |z.M,z.N = C.OA: tangent_from (z.P)| \\
+\Imeth{circle}{inversion (line)} & |L or C = C.AC:inversion (L.EF)|\\
 \midrule 
  \textbf{Circles} &\\
 \midrule 
 \Imeth{circle}{orthogonal\_from (pt)}  & |C= C.OA: orthogonal_from (z.P)|   \\
 \Imeth{circle}{orthogonal\_through (pta,ptb)}  & |C = C.OA: orthogonal_through (z.z1,z.z2)|\\
+\Imeth{circle}{inversion (circle)} & |L or C = C.AC:inversion (C.EF)|\\
+
 \midrule 
  \textbf{Miscellaneous} &\\
 \midrule 
 \Imeth{circle}{power (pt)}     &| p = C.OA: power (z.M)| \tkzar   power  with respect to a circle   \\
 \Imeth{circle}{in\_out (pt)} & |C.OA : in_out (z.M)| \tkzar boolean  \\
+\Imeth{circle}{in\_out\_disk (pt)} & |C.OA : in_out_disk (z.M)| \tkzar boolean  \\
 \Imeth{circle}{draw ()} & for further use\\
 \bottomrule %
 \end{tabular}
 \end{center}
 \egroup
-% subsubsection methods_circle (end)
+% subsection methods_circle (end)
+
+
+
 
 \subsubsection{Altshiller} % (fold)
 \label{ssub:altshiller}
@@ -252,6 +258,182 @@ z.R   = intersection (L.tC,T.ab)
 \hspace*{\fill}
 %\caption{Lemoine line}
 % subsubsection lemoine (end)
+
+
+\subsubsection{Inversion: point, line and circle} % (fold)
+\label{ssub:inversion}
+
+The "inversion" method can be used on a point, a line or a circle. Depending on the type of object, the function determines the correct algorithm to use.
+
+\subsubsection{Inversion: point} % (fold)
+\label{ssub:inversion_point}
+
+The "inversion" method can be used on a point, a line or a circle. Depending on the type of object, the function determines the correct algorithm to use.
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = 1.5
+   z.o   = point:    new (-1,2)
+   z.a   = point:    new (2,1)
+   C.oa  = circle:   new (z.o,z.a)
+   z.c   = point:    new (3,4)
+   z.d   = C.oa:     inversion (z.c)
+   p     = C.oa:     power (z.c)
+\end{tkzelements}
+\begin{tikzpicture}
+    \tkzGetNodes   
+    \tkzDrawCircle(o,a)
+    \tkzDrawSegments(o,a o,c)
+    \tkzDrawPoints(a,o,c,d)
+    \tkzLabelPoints(a,o,c,d)
+    \tkzLabelSegment[sloped,above=1em](c,d){La puissance de c est \tkzUseLua{p}}
+ \end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale = 1.5
+   z.o   = point:    new (-1,2)
+   z.a   = point:    new (2,1)
+   C.oa  = circle:   new (z.o,z.a)
+   z.c   = point:    new (3,4)
+   z.d   = C.oa:     inversion (z.c)
+   p     = C.oa:     power (z.c)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+    \tkzGetNodes   
+    \tkzDrawCircle(o,a)
+    \tkzDrawSegments(o,a o,c)
+    \tkzDrawPoints(a,o,c,d)
+    \tkzLabelPoints(a,o,c,d)
+    \tkzLabelSegment[sloped,above=1em](c,d){La puissance de c est \tkzUseLua{p}}
+ \end{tikzpicture}
+\hspace*{\fill}
+
+\subsubsection{Inversion: line} % (fold)
+\label{ssub:inversion_line}
+
+The result is either a straight line or a circle.
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale    = 1
+   z.o      = point:    new (-1,1)
+   z.a      = point:    new (1,3)
+   C.oa     = circle:   new (z.o,z.a)
+   z.c      = point:    new (3,2)
+   z.d      = point:    new (0,4)
+   L.cd     = line:    new (z.c,z.d)
+   C.OH     = C.oa: inversion (L.cd)
+   z.O,z.H  = get_points(C.OH)
+\end{tkzelements}
+\begin{tikzpicture}
+    \tkzGetNodes    
+    \tkzDrawCircles(o,a O,H)
+    \tkzDrawLines(c,d o,H)
+    \tkzDrawPoints(a,o,c,d,H)
+    \tkzLabelPoints(a,o,c,d,H)
+ \end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+   scale    = 1
+   z.o      = point:    new (-1,1)
+   z.a      = point:    new (1,3)
+   C.oa     = circle:   new (z.o,z.a)
+   z.c      = point:    new (3,2)
+   z.d      = point:    new (0,4)
+   L.cd     = line:    new (z.c,z.d)
+   C.OH     = C.oa: inversion (L.cd)
+   z.O,z.H  = get_points(C.OH)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+    \tkzGetNodes    
+    \tkzDrawCircles(o,a O,H)
+    \tkzDrawLines(c,d o,H)
+    \tkzDrawPoints(a,o,c,d,H)
+    \tkzLabelPoints(a,o,c,d,H)
+ \end{tikzpicture}
+ \hspace*{\fill}
+ 
+ \subsubsection{Inversion: circle} % (fold)
+ \label{ssub:inversion_circle}
+
+The result is either a straight line or a circle.
+
+\begin{tkzexample}[latex=0cm,small,code only]
+ \begin{tkzelements}
+    scale = 1
+    z.o   = point:    new (-1,1)
+    z.a   = point:    new (2,3)
+    C.oa  = circle:   new (z.o,z.a)
+    z.c   = point:    new (-2,1)
+    z.e   = point:    new (-2,8)
+     z.d  = point:    new (-2,5)
+    C.ed  = circle:   new (z.e,z.d)
+    C.co  = circle:   new (z.c,z.o)
+    obj   = C.oa: inversion (C.co)
+    if obj.type == "line"
+       then
+           z.p,z.q = get_points(obj)
+       else
+          z.O,z.H = get_points(obj)
+    end
+     obj   = C.oa: inversion(C.ed)
+    if obj.type == "line"
+       then
+           z.p,z.q = get_points(obj)
+       else
+          z.O,z.H = get_points(obj)
+    end
+ \end{tkzelements}
+ \begin{tikzpicture}
+     \tkzGetNodes 
+     \tkzDrawCircles(o,a c,o e,d O,H)
+     \tkzDrawLines(p,q)
+     \tkzDrawPoints(a,o,c,d,e,p,q,O,H)
+    \tkzLabelPoints(a,o,c,d,e,p,q,O,H)
+  \end{tikzpicture}
+\end{tkzexample}
+ 
+ \begin{tkzelements}
+    scale = 1
+    z.o   = point:    new (-1,1)
+    z.a   = point:    new (2,3)
+    C.oa  = circle:   new (z.o,z.a)
+    z.c   = point:    new (-2,1)
+    z.e   = point:    new (-2,8)
+     z.d  = point:    new (-2,5)
+    C.ed  = circle:   new (z.e,z.d)
+    C.co  = circle:   new (z.c,z.o)
+    obj   = C.oa: inversion (C.co)
+    if obj.type == "line"
+       then
+           z.p,z.q = get_points(obj)
+       else
+          z.O,z.H = get_points(obj)
+    end
+     obj   = C.oa: inversion(C.ed)
+    if obj.type == "line"
+       then
+           z.p,z.q = get_points(obj)
+       else
+          z.O,z.H = get_points(obj)
+    end
+ \end{tkzelements}
+
+\hspace*{\fill}
+ \begin{tikzpicture}
+     \tkzGetNodes 
+     \tkzDrawCircles(o,a c,o e,d O,H)
+     \tkzDrawLines(p,q)
+     \tkzDrawPoints(a,o,c,d,e,p,q,O,H)
+    \tkzLabelPoints(a,o,c,d,e,p,q,O,H)
+  \end{tikzpicture}
+ \hspace*{\fill} 
+% subsubsection inversion (end)
 % subsection methods_of_the_class_circle (end)
 
 
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-ellipse.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-ellipse.tex
index 4480417f08..0d5c00b38c 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-ellipse.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-ellipse.tex
@@ -56,13 +56,12 @@ The first attributes are the three points that define the ellipse : \Iattr{ellip
    z.S   = E.south
    z.Co  = E.covertex
    z.Ve  = E.vertex
-   set_lua_to_tex {'a','b','slope'}
 \end{tkzelements}
 \begin{tikzpicture}
    \pgfkeys{/pgf/number format/.cd,fixed,precision=2}
    \tkzGetNodes
    \tkzDrawCircles[teal](C,A)
-   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
    \tkzDrawPoints(C,A,B,b,W,S,F1,F2)
    \tkzLabelPoints(C,A,B)
    \tkzDrawLine[add = .5 and .5](A,W)
@@ -94,7 +93,6 @@ z.W  = E.west
 z.S  = E.south
 z.Co = E.covertex
 z.Ve = E.vertex
-set_lua_to_tex {'a','b','slope'}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -102,11 +100,11 @@ set_lua_to_tex {'a','b','slope'}
 \pgfkeys{/pgf/number format/.cd,fixed,precision=2}
 \tkzGetNodes
 \tkzDrawCircles[teal](C,A)
-\tkzDrawEllipse[red](C,\a,\b,\slope)
+\tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
 \tkzDrawPoints(C,A,B,b,W,S,F1,F2)
 \tkzLabelPoints(C,A,B)
 \tkzDrawLine[add = .5 and .5](A,W)
-\tkzLabelSegment[pos=1.5,above,sloped](A,W){slope = \pgfmathprintnumber{\slope}}
+\tkzLabelSegment[pos=1.5,above,sloped](A,W){slope = \pgfmathprintnumber{\tkzUseLua{slope}}}
 \tkzLabelPoint[below](S){South}
 \tkzLabelPoint[below left](F1){Focus 1}
 \tkzLabelPoint[below left](F2){Focus 2}
@@ -165,12 +163,11 @@ For attributes see  \ref{sec:classe_ellipse}
    a        = E.Rx
    b        = E.Ry
    slope    = math.deg(E.Sl)
-   set_lua_to_tex {'a','b','slope'}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawCircles[teal](C,A)
-   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
    \tkzDrawPoints(C,A,B)
    \tkzLabelPoints(C,A,B)
 \end{tikzpicture}
@@ -186,12 +183,11 @@ E     = ellipse: new (z.C,z.A,z.B)
 a     = E.Rx
 b     = E.Ry
 slope = math.deg(E.slope)
-set_lua_to_tex {'a','b','slope'}
 \end{tkzelements}
 \begin{tikzpicture}
 \tkzGetNodes
 \tkzDrawCircles[teal](C,A)
-\tkzDrawEllipse[red](C,\a,\b,\slope)
+\tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
 \tkzDrawPoints(C,A,B)
 \tkzLabelPoints(C,A,B)
 \end{tikzpicture}
@@ -230,7 +226,6 @@ The first two points are the foci of the ellipse. The third one is the vertex. W
    z.R,z.S  = intersection (L.XO,E)
    a,b      = E.Rx,E.Ry
    ang      = math.deg(E.slope)
-   set_lua_to_tex{'a','b','ang'}
 \end{tkzelements}
 \end{tkzexample}
 \begin{minipage}{0.6\textwidth}
@@ -240,7 +235,7 @@ The first two points are the foci of the ellipse. The third one is the vertex. W
    \tkzDrawPolygon(A,B,C)
    \tkzDrawCircles[cyan](O,A N,I)
    \tkzDrawSegments(X,R A,X)
-   \tkzDrawEllipse[red](N,\a,\b,\ang)
+   \tkzDrawEllipse[red](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
    \tkzDrawLines[add=.2 and .5](I,H)
    \tkzDrawPoints(A,B,C,N,O,X,H,R,S,I)
    \tkzLabelPoints[above](C,X)
@@ -275,14 +270,13 @@ The first two points are the foci of the ellipse. The third one is the vertex. W
    z.R,z.S   = intersection (L.XO,E)
    a,b   = E.Rx,E.Ry
    ang   = math.deg(E.slope)
-   set_lua_to_tex{'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
 \tkzGetNodes
 \tkzDrawPolygon(A,B,C)
 \tkzDrawCircles[cyan](O,A N,I)
 \tkzDrawSegments(X,R A,X)
-\tkzDrawEllipse[red](N,\a,\b,\ang)
+\tkzDrawEllipse[red](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \tkzDrawLines[add=.2 and .5](I,H)
 \tkzDrawPoints(A,B,C,N,O,X,H,R,S,I)
 \tkzLabelPoints[above](C,X)
@@ -321,7 +315,6 @@ The first two points are the foci of the ellipse. The third one is the vertex. W
    z.N         = L.tb.pb
    L.K         = E :tangent_at (z.K)
    z.ka,z.kb   = get_points(L.K)
-   set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
@@ -329,7 +322,7 @@ The first two points are the foci of the ellipse. The third one is the vertex. W
    \tkzDrawLines(x,y A,M A,N ka,kb)
    \tkzLabelSegment(C,V){$a$}
    \tkzLabelSegment[right](C,CoV){$b$}
-   \tkzDrawEllipse[teal](C,\a,\b,\ang)
+   \tkzDrawEllipse[teal](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
    \tkzDrawPoints(C,V,CoV,X,x,y,M,N,A,K)
    \tkzLabelPoints(C,V,A,M,N,K)
    \tkzLabelPoints[above left](CoV)
@@ -356,7 +349,6 @@ z.M         = L.ta.pb
 z.N         = L.tb.pb
 L.K         = E :tangent_at (z.K)
 z.ka,z.kb   = get_points(L.K)
-set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
 \tkzGetNodes
@@ -364,7 +356,7 @@ set_lua_to_tex  {'a','b','ang'}
 \tkzDrawLines(x,y A,M A,N ka,kb)
 \tkzLabelSegment(C,V){$a$}
 \tkzLabelSegment[right](C,CoV){$b$}
-\tkzDrawEllipse[teal](C,\a,\b,\ang)
+\tkzDrawEllipse[teal](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \tkzDrawPoints(C,V,CoV,X,x,y,M,N,A,K)
 \tkzLabelPoints(C,V,A,M,N,K)
 \tkzLabelPoints[above left](CoV)
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
index de11a45a51..62ea40d1f3 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
@@ -50,7 +50,6 @@ The attributes are :
    z.s   = L.ab.south_pb
    sl    = L.ab.slope
    len   = L.ab.length
-   set_lua_to_tex{"sl","len"}
 \end{tkzelements}
 
 \begin{tikzpicture}
@@ -59,8 +58,8 @@ The attributes are :
    \tkzLabelPoints(a,b,e,r,s,w)
    \tkzLabelPoints[above](m)
    \tkzDrawLine(a,b)
-   \tkzLabelSegment[sloped](a,b){ab = \len}
-   \tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \sl}
+   \tkzLabelSegment[sloped](a,b){ab = \tkzUseLua{len}}
+   \tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \tkzUseLua{sl}}
 \end{tikzpicture}
 \end{tkzexample}
 
@@ -76,7 +75,6 @@ z.r = L.ab.north_pa
 z.s = L.ab.south_pb
 sl = L.ab.slope
 len = L.ab.length
-set_lua_to_tex{"sl","len"}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -86,8 +84,8 @@ set_lua_to_tex{"sl","len"}
 \tkzLabelPoints(a,b,e,r,s,w)
 \tkzLabelPoints[above](m)
 \tkzDrawLine(a,b)
-\tkzLabelSegment[sloped](a,b){ab = \len}
-\tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \sl}
+\tkzLabelSegment[sloped](a,b){ab = \tkzUseLua{len}}
+\tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \tkzUseLua{sl}}
 \end{tikzpicture}
 \hspace*{\fill}
 % \caption{Class Line}
@@ -160,6 +158,8 @@ Here's the list of methods for the \tkzNameObj{line} object. The results are eit
  \textbf{Points} &\\
 \midrule 
 \Imeth{line}{gold\_ratio ()}  & |z.C = L.AB : gold_ratio()|   \tkzar gold ratio   \\
+\Imeth{line}{normalize ()}  & |z.C = L.AB : normalize()| \tkzar AC =1 and $C\in (AB)$   \\
+\Imeth{line}{normalize_inv ()}  & |z.C = L.AB : normalize_inv()|   \tkzar CB =1 and $C\in (AB)$  \\
 \Imeth{line}{barycenter (ka,kb)}    & |z.C = L.AB : barycenter (1,2)| $C$ --> barycenter of |{(A,1)(B,2)}|\\
 \Imeth{line}{point (t)} & |z.C = L.AB : point (2)| \tkzar  $\overrightarrow{AC} = 2\overrightarrow{AB}$\\
 \Imeth{line}{midpoint ()}    & |z.M = L.AB : midpoint ()| \tkzar better is |z.M = L.AB.mid|  \\
@@ -170,6 +170,9 @@ Here's the list of methods for the \tkzNameObj{line} object. The results are eit
 \Imeth{line}{set\_projection (...)}   & projection of a list of points \\
 \Imeth{line}{symmetry\_axial ( pt )}  & |z.Cp = L.AB : symmetry_axial (z.C)|\\
 \Imeth{line}{set\_symmetry\_axial (...) }&symmetry_axial of a list of points  \\
+\Imeth{line}{translation ( pt )}  & |z.Cp = L.AB : translation (z.C)|\\
+\Imeth{line}{set\_translation(...) }&translation of a list of points  \\
+
 \Imeth{line}{square ()} & |z.C,z.D = L.AB : square () | \tkzar  creates 2 points to make a square.\\
 \midrule 
  \textbf{Lines} &\\
@@ -367,6 +370,50 @@ z.a,z.b = L.ab.pa,L.ab.pb
 
 % subsubsection example_combination_of_methods (end)
 
+\subsubsection{Example: translation} % (fold)
+\label{ssub:example_translation}
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A  = point:  new (0,0)
+   z.B  = point:  new (1,2)
+   z.C  = point:  new (-3,2)
+   z.D  = point:  new (0,2)
+   L.AB = line : new (z.A,z.B)
+ -- z.E = L.AB : translation (z.C)
+   z.E,z.F = L.AB : set_translation (z.C,z.D)
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(A,...,F)
+\tkzLabelPoints(A,...,F)
+\tkzDrawSegments[->,red,> =latex](C,E D,F A,B) )
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+   z.A  = point:  new (0,0)
+   z.B  = point:  new (1,2)
+   z.C  = point:  new (-3,2)
+   z.D  = point:  new (0,2)
+   L.AB = line : new (z.A,z.B)
+ -- z.E = L.AB : translation (z.C)
+   z.E,z.F = L.AB : set_translation (z.C,z.D)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(A,...,F)
+\tkzLabelPoints(A,...,F)
+\tkzDrawSegments[->,red,> =latex](C,E D,F A,B) )
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+% subsubsection example_translation (end)
+
 \subsubsection{Example: distance and projection} % (fold)
 \label{ssub:example_distance_and_projection}
 
@@ -379,7 +426,6 @@ z.a,z.b = L.ab.pa,L.ab.pb
    L.AB   = line : new (z.A,z.B)
    d      = L.AB : distance (z.C)
    z.H    = L.AB : projection (z.C)
-   set_lua_to_tex{'d'}
 \end{tkzelements}
 \begin{tikzpicture}
   \tkzGetNodes
@@ -387,7 +433,7 @@ z.a,z.b = L.ab.pa,L.ab.pb
   \tkzDrawPoints(A,B,C,H)
   \tkzLabelPoints(A,B,C,H)
   \tkzLabelSegment[above left,
-                   draw](C,H){$CH = \d$}
+                   draw](C,H){$CH = \tkzUseLua{d}$}
 \end{tikzpicture}
 \end{tkzexample}
 \end{minipage}
@@ -399,7 +445,6 @@ z.a,z.b = L.ab.pa,L.ab.pb
    L.AB   = line : new (z.A,z.B)
    d      = L.AB : distance (z.C)
    z.H    = L.AB : projection (z.C)
-   set_lua_to_tex{'d'}
 \end{tkzelements}
 \hspace*{\fill}
 \begin{tikzpicture}
@@ -407,7 +452,7 @@ z.a,z.b = L.ab.pa,L.ab.pb
 \tkzDrawLines(A,B C,H)
 \tkzDrawPoints(A,B,C,H)
 \tkzLabelPoints(A,B,C,H)
-\tkzLabelSegment[above left,draw](C,H){$CH = \d$}
+\tkzLabelSegment[above left,draw](C,H){$CH = \tkzUseLua{d}$}
 \end{tikzpicture}
 \hspace*{\fill}
 \end{minipage}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-misc.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-misc.tex
index 9bb092ce56..65834bf78e 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-misc.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-misc.tex
@@ -21,9 +21,13 @@
 \Igfct{math}{islinear (z1,z2,z3) }   & Are the points aligned? (z2-z1) $\parallel$ (z3-z1) ?  \\
 \Igfct{math}{isortho (z1,z2,z3)} &  (z2-z1) $\perp$ (z3-z1)  ? boolean\\
 \Igfct{package}{set\_lua\_to\_tex (list)}   & set\_lua\_to\_tex('a','n') defines |\a| and |\n|   \\
+\Igfct{package}{tkzUseLua (variable)}   & |\textbackslash\tkzUseLua{a}| prints  the value of a\\
 %parabola (a,b,c)   & to get   \\
-\Igfct{math}{value (v) }     &  apply |scale| to the value     \\
+\Igfct{math}{value (v) }     &  apply |scale * value |    \\
+\Igfct{math}{real (v) }     &  apply  | value /scale |     \\
 \Igfct{math}{angle\_normalize (a) }   &  to get a value between 0 and $2\pi$ \\
+\Igfct{math}{radical\_center (C1,C2,C3)} & see \ref{sub:radical_center}    \\
+\Igfct{math}{radical\_circle (C1,C2,C3)} & see \ref{sub:radical_circle}  \\
 \bottomrule
 \end{tabular}
 \end{center}
@@ -108,9 +112,6 @@
 
 % subsubsection function_islinear (end)
 
-
-
-
 \subsubsection{Function  \tkzfname{value} }% (fold)
 \label{ssub:function_value}
 
@@ -118,15 +119,59 @@ value to apply scaling if necessary
 
 If |scale = 1.2| with a = value(5) the actual value of |a| will be $5\times 1.2 = 6$.
 
-
 % subsubsection function_value (end)
 
+\subsubsection{Function  \tkzfname{real} }% (fold)
+\label{ssub:function_real}
+
+If |scale = 1.2| with a = 6 then real(a) = $6 / 1.2 = 5$ .
+
+% subsubsection function_real (end)
+
+
 \subsubsection{Transfer from lua to \TEX} % (fold)
 \label{ssub:transfer_from_lua_to_tex}
+It's possible to transfer variable from Lua to \TEX{} with 
+\Igfct{package}{\textbackslash{tkzUseLua}} in the environment "tikzpicture".
+
 
- \Igfct{package}{set\_lua\_to\_tex (list)}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A            = point : new (0 , 0)
+   z.B            = point : new (4 , 3)
+   z.C            = point : new (2 , 5)
+   L.AB           = line : new (z.A,z.B)
+   d              = L.AB : distance (z.C)
+   l              = L.AB.length
+   z.H            = L.AB : projection (z.C)
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B C,H)
+\tkzDrawPoints(A,B,C,H)
+\tkzLabelPoints(A,B,C,H)
+\tkzLabelSegment[above left,draw](C,H){$CH = \tkzUseLua{d}$}
+\tkzLabelSegment[below left,draw](C,H){$AB = \tkzUseLua{l}$}
+\end{tikzpicture}
+\end{tkzexample}
 
-see examples \ref{ssub:get_angle}, \ref{ssub:dot_or_scalar_product}
+\begin{tkzelements}
+   z.A            = point : new (0 , 0)
+   z.B            = point : new (4 , 3)
+   z.C            = point : new (2 , 5)
+   L.AB           = line : new (z.A,z.B)
+   d              = L.AB : distance (z.C)
+   l              = L.AB.length
+   z.H            = L.AB : projection (z.C)
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B C,H)
+\tkzDrawPoints(A,B,C,H)
+\tkzLabelPoints(A,B,C,H)
+\tkzLabelSegment[above left,draw](C,H){$CH = \tkzUseLua{d}$}
+\tkzLabelSegment[below left,draw](C,H){$AB = \tkzUseLua{l}$}
+\end{tikzpicture}
 % subsubsection transfer_from_lua_to_tex (end)
 
 \subsubsection{Normalized angles : Slope of lines (ab), (ac) and (ad)} % (fold)
@@ -197,7 +242,6 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    z.c   = point: new(0, 3)
    angcb = tkzround ( get_angle (z.a,z.c,z.b),3)
    angbc = tkzround ( get_angle (z.a,z.b,z.c),3)
-   set_lua_to_tex{"angcb","angbc"}
 \end{tkzelements}
 
 \begin{tikzpicture}
@@ -206,9 +250,9 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    \tkzDrawPoints(a,b,c)
    \tkzLabelPoints(a,b,c)
    \tkzMarkAngle[->](c,a,b)
-   \tkzLabelAngle(c,a,b){\angcb}
+   \tkzLabelAngle(c,a,b){\tkzUseLua{angcb}}
    \tkzMarkAngle[->](b,a,c)
-   \tkzLabelAngle(b,a,c){\angbc}
+   \tkzLabelAngle(b,a,c){\tkzUseLua{angbc}}
 \end{tikzpicture}
 \end{tkzexample}
 \end{minipage}
@@ -220,7 +264,6 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    z.c   = point: new(0, 3)
    angcb = tkzround ( get_angle (z.a,z.c,z.b),3)
    angbc = tkzround ( get_angle (z.a,z.b,z.c),3)
-   set_lua_to_tex{"angcb","angbc"}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -230,9 +273,9 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
 \tkzDrawPoints(a,b,c)
 \tkzLabelPoints(a,b,c)
 \tkzMarkAngle[->](c,a,b)
-\tkzLabelAngle(c,a,b){\angcb}
+\tkzLabelAngle(c,a,b){\tkzUseLua{angcb}}
 \tkzMarkAngle[->](b,a,c)
-\tkzLabelAngle(b,a,c){\angbc}
+\tkzLabelAngle(b,a,c){\tkzUseLua{angbc}}
 \end{tikzpicture}
 \hspace*{\fill}
 \end{minipage}
@@ -254,7 +297,6 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    z.B_1,
    z.C_1  = get_points (T.ABC: anti ())
    x  = dot_product (z.A,z.B,z.C)
-   set_lua_to_tex{"x"}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
@@ -262,6 +304,7 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    \tkzDrawPoints(A,B,C,A_1,B_1,C_1)
    \tkzLabelPoints(A,B,C,A_1,B_1,C_1)
    \tkzDrawPolygon[blue](A_1,B_1,C_1)
+   \tkzText[right](0,-1){dot product =\tkzUseLua{x}}
 \end{tikzpicture}
 \end{tkzexample}
 \end{minipage}
@@ -276,7 +319,6 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
  z.B_1,
  z.C_1  = get_points (T.ABC: anti ())
  x  = dot_product (z.A,z.B,z.C)
- set_lua_to_tex{"x"}
 \end{tkzelements}
 \hspace*{\fill}
 \begin{tikzpicture}
@@ -285,14 +327,14 @@ The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarro
    \tkzDrawPoints(A,B,C,A_1,B_1,C_1)
    \tkzLabelPoints(A,B,C,A_1,B_1,C_1)
    \tkzDrawPolygon[blue](A_1,B_1,C_1)
+   \tkzText[right](0,-1){dot product =\tkzUseLua{x}}
    \end{tikzpicture}
 \hspace*{\fill}
 \end{minipage}
 
 %\caption{Dot or scalar product}
 
-
-The scalar product of the vectors $\overrightarrow{AC}$ and $\overrightarrow{AB}$ is equal to $\x$, so these vectors are orthogonal.
+The scalar product of the vectors $\overrightarrow{AC}$ and $\overrightarrow{AB}$ is equal to $\tkzUseLua{x}$, so these vectors are orthogonal.
 % subsubsection dot_or_scalar_product (end)
 
 \subsubsection{Alignment or orthogonality} % (fold)
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
index 311debb4a6..a9a1785ef1 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
@@ -47,7 +47,6 @@ This is the creation of a fixed point with coordinates 1 and 2 and which is name
    ty    = z.a.type
    arg   = z.a.argument
    m     = z.a.modulus
-   set_lua_to_tex{"x","y","ty","arg","m"}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
@@ -57,7 +56,7 @@ This is the creation of a fixed point with coordinates 1 and 2 and which is name
    \tkzLabelPoints[above](O,a)
    \tkzLabelPoint[below](a){
    \begin{minipage} {5cm}
-   x=\x\\ y=\y\\ type =\ty\\ argument = \arg \\ module = \m
+   x=\tkzUseLua{x}\\ y=\tkzUseLua{y}\\ type =\tkzUseLua{ty}\\ argument = \tkzUseLua{arg} \\ module = \tkzUseLua{m}
     \end{minipage}}
 \end{tikzpicture}
 \end{tkzexample}
@@ -70,7 +69,6 @@ This is the creation of a fixed point with coordinates 1 and 2 and which is name
    ty = z.a.type
    arg = z.a.argument
    m = z.a.modulus
-   set_lua_to_tex{"x","y","ty","arg","m"}
 \end{tkzelements}
 
  \hspace*{\fill}
@@ -82,7 +80,9 @@ This is the creation of a fixed point with coordinates 1 and 2 and which is name
    \tkzLabelPoints[above](O,a)
    \tkzLabelPoint[below right](a){
    \begin{minipage} {5cm}
-   x=\x\\ y=\y\\ type =\ty\\ argument = \arg \\ module = \m
+   x=\tkzUseLua{x}\\ y=\tkzUseLua{y}\\ 
+   type =\tkzUseLua{ty}\\ argument = \tkzUseLua{arg} \\
+    module = \tkzUseLua{m}
     \end{minipage}}
    \end{tikzpicture}
     \hspace*{\fill}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
index 2b3056ff92..45515c3b7a 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
@@ -54,7 +54,6 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
    alpha =  T.abc.alpha
    beta  =  T.abc.beta
    gamma =  T.abc.gamma
-   set_lua_to_tex{"a","b","c","alpha","beta","gamma"}
 \end{tkzelements}
 
 \begin{tikzpicture}
@@ -64,8 +63,8 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
    \tkzLabelPoints(a,b,c,O,G,I)
    \tkzLabelPoints[above right](H)
    \tkzDrawCircles(O,a)
-   \tkzLabelSegment[sloped](a,b){\c}
-   \tkzLabelSegment[sloped,above](b,c){\a}
+   \tkzLabelSegment[sloped](a,b){\tkzUseLua{c}}
+   \tkzLabelSegment[sloped,above](b,c){\tkzUseLua{a}}
 \end{tikzpicture}
 \end{tkzexample}
 
@@ -85,7 +84,6 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
    alpha =  T.abc.alpha
    beta =  T.abc.beta
    gamma =  T.abc.gamma
-   set_lua_to_tex{"a","b","c","alpha","beta","gamma"}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -96,8 +94,8 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
 \tkzLabelPoints(a,b,c,O,G,I)
 \tkzLabelPoints[above right](H)
 \tkzDrawCircles(O,a)
-\tkzLabelSegment[sloped](a,b){\c}
-\tkzLabelSegment[sloped,above](b,c){\a}
+\tkzLabelSegment[sloped](a,b){\tkzUseLua{c}}
+\tkzLabelSegment[sloped,above](b,c){\tkzUseLua{a}}
 \end{tikzpicture}
 \hspace*{\fill}
 %  \caption{Class Triangle}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-convention.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-convention.tex
index 916e6bd1fb..444033e75b 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-convention.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-convention.tex
@@ -20,9 +20,9 @@ More generally, with |z.A = point: new (a,b)|, we define a complex number |z.A =
 There are two cases. Either you want to keep the point to use it with the package that will allow you to draw, or the point is intermediate and you can abandon it.
 
 \vspace{12pt}
-In the second case, simply don't store the point in the |z| table. For example, |A = point : new (1,2)| defines a point $A$ that will not be transferred. Another way of avoiding a transfer is to assign |nil| to the point: |z.A = nil| before exiting the environment \tkzNameEnv{elements}.
+In the second case, simply don't store the point in the |z| table. For example, |A = point : new (1,2)| defines a point $A$ that will not be transferred. Another way of avoiding a transfer is to assign |nil| to the point: |z.A = nil| before exiting the environment \tkzNameEnv{tkzelements}.
 
- In the first case, you must store the point in the table |z|. The points which occur in the  environment \tkzNameEnv{elements} must respect a convention which is |z.name| such that |name| will be the name of the corresponding \tkzname{node}. \footnote{ However, that a point can be deleted with |z.name = nil|.}
+ In the first case, you must store the point in the table |z|. The points which occur in the  environment \tkzNameEnv{tkzelements} must respect a convention which is |z.name| such that |name| will be the name of the corresponding \tkzname{node}. \footnote{ However, that a point can be deleted with |z.name = nil|.}
  
 What are the conventions for designating |name|? You have to respect the Lua conventions in  particular cases.
 \begin{enumerate}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
index bcf0ccacce..68c894037c 100644..100755
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
@@ -828,7 +828,7 @@ z.O3  = L.Bpt.mid
 %
 % subsection excircle (end)
 
-\subsection{In/Out of a circle} % (fold)
+\subsection{In/Out of a circle or a disk} % (fold)
 \label{sub:in_out_of_a_circle}
 
 
@@ -839,7 +839,7 @@ z.O3  = L.Bpt.mid
    z.B      = point: new (1,2)
    z.X      = point: new (-2,2)
    C        = circle :  new (z.A,z.B)
-   if C:in_out(z.X)
+   if C:in_out(z.X) -- in_out_disk
    then
   tex.print("In")
    else
@@ -1024,14 +1024,13 @@ z.L      = C: point (2)
 L.J,L.K  = E: tangent_from (z.L)
 z.J      = L.J.pb
 z.K      = L.K.pb
-set_lua_to_tex {'a','b'}
 \end{tkzelements}
  \begin{tikzpicture}
  \tkzGetNodes
  \tkzDrawPoints(F1,F2,O)
 \tkzDrawCircles[teal](O,P)
 \tkzDrawPolygon(H,O,A,P)
-\tkzDrawEllipse[red](O,\a,\b,0)
+\tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{b},0)
 \tkzDrawSegments[orange](O,P O,L L,J L,K)
 \tkzDrawPoints(F1,F2,O,H,A,P,L,J,K)
 \tkzLabelPoints(F1,F2,O,H,A,P,L,J,K)
@@ -1055,7 +1054,6 @@ z.L   = C: point (2)
 L.J,L.K  = E: tangent_from (z.L)
 z.J      = L.J.pb
 z.K      = L.K.pb
-set_lua_to_tex {'a','b'}
 \end{tkzelements}
 
 
@@ -1065,7 +1063,7 @@ set_lua_to_tex {'a','b'}
 \tkzDrawPoints(F1,F2,O)
 \tkzDrawCircles[teal](O,P)
 \tkzDrawPolygon(H,O,A,P)
-\tkzDrawEllipse[red](O,\a,\b,0)
+\tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{b},0)
 \tkzDrawSegments[orange](O,P O,L L,J L,K)
 \tkzDrawPoints(F1,F2,O,H,A,P,L,J,K)
 \tkzLabelPoints(F1,F2,O,H,A,P,L,J,K)
@@ -1087,15 +1085,14 @@ set_lua_to_tex {'a','b'}
    d        = L.AB : distance (z.C)
    l        = L.AB.length
    z.H      = L.AB : projection (z.C)
-   set_lua_to_tex{'d','l'}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawLines(A,B C,H)
    \tkzDrawPoints(A,B,C,H)
    \tkzLabelPoints(A,B,C,H)
-   \tkzLabelSegment[above left,draw](C,H){$CH = \d$}
-   \tkzLabelSegment[below left,draw](C,H){$AB = \l$}
+   \tkzLabelSegment[above left,draw](C,H){$CH = \tkzUseLua{d}$}
+   \tkzLabelSegment[below left,draw](C,H){$AB =\tkzUseLua{l}$}
 \end{tikzpicture}
 \end{tkzexample}
 
@@ -1107,7 +1104,6 @@ L.AB   = line : new (z.A,z.B)
 d      = L.AB : distance (z.C)
 l      = L.AB.length
 z.H    = L.AB : projection (z.C)
-set_lua_to_tex{'d','l'}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -1116,8 +1112,8 @@ set_lua_to_tex{'d','l'}
 \tkzDrawLines(A,B C,H)
 \tkzDrawPoints(A,B,C,H)
 \tkzLabelPoints(A,B,C,H)
-\tkzLabelSegment[above left,draw](C,H){$CH = \d$}
-\tkzLabelSegment[below left,draw](C,H){$AB = \l$}
+\tkzLabelSegment[above left,draw](C,H){$CH = \tkzUseLua{d}$}
+\tkzLabelSegment[below left,draw](C,H){$AB =\tkzUseLua{l}$}
 \end{tikzpicture}
 \hspace*{\fill}
 %\caption{Distance to a line}
@@ -1212,12 +1208,12 @@ z.O     = C.AB: antipode (z.B)
    a         = E.Rx
    b         = E.Ry
    slope     = math.deg(E.slope)
-   set_lua_to_tex {'a','b','slope'}
+
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawCircles[teal](C,A)
-   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
    \tkzDrawPoints(C,A,B,b)
    \tkzLabelPoints(C,A,B)
 \end{tikzpicture}
@@ -1234,14 +1230,13 @@ E    = ellipse: new (z.C,z.A,z.B)
 a    = E.Rx
 b    = E.Ry
 slope    = math.deg(E.slope)
-set_lua_to_tex {'a','b','slope'}
 \end{tkzelements}
 
    \hspace*{\fill}
    \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawCircles[teal](C,A)
-   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawEllipse[red](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{slope})
    \tkzDrawPoints(C,A,B,b)
    \tkzLabelPoints(C,A,B)
    \end{tikzpicture}
@@ -1264,11 +1259,10 @@ ang      = math.deg(math.pi/4)
 E        = ellipse: radii (z.C,a,b,math.pi/4)
 z.V      = E : point (0)
 z.CoV    = E : point (math.pi/2)
-set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
 \tkzGetNodes
-\tkzDrawEllipse[blue](C,\a,\b,\ang)
+\tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \tkzDrawPoints(C,V,CoV)
 \end{tikzpicture}
 \end{tkzexample}
@@ -1283,13 +1277,12 @@ ang    = math.deg(math.pi/4)
 E  = ellipse: radii (z.C,a,b,math.pi/4)
 z.V    = E : point (0)
 z.CoV  = E : point (math.pi/2)
-set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 
 \hspace*{\fill}
 \begin{tikzpicture}
 \tkzGetNodes
-\tkzDrawEllipse[blue](C,\a,\b,\ang)
+\tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \tkzDrawPoints(C,V,CoV)
 \end{tikzpicture}
 \hspace*{\fill}
@@ -1318,13 +1311,12 @@ set_lua_to_tex  {'a','b','ang'}
    L.ta,L.tb   = E: tangent_from (z.K)
    z.F         = L.ta.pb
    z.G         = L.tb.pb
-   set_lua_to_tex{'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawPoints(A,B,C,K,F,G,V,cV)
    \tkzLabelPoints(A,B,C,K,F,G,V,cV)
-   \tkzDrawEllipse[teal](C,\a,\b,\ang)
+   \tkzDrawEllipse[teal](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
    \tkzDrawLines(K,F K,G)
 \end{tikzpicture}
 \end{tkzexample}
@@ -1347,7 +1339,6 @@ ang         = math.deg(E.slope)
 L.ta,L.tb   = E: tangent_from (z.K)
 z.F         = L.ta.pb
 z.G         = L.tb.pb
-set_lua_to_tex{'a','b','ang'}
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -1355,7 +1346,7 @@ set_lua_to_tex{'a','b','ang'}
   \tkzGetNodes
   \tkzDrawPoints(A,B,C,K,F,G,V,cV)
   \tkzLabelPoints(A,B,C,K,F,G,V,cV)
-  \tkzDrawEllipse[teal](C,\a,\b,\ang)
+  \tkzDrawEllipse[teal](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
   \tkzDrawLines(K,F K,G)
 \end{tikzpicture}
  \hspace*{\fill}
@@ -2268,6 +2259,7 @@ _,z.Tp  = get_points (L)
    L.aap    = line : new (z.a,z.ap)
    L.bbp    = line : new (z.b,z.bp)
    z.X      = intersection (L.aap,L.bbp)
+-- or z.X   = radical_center(C.Ox,C.Pz,C.Opy)
    L.OOp    = line : new (z.O,z.Op)
    z.H      = L.OOp : projection (z.X)
 \end{tkzelements}
@@ -2311,6 +2303,64 @@ z.H         = L.OOp : projection (z.X)
 \hspace*{\fill}
 %\caption{Radical center}
 % subsection radical_center (end)
+
+\subsection{Radical circle} % (fold)
+\label{sub:radical_circle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale       = .25
+   z.A         = point: new (0,0)
+   z.B         = point: new (6,0)
+   z.C         = point: new (0.8,4)
+   T.ABC       = triangle : new ( z.A,z.B,z.C ) 
+   C.exa       = T.ABC : ex_circle ()
+   z.I_a,z.Xa  = get_points (C.exa)
+   C.exb       = T.ABC : ex_circle (1)
+   z.I_b,z.Xb  = get_points (C.exb)
+   C.exc       = T.ABC : ex_circle (2)
+   z.I_c,z.Xc  = get_points (C.exc)
+   C.ortho     = radical_circle (C.exa,C.exb,C.exc)
+   z.w,z.a     = get_points (C.ortho)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
+   \tkzDrawCircles[red,thick](w,a)
+   \tkzDrawPoints(A,B,C)
+   \tkzLabelPoints(A,B,C)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale       = .25
+   z.A         = point: new (0,0)
+   z.B         = point: new (6,0)
+   z.C         = point: new (0.8,4)
+   T.ABC       = triangle : new ( z.A,z.B,z.C ) 
+   C.exa       = T.ABC : ex_circle ()
+   z.I_a,z.Xa  = get_points (C.exa)
+   C.exb       = T.ABC : ex_circle (1)
+   z.I_b,z.Xb  = get_points (C.exb)
+   C.exc       = T.ABC : ex_circle (2)
+   z.I_c,z.Xc  = get_points (C.exc)
+   C.ortho     = radical_circle (C.exa,C.exb,C.exc)
+   z.w,z.a     = get_points (C.ortho)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
+   \tkzDrawCircles[red,thick](w,a)
+   \tkzDrawPoints(A,B,C)
+   \tkzLabelPoints(A,B,C)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Radical circle}
+% subsection radical_circle (end)
  
 \subsection{Hexagram} % (fold)
 \label{sub:hexagram}
@@ -2350,7 +2400,6 @@ z.H         = L.OOp : projection (z.X)
    z.U               = intersection (L.XO,E)
   _,z.V              = intersection (L.YO,E)
   _,z.W              = intersection (L.ZO,E)
-   set_lua_to_tex {'a','b','ang'} 
  \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
@@ -2364,7 +2413,7 @@ z.H         = L.OOp : projection (z.X)
    \tkzLabelPoints[blue,right](O,N,G,H,I,J)
    \tkzDrawPoints(I,J,U,V,W)
    \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
-   \tkzDrawEllipse[blue](N,\a,\b,\ang)
+   \tkzDrawEllipse[blue](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \end{tikzpicture}
 \end{tkzexample}
 
@@ -2404,8 +2453,7 @@ L.ZO    = line: new (z.Z,z.O)
 z.x     = intersection (L.BC,L.XO)
 z.U     = intersection (L.XO,E)
 _,z.V   = intersection (L.YO,E)
-_,z.W   = intersection (L.ZO,E)
-set_lua_to_tex {'a','b','ang'} 
+_,z.W   = intersection (L.ZO,E) 
 \end{tkzelements}
 
 \hspace*{\fill}
@@ -2421,7 +2469,7 @@ set_lua_to_tex {'a','b','ang'}
 \tkzLabelPoints[blue,right](O,N,G,H,I,J)
 \tkzDrawPoints(I,J,U,V,W)
 \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
-\tkzDrawEllipse[blue](N,\a,\b,\ang)
+\tkzDrawEllipse[blue](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
 \end{tikzpicture}
 \hspace*{\fill}
 %\caption{Hexagram Lemoine,Pascal}
@@ -2573,98 +2621,78 @@ z.O  = C.DC : inversion (z.W)
 \label{sub:apollonius_circle_v1_with_inversion}
 \begin{tkzexample}[code only,small]
 \begin{tkzelements}
-scale = .75
-  z.A                = point: new (0,0)
-  z.B                = point: new (6,0)
-  z.C                = point: new (0.8,4)
-  T.ABC              = triangle : new (z.A,z.B,z.C) 
-  C.euler            = T.ABC: euler_circle ()
-  z.N,z.Ma           = get_points (C.euler)  
-  z.I_a,z.I_b,z.I_c  = get_points (T.ABC : excentral())
-  z.Ea,z.Eb,z.Ec     = get_points (T.ABC : feuerbach ())
-  -- The Feuerbach triangle is the triangle formed by the three points
-  -- of tangency of the nine-point circle with the excircles
-  z.S,z.p            = get_points (T.ABC: spieker_circle ())
- --  z.Xa,z.Xb,z.Xc  = get_points (T.ABC : extouch())
-  C.exa              = T.ABC : ex_circle ()
-  z.Ia,z.Xa          = get_points (C.exa)
-  C.exb              = T.ABC : ex_circle (1)
-  z.Ib,z.Xb          = get_points (C.exb)
-  C.exc              = T.ABC : ex_circle (2)
-  z.Ic,z.Xc          = get_points (C.exc)
-  -- S spieker point is the radical center of the last three circles
-  L.fa               = line : new (z.S,z.Ea) 
-  L.fb               = line : new (z.S,z.Eb)
-  L.fc               = line : new (z.S,z.Ec)
-  z.f_a              = intersection (L.fa,C.exa)
-  z.f_b              = intersection (L.fb,C.exb)
-  _,z.f_c            = intersection (L.fc,C.exc)
-  T                  = triangle : new ( z.f_a, z.f_b , z.f_c )
-  z.o                = T.circumcenter
-  _,z.l              = get_points (C.exa : orthogonal_from (z.S))
-  -- S center of inversion !!
+   scale             = .7
+   z.A               = point: new (0,0)
+   z.B               = point: new (6,0)
+   z.C               = point: new (0.8,4)
+   T.ABC             = triangle : new ( z.A,z.B,z.C )
+   z.N               = T.ABC.eulercenter
+   z.Ea,z.Eb,z.Ec    = get_points ( T.ABC : feuerbach () )
+   z.Ja,z.Jb,z.Jc    = get_points ( T.ABC : excentral () )
+   z.S               = T.ABC : spieker_center ()
+   C.JaEa            = circle : new (z.Ja,z.Ea)
+   C.ortho           = circle : radius (z.S,math.sqrt(C.JaEa : power (z.S) ))
+   z.a               = C.ortho.south
+   C.euler           = T.ABC: euler_circle ()
+   C.apo             = C.ortho : inversion (C.euler)
+   z.O               = C.apo.center
+   z.xa,z.xb,z.xc    = C.ortho : set_inversion (z.Ea,z.Eb,z.Ec)
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
-   \tkzDrawCircles[red](o,f_a  N,Ma)
-   \tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
-   \tkzClipCircle(o,f_a)
-   \tkzDrawLines[add=3 and 3](A,B A,C B,C)
-   \tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
-   \tkzDrawCircles[cyan](S,l)
-   \tkzDrawPoints(A,B,C)
-   \tkzDrawPoints[cyan](S)
-   \tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
-   \tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
+\tkzDrawCircles[red](O,xa N,Ea)
+\tkzFillCircles[green!30!black,opacity=.3](O,xa)
+\tkzFillCircles[yellow!30,opacity=.7](Ja,Ea Jb,Eb Jc,Ec)
+\tkzFillCircles[teal!30!black,opacity=.3](S,a)
+\tkzFillCircles[green!30,opacity=.3](N,Ea)
+\tkzDrawPoints[red](Ea,Eb,Ec,xa,xb,xc,N)
+\tkzClipCircle(O,xa)
+\tkzDrawLines[add=3 and 3](A,B A,C B,C)
+\tkzDrawCircles(Ja,Ea Jb,Eb Jc,Ec)
+\tkzFillCircles[lightgray!30,opacity=.7](Ja,Ea Jb,Eb Jc,Ec)
+\tkzDrawCircles[teal](S,a)
+\tkzDrawPoints(A,B,C,O)
+\tkzDrawPoints[teal](S)
+\tkzLabelPoints(A,B,C,O,S,N)
 \end{tikzpicture}
 \end{tkzexample}
 
 \begin{tkzelements}
-scale = .5
-z.A      = point: new (0,0)
-z.B      = point: new (6,0)
-z.C      = point: new (0.8,4)
-T.ABC    = triangle : new (z.A,z.B,z.C) 
-C.euler      = T.ABC: euler_circle ()
-z.N,z.Ma     = get_points (C.euler)  
-z.I_a,z.I_b,z.I_c    = get_points (T.ABC : excentral())
-z.Ea,z.Eb,z.Ec   = get_points (T.ABC : feuerbach ())
--- The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles
-z.S,z.p      = get_points (T.ABC: spieker_circle ())
- --  z.Xa,z.Xb,z.Xc    = get_points (T.ABC : extouch())
-C.exa  = T.ABC : ex_circle ()
-z.Ia,z.Xa  = get_points (C.exa)
-C.exb  = T.ABC : ex_circle (1)
-z.Ib,z.Xb  = get_points (C.exb)
-C.exc  = T.ABC : ex_circle (2)
-z.Ic,z.Xc  = get_points (C.exc)
-
--- S spieker point is the radical center of the last three circles
-L.fa     = line : new (z.S,z.Ea) 
-L.fb     = line : new (z.S,z.Eb)
-L.fc     = line : new (z.S,z.Ec)
-z.f_a    = intersection (L.fa,C.exa)
-z.f_b    = intersection (L.fb,C.exb)
-_,z.f_c      = intersection (L.fc,C.exc)
-T  = triangle : new ( z.f_a, z.f_b , z.f_c )
-z.o      = T.circumcenter
-_,z.l    = get_points (C.exa : orthogonal_from (z.S))
--- S center of inversion !!
+   scale             = .5
+   z.A               = point: new (0,0)
+   z.B               = point: new (6,0)
+   z.C               = point: new (0.8,4)
+   T.ABC             = triangle : new ( z.A,z.B,z.C )
+   z.N               = T.ABC.eulercenter
+   z.Ea,z.Eb,z.Ec    = get_points ( T.ABC : feuerbach () )
+   z.Ja,z.Jb,z.Jc    = get_points ( T.ABC : excentral () )
+   z.S               = T.ABC : spieker_center ()
+   C.JaEa            = circle : new (z.Ja,z.Ea)
+   C.ortho           = circle : radius (z.S,math.sqrt(C.JaEa : power (z.S) ))
+   z.a               = C.ortho.south
+   C.euler           = T.ABC: euler_circle ()
+   C.apo             = C.ortho : inversion (C.euler)
+   z.O               = C.apo.center
+   z.xa,z.xb,z.xc    = C.ortho : set_inversion (z.Ea,z.Eb,z.Ec)
 \end{tkzelements}
 
 \hspace*{\fill}
 \begin{tikzpicture}
-\tkzGetNodes
-\tkzDrawCircles[red](o,f_a  N,Ma)
-\tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
-\tkzClipCircle(o,f_a)
+   \tkzGetNodes
+\tkzDrawCircles[red](O,xa N,Ea)
+\tkzFillCircles[green!30!black,opacity=.3](O,xa)
+\tkzFillCircles[yellow!30,opacity=.7](Ja,Ea Jb,Eb Jc,Ec)
+\tkzFillCircles[teal!30!black,opacity=.3](S,a)
+\tkzFillCircles[green!30,opacity=.3](N,Ea)
+\tkzDrawPoints[red](Ea,Eb,Ec,xa,xb,xc,N)
+\tkzClipCircle(O,xa)
 \tkzDrawLines[add=3 and 3](A,B A,C B,C)
-\tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
-\tkzDrawCircles[cyan](S,l)
-\tkzDrawPoints(A,B,C)
-\tkzDrawPoints[cyan](S)
-\tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
-\tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
+\tkzDrawCircles(Ja,Ea Jb,Eb Jc,Ec)
+\tkzFillCircles[lightgray!30,opacity=.7](Ja,Ea Jb,Eb Jc,Ec)
+\tkzDrawCircles[teal](S,a)
+\tkzDrawPoints(A,B,C,O)
+\tkzDrawPoints[teal](S)
+\tkzLabelPoints(A,B,C,O,S,N)
 \end{tikzpicture}
 \hspace*{\fill}
 %\caption{Apollonius circle V1}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-howtouse.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-howtouse.tex
index 0b94576633..5d47e005a7 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-howtouse.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-howtouse.tex
@@ -117,7 +117,7 @@ All points are defined and stored in the |z| table. The macro \tkzcname{tkzGetNo
 
 \subsubsection{Points transfer} % (fold)
 \label{ssub:points_transfer}
-We use an environment \tkzname{elements}  outside an environment \tkzname{tikzpicture} which allows us to carry out all the necessary calculations, then we launch the macro \tkzcname{tkzGetNodes} which transforms the affixes of the table \tkzname{z} into a list of \tkzname{Nodes}. It only remains to draw.
+We use an environment \tkzname{tkzelements}  outside an environment \tkzname{tikzpicture} which allows us to carry out all the necessary calculations, then we launch the macro \tkzcname{tkzGetNodes} which transforms the affixes of the table \tkzname{z} into a list of \tkzname{Nodes}. It only remains to draw.
 
 Currently the drawing program is either \TIKZ\ or \pkg{tkz-euclide}. You have the possibility to use another package to trace but for that you have to create a macro similar to \tkzcname{tkzGetNodes}. Of course, this package must be able to store the points as does \TIKZ\ or \pkg{tkz-euclide}. 
 
@@ -138,7 +138,7 @@ end}
 }
 \end{tkzexample}
 
-The environment \tkzNameEnv{elements} allows to use the underscore |_| and the macro \tkzcname{tkzGetNodes} allows to obtain names of nodes containing \tkzname{prime}. (see the next example)
+The environment \tkzNameEnv{tkzelements} allows to use the underscore |_| and the macro \tkzcname{tkzGetNodes} allows to obtain names of nodes containing \tkzname{prime}. (see the next example)
 
 \begin{minipage}{0.5\textwidth}
 \begin{tkzexample}[latex=0cm,small,code only]
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-intersection.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-intersection.tex
index db290e3447..cab5aa7aeb 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-intersection.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-intersection.tex
@@ -195,14 +195,13 @@ The designation of intersection points is a little more complicated than the pre
    a        = E.Rx
    b        = E.Ry
    ang      = math.deg(E.slope)
-   set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 \begin{tikzpicture}
    \tkzGetNodes
    \tkzDrawLines[red](a,b u,v) % p,s p,t
    \tkzDrawPoints(a,b,c,e,u,v) %
    \tkzLabelPoints(a,b,c,u,v)
-   \tkzDrawEllipse[teal](c,\a,\b,\ang)
+   \tkzDrawEllipse[teal](c,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
    \tkzDrawSegments(c,u c,v)
    \tkzFillAngles[green!30,opacity=.4](e,c,v)
    \tkzFillAngles[green!80,opacity=.4](e,c,u)
@@ -226,7 +225,6 @@ The designation of intersection points is a little more complicated than the pre
    a     = E.Rx
    b     = E.Ry
    ang   = math.deg(E.slope)
-   set_lua_to_tex  {'a','b','ang'}
 \end{tkzelements}
 \hspace*{\fill}   
 \begin{tikzpicture}
@@ -234,7 +232,7 @@ The designation of intersection points is a little more complicated than the pre
    \tkzDrawLines[red](a,b u,v) % p,s p,t
    \tkzDrawPoints(a,b,c,e,u,v) %
    \tkzLabelPoints(a,b,c,u,v)
-   \tkzDrawEllipse[teal](c,\a,\b,\ang)
+   \tkzDrawEllipse[teal](c,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
    \tkzFillAngles[green!30,opacity=.4](e,c,v)
    \tkzFillAngles[green!80,opacity=.4](e,c,u)
    \tkzDrawSegments(c,u c,v)
@@ -262,7 +260,6 @@ Other examples: \ref{ssub:function_tkzname_ellipse__foci}, \ref{sub:hexagram}
 %    a        = E.Rx
 %    b        = E.Ry
 %    ang      = math.deg(E.slope)
-%    set_lua_to_tex  {'a','b','ang'}
 % \end{tkzelements}
 %
 % \begin{tikzpicture}
@@ -270,7 +267,8 @@ Other examples: \ref{ssub:function_tkzname_ellipse__foci}, \ref{sub:hexagram}
 %    \tkzDrawLines[red](a,b u,v) % p,s p,t
 %    \tkzDrawPoints(a,b,c,e,u,v) %
 %    \tkzLabelPoints(a,b,c,u,v)
-%    \tkzDrawEllipse[teal](c,\a,\b,\ang)
+%    \tkzDrawEllipse[teal](c,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
+%    \tkzFillAngles[green!30,opacity=.4](e,c,v)
 %    \tkzDrawSegments(c,u c,v)
 %    \tkzFillAngles[green!30,opacity=.4,size=1.2](e,c,v)
 %    \tkzFillAngles[green!80,opacity=.4](e,c,u)
@@ -293,7 +291,6 @@ Other examples: \ref{ssub:function_tkzname_ellipse__foci}, \ref{sub:hexagram}
 %    a     = E.Rx
 %    b     = E.Ry
 %    ang   = math.deg(E.slope)
-%    set_lua_to_tex  {'a','b','ang'}
 % \end{tkzelements}
 %
 %
@@ -303,7 +300,8 @@ Other examples: \ref{ssub:function_tkzname_ellipse__foci}, \ref{sub:hexagram}
 %    \tkzDrawLines[red](a,b u,v) % p,s p,t
 %    \tkzDrawPoints(a,b,c,e,u,v) %
 %    \tkzLabelPoints(a,b,c,u,v)
-%    \tkzDrawEllipse[teal](c,\a,\b,\ang)
+%    \tkzDrawEllipse[teal](c,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
+%   \tkzFillAngles[green!30,opacity=.4](e,c,v)
 %    \tkzDrawSegments(c,u c,v)
 %    \tkzFillAngles[green!30,opacity=.4,size=1.2](e,c,v)
 %    \tkzFillAngles[green!80,opacity=.4](e,c,u)
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
index 6fa4bc6166..202ff31ba7 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
@@ -21,10 +21,10 @@
                headings    = small
                ]{tkz-doc}
 \gdef\tkznameofpack{tkz-elements}
-\gdef\tkzversionofpack{1.00b}
+\gdef\tkzversionofpack{1.20b}
 \gdef\tkzdateofpack{\today}
 \gdef\tkznameofdoc{tkz-elements.pdf}
-\gdef\tkzversionofdoc{1.00b}
+\gdef\tkzversionofdoc{1.20b}
 \gdef\tkzdateofdoc{\today}
 \gdef\tkzauthorofpack{Alain Matthes}
 \gdef\tkzadressofauthor{}
@@ -93,7 +93,7 @@
 \usepackage[english]{babel}
 \usepackage[normalem]{ulem}
 \usepackage{multirow,multido,booktabs,cellspace}
-\usepackage{shortvrb,fancyvrb,bookmark} 
+\usepackage{shortvrb,bookmark} 
 \usepackage{makeidx}
 %\usepackage{float}
 \makeindex 
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf b/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
index 7c2839b3f4..0684fccc1f 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
diff --git a/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo-1.pdf b/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo-1.pdf
deleted file mode 100644
index 0c97b2e50b..0000000000
--- a/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo-1.pdf
+++ /dev/null
diff --git a/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.pdf b/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.pdf
new file mode 100644
index 0000000000..5d703157aa
--- /dev/null
+++ b/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.pdf
diff --git a/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.tex b/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.tex
new file mode 100644
index 0000000000..3242fea11a
--- /dev/null
+++ b/macros/latex/contrib/tkz/tkz-elements/examples/tkz-elements-demo_4.tex
@@ -0,0 +1,30 @@
+% !TEX TS-program = lualatex
+% Created by Alain Matthes on 2023-02-25.
+% Copyright (c) 2023 AlterMundus.
+
+\documentclass{standalone} 
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document} 
+    
+\begin{tkzelements}
+   scale       = 2
+   z.A         = point: new(0,0)
+   z.B         = point: new(5,0)
+   z.C         = point: new(1,4)
+   T.ABC       = triangle: new (z.A,z.B,z.C)
+   T.EFG       = T.ABC: medial ()
+   z.E,z.F,z.G = get_points (T.EFG)
+   z.S         = T.ABC: medial (): circum_circle ().south
+   z.O         = T.ABC: medial ().circumcenter
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(A,B,C E,F,G)
+   \tkzDrawCircle(O,E)
+   \tkzDrawPoints(A,B,C,O,S,E,F,G)
+   \tkzLabelPoints(A,B,O,S,E,F,G)
+   \tkzLabelPoints[above](C)
+\end{tikzpicture}
+
+\end{document}
\ No newline at end of file
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz-elements.sty b/macros/latex/contrib/tkz/tkz-elements/latex/tkz-elements.sty
index a147a045aa..80a39af083 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz-elements.sty
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz-elements.sty
@@ -1,5 +1,5 @@
 % encoding : utf8 
-% tkz-elements v1.00b
+% tkz-elements v1.20b
 % Copyright 2023  Alain Matthes
 % This work may be distributed and/or modified under the
 % conditions of the LaTeX Project Public License, either version 1.3
@@ -11,13 +11,18 @@
 % This work has the LPPL maintenance status “maintained”.
 % The Current Maintainer of this work is Alain Matthes.
 
-\ProvidesPackage{tkz-elements}[2023/10/20 v1.00b Graphic Object Library]
+\ProvidesPackage{tkz-elements}[2023/11/10 v1.20b Graphic Object Library]
 \RequirePackage{luacode}
 \RequirePackage{filecontents}
 \directlua{require "tkz_elements_main"}
 
 \newenvironment{tkzelements}
-  {\directlua{scale=1}
+  {   \directlua{scale=1}
+      \directlua{for k,v in pairs(z) do z[k] = nil end}
+      \directlua{for k,v in pairs(L) do L[k] = nil end}
+      \directlua{for k,v in pairs(C) do C[k] = nil end}
+      \directlua{for k,v in pairs(T) do T[k] = nil end}
+      \directlua{for k,v in pairs(E) do E[k] = nil end}
    \luacode}
   {\endluacode}
 \def\tkzGetNodes{\directlua{%
@@ -32,4 +37,12 @@
   tex.print("\\coordinate ("..K..") at ("..V.re..","..V.im..") ;\\\\")
 end}
 }
+\def\tkzEraseTables{
+      \directlua{for k,v in pairs(z) do z[k] = nil end}
+      \directlua{for k,v in pairs(L) do L[k] = nil end}
+      \directlua{for k,v in pairs(C) do C[k] = nil end}
+      \directlua{for k,v in pairs(T) do T[k] = nil end}
+      \directlua{for k,v in pairs(E) do E[k] = nil end}
+}
+\def\tkzUseLua#1{\directlua{tex.print(tostring(#1))}} 
 \endinput
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_circles.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_circles.lua
index 52da83fc25..7af14e473c 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_circles.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_circles.lua
@@ -1,6 +1,6 @@
 -- tkz_elements-circles.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -27,18 +27,29 @@ function circle: new (c, t) -- c --> center t --> through
     setmetatable(new_circle, {__index = circle})
     return new_circle
 end
+-- other definition
 
-function circle: antipode (pt)
-   return 2 * self.center - pt
+function circle: radius (center, radius) -- c --> center r --> radius
+   local through
+   through = center + point( radius,  0 )
+   return circle : new  (center, through )
 end
-
-function circle: power (pt)
-    local d
-    d = point.abs (self.center - pt)
-    return     d * d - self.radius * self.radius
+-----------------------
+-- boolean --
+-----------------------
+function circle: in_out (pt)
+    local d,epsilon
+     epsilon = 10^(-12)
+    d = point.abs (pt - self.center)
+    if math.abs(d-self.radius) < epsilon
+     then
+       return true
+    else
+       return false
+    end
 end
 
-function circle: in_out (pt)
+function circle: in_out_disk (pt)
     local d
     d = point.abs (pt - self.center)
     if d <= self.radius
@@ -48,22 +59,78 @@ function circle: in_out (pt)
        return false
     end
 end
+-----------------------
+-- real --
+-----------------------
 
--- function circle: tangent_at (pt)
---     return tangent_at_ (self.center,self.through,pt)
---  end
+function circle: power (pt)
+    local d
+    d = point.abs (self.center - pt)
+    return     d * d - self.radius * self.radius
+end
+-----------------------
+-- points --
+-----------------------
+function circle: antipode (pt)
+   return 2 * self.center - pt
+end
+
+function circle: set_inversion (...)
+	local tp = table.pack(...)
+	local i
+    local t = {}
+	for i=1,tp.n do
+        table.insert( t , inversion_ ( self.center,self.through, tp[i] ) ) 
+	end
+  return table.unpack ( t )
+end
+
+function circle: midarc (z1,z2)
+   local phi = 0.5 * get_angle_(self.center,z1,z2 )
+   return rotation_ (self.center,phi,z1)
+end
+
+function circle: point (phi)
+   return point (self.center.re+self.radius*math.cos(phi),self.center.im+self.radius*math.sin(phi) )
+end
 
+function circle: random_pt(lower, upper)
+local t
+     math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
+      phi = lower + math.random() * (upper - lower)
+return point (self.center.re+self.radius*math.cos(phi),self.center.im+self.radius*math.sin(phi) )
+end
+
+function circle: internal_similitude (C)
+  return barycenter_ ({self.center,C.radius},{C.center,self.radius})
+end
+
+function circle: external_similitude (C)
+  return  barycenter_ ({C.center,self.radius},{self.center,-C.radius})
+end
+
+
+-----------------------
+-- lines --
+-----------------------
 function circle: tangent_at (pt)
     return line : new ( rotation_ (pt,math.pi/2,self.center),rotation_ (pt,-math.pi/2,self.center))
  end
  
-
 function circle: tangent_from (pt)
    local t1,t2
    t1,t2 = tangent_from_ (self.center,self.through,pt) 
     return line :new (pt,t1),line : new (pt,t2)
  end
-
+ 
+ function circle: radical_axis (C)
+    local t1,t2
+    t1,t2 = radical_axis_ (self.center,self.through,C.center,C.through)
+ return line : new (t1,t2)
+ end
+ -----------------------
+ -- circles --
+ -----------------------
 function circle: orthogonal_from (pt)
     local t1,t2
      t1,t2 = tangent_from_ (self.center,self.through,pt) 
@@ -73,50 +140,44 @@ end
 function circle: orthogonal_through (pta,ptb)
     return circle : new (orthogonal_through_ (self.center,self.through,pta,ptb),pta)
  end
- 
- function circle: inversion (pt)
- return inversion_ (self.center,self.through,pt)
- end
 
- function circle: set_inversion (...)
- 	local tp = table.pack(...)
- 	local i
-     local t = {}
- 	for i=1,tp.n do
-         table.insert( t , inversion_ ( self.center,self.through, tp[i] ) ) 
- 	end
-   return table.unpack ( t )
- end
- 
- function circle: midarc (z1,z2)
-    local phi = 0.5 * get_angle_(self.center,z1,z2 )
-    return rotation_ (self.center,phi,z1)
+ function circle: inversion_L (L)
+    local p,q
+    if L: in_out (self.center) then
+    return L
+  else 
+   p =  L: projection (self.center)
+   q = inversion_ (self.center,self.through,p) 
+   return   circle: new (midpoint_(self.center,q),q) 
+  end
  end
-
- function circle: point (phi)
-    return point (self.center.re+self.radius*math.cos(phi),self.center.im+self.radius*math.sin(phi) )
+   
+ function circle: inversion_C (C)
+    local p,q,x,y
+    if C: in_out (self.center) then
+       p = C : antipode (self.center)
+       q = inversion_ (self.center,self.through,p) 
+       x = ortho_from_ ( q , self.center , p )
+       y = ortho_from_ ( q , p, self.center)
+    return line : new  (x,y)
+  else 
+      x,y = intersection_lc_ (self.center,C.center,C.center,C.through)
+      X = inversion_ (self.center,self.through,x) 
+      Y = inversion_ (self.center,self.through,y) 
+      return circle : new (midpoint_(X,Y),X)
+   end
  end
  
-function circle: random_pt(lower, upper)
-local t
-     math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-      phi = lower + math.random() * (upper - lower)
-return point (self.center.re+self.radius*math.cos(phi),self.center.im+self.radius*math.sin(phi) )
-end
-   
-function circle: radical_axis (C)
-   local t1,t2
-   t1,t2 = radical_axis_ (self.center,self.through,C.center,C.through)
-return line : new (t1,t2)
-end
-
-function circle: internal_similitude (C)
-  return barycenter_ ({self.center,C.radius},{C.center,self.radius})
-end
-
-function circle: external_similitude (C)
-  return  barycenter_ ({C.center,self.radius},{self.center,-C.radius})
+ function circle: inversion (obj)
+    if obj.type == "point" then
+ return inversion_ (self.center,self.through,obj)
+ elseif  obj.type == "line" then
+   return self: inversion_L (obj)
+else
+    return self: inversion_C (obj)
 end
+ end
+  
 
 function circle: draw ()
    local x,y
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_ellipses.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_ellipses.lua
index 0e15d5ab86..4bc34c61b7 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_ellipses.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_ellipses.lua
@@ -1,6 +1,6 @@
 -- tkz_elements-ellipses.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_circles.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_circles.lua
index e1d6b4bd53..fe9c91d2f7 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_circles.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_circles.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_functions_circles.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -14,23 +14,28 @@
 
 --  define a circle by the center and a radius
 
-function circle_cr ( c, r )
-    return c +  point(r,0)
-end
+-- function circle_cr ( c, r )
+--     return c +  point(r,0)
+-- end
 
 function midarc_ (o,a,b) -- a -> b
    local phi = 0.5 * get_angle_ ( a,o,b )
    return rotation_ (o,phi,b)
 end
----------------------------------------------------------------------------
--- -- possible (C,p) with C.center and C.through
--- function tangent_from (c,p)
---      local m = midpoint_ (c.center,p)
---      return intersection_cc_ (c.center,c.through,m,p)
---  end
----------------------------------------------------------------------------
---        tangente à un cercle
----------------------------------------------------------------------------
+
+function radical_center (C1,C2,C3)
+   local t1,t2,t3,t4
+   t1,t2 = radical_axis_ (C3.center,C3.through,C1.center,C1.through)
+   t3,t4 = radical_axis_ (C3.center,C3.through,C2.center,C2.through)
+return intersection_ll_ (t1,t2,t3,t4)
+end
+
+function  radical_circle (C1,C2,C3)
+   local rc
+   rc = radical_center (C1,C2,C3)
+ return C1 : orthogonal_from (rc)
+end
+
 function tangent_from_ (c,p,pt)
   local o
    o  = midpoint_ ( c,pt )
@@ -38,7 +43,7 @@ function tangent_from_ (c,p,pt)
 end
 
 function tangent_at_ (a,b,p)
-     return rotation_ (p,math.pi/2,a),rotation_ (p,-math.pi/2,a)
+   return rotation_ (p,math.pi/2,a),rotation_ (p,-math.pi/2,a)
 end
 
 function orthogonal_from_ (a,b,p)
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_intersections.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_intersections.lua
index 8c5123129d..f52c4bc2b1 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_intersections.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_intersections.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_intersections.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_lines.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_lines.lua
index 87ea1de043..c78004be6a 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_lines.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_lines.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_functions_lines.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -15,6 +15,9 @@
 ---------------------------------------------------------------------------
 --                 Lines
 ---------------------------------------------------------------------------
+function normalize_ (a,b)
+   return a+(b-a)/point.mod(b-a)
+end
 
 function ortho_from_ ( p , a , b )
 	return  p+(b-a)*point(0,1) 
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_maths.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_maths.lua
index 866912468a..f38458e1f1 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_maths.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_maths.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_functions_maths.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -101,6 +101,10 @@ function value (v)
    return scale * v
 end
 
+function real (v)
+   return v/scale
+end
+
 function get_angle (a,b,c)
   return angle_normalize(get_angle_( a,b,c ))
 end 
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_points.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_points.lua
index fcd249d891..ea468a9c6d 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_points.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_points.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_functions_points.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -34,9 +34,9 @@ end
 return sum/weight
 end
 
-function rotation_ (center,alpha,pt)
-  local z = point( math.cos(alpha) , math.sin(alpha) )
-  return z*(pt-center)+center
+function rotation_ (c,a,pt)
+  local z = point( math.cos(a) , math.sin(a) )
+  return z*(pt-c)+c
 end
 
 function symmetry_(c,pt)
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_triangles.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_triangles.lua
index b4e41104d1..166d3b7647 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_triangles.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_triangles.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_functions_triangles.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -200,7 +200,7 @@ function incentral_tr_ (a,b,c)
     r = intersection_ll_ ( a,i , b,c)
     s = intersection_ll_ ( b,i , a,c)
     t = intersection_ll_ ( c,i , a,b)
-return    i,r,s,t
+return    r,s,t
 end
 
 function excentral_tr_ (a,b,c)
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_lines.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_lines.lua
index 05d4196938..11d8f49d41 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_lines.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_lines.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_lines.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -34,9 +34,47 @@ function line: new(za, zb)
     setmetatable(new_line, {__index = line})
     return new_line
 end
+
+-------------------
+-- Result -> real
+-------------------
+function line: distance (pt)   
+    return point.mod(projection(self,pt)-pt)
+end
+
+function line: slope ()
+   return slope_(self.pa,self.pb)
+end
+-------------------
+-- Result -> boolean
+-------------------
+function line: in_out (pt)
+    local sc,epsilon
+    epsilon = 10^(-12)
+    sc = math.abs ((pt-self.pa)^(pt-self.pb))
+    if sc <= epsilon
+     then
+       return true
+    else
+       return false
+    end
+end
+
 -------------------
 -- Result -> point
 -------------------
+function line: translation ( pt )
+    return translation_ ( self.pb-self.pa,pt )
+end
+
+function line: set_translation ( ...)
+    return set_translation_ ( self.pb-self.pa,... )
+end
+
+function line: projection ( pt )
+    return  projection_ ( self.pa,self.pb,pt )
+end
+
 function line: set_projection (...)
 	local tp = table.pack(...)
 	local i
@@ -60,7 +98,7 @@ function line: set_symmetry_axial (...)
 	end
   return table.unpack ( t )
 end
--- k_div ig "gold" or "phi" then 
+
 
 function line: barycenter (ka,kb)
     return barycenter_({self.pa,ka},{self.pb,kb})
@@ -89,6 +127,14 @@ end
 function line: gold_ratio()
    return self.pa + (self.pb-self.pa)*tkzinvphi
 end
+
+function line: normalize ()
+   return  self.pa+(self.pb-self.pa)/point.mod(self.pb-self.pa)
+end
+
+function line: normalize_inv ()
+   return normalize_ (self.pb,self.pa)
+end
 -------------------
 -- Result -> line
 -------------------
@@ -100,10 +146,6 @@ function line: ortho_from ( pt )
 	return  line : new (pt,pt+(self.pb-self.pa)*point(0,1))
 end
 
-function line: projection ( pt )
-    return  projection_ ( self.pa,self.pb,pt )
-end
-
 function line: mediator () 
    local m
    m = midpoint_ (self.pa,self.pb)
@@ -119,30 +161,7 @@ end
 function line: circle_swap ()   
     return circle : new (self.pb,self.pa)
 end
--------------------
--- Result -> real
--------------------
-function line: distance (pt)   
-    return point.mod(projection(self,pt)-pt)
-end
--------------------
--- Result -> boolean
--------------------
-function line: in_out (pt)
-    local sc,epsilon
-    epsilon = 10^(-12)
-    sc = math.abs ((pt-self.pa)^(pt-self.pb))
-    if sc <= epsilon
-     then
-       return true
-    else
-       return false
-    end
-end
- 
-function line: slope ()
-   return slope_(self.pa,self.pb)
-end
+
 ----------------------
 -- Result -> triangle
 ----------------------
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_main.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_main.lua
index 92e006fe78..10b96d1430 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_main.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_main.lua
@@ -1,6 +1,6 @@
 -- tkz_elements-main.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -43,5 +43,7 @@ if obj.type == 'line' then return   obj.pa,obj.pb
   obj.type  == 'triangle' then return   obj.pa,obj.pb,obj.pc
   elseif 
   obj.type == 'circle' then   return obj.center,obj.through
+  elseif 
+  obj.type == 'ellipse' then   return obj.pc,obj.pa,obj.pb
 end
 end
\ No newline at end of file
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_point.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_point.lua
index 0b2e3dec4a..5d459e3028 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_point.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_point.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_point.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_points.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_points.lua
index bcaff010cc..74ad16a165 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_points.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_points.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_points.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_triangles.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_triangles.lua
index 1960248e50..6ea35c5b6e 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_triangles.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_triangles.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_triangles.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3
@@ -20,6 +20,7 @@ function triangle: new (za, zb ,zc)
    local incenter = in_center_ (za , zb , zc)
    local orthocenter = ortho_center_  (za , zb , zc)
    local eulercenter = euler_center_  (za , zb , zc)
+   local spiekercenter = spieker_center_  (za , zb , zc)
    local c = point.abs(zb-za)
    local a = point.abs(zc-zb)
    local b = point.abs(za-zc)
@@ -31,8 +32,8 @@ function triangle: new (za, zb ,zc)
    local bc =line : new (zb,zc)
    local new_triangle = {pa = za, pb = zb, pc = zc, type = type,
  circumcenter=circumcenter,centroid=centroid,incenter=incenter,
- eulercenter=eulercenter, orthocenter=orthocenter,a=a,b=b,c=c,ab=ab,ac=ac,bc=bc,
- alpha=alpha,beta=beta,gamma=gamma}
+ eulercenter=eulercenter, orthocenter=orthocenter,spiekercenter=spiekercenter,
+ a=a,b=b,c=c,ab=ab,ac=ac,bc=bc,alpha=alpha,beta=beta,gamma=gamma}
     setmetatable(new_triangle, {__index = triangle})
     return new_triangle
 end
diff --git a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_vectors.lua b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_vectors.lua
index 44ea2f7f2e..26ec57e695 100644
--- a/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_vectors.lua
+++ b/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_vectors.lua
@@ -1,6 +1,6 @@
 -- tkz_elements_vectors.lua
--- date 2023/10/20
--- version 1.00b
+-- date 2023/11/10
+-- version 1.20b
 -- Copyright 2023  Alain Matthes
 -- This work may be distributed and/or modified under the
 -- conditions of the LaTeX Project Public License, either version 1.3