@@ -1,353 +1,353 @@
-\section{Gnuplot package}
-
-\begin{Introduction}{GNUPLOT and REDUCE}
-
-The GNUPLOT system provides easy to use graphics output
-for curves or surfaces which are defined by
-formulas and/or data sets. GNUPLOT supports
-a great variety of output devices
-such as X-windows, VGA screen, postscript, picTeX.
-The REDUCE GNUPLOT package lets one use the GNUPLOT
-graphical output directly from inside REDUCE, either for
-the interactive display of curves/surfaces or for the production
-of pictures on paper.
-
-Note that this package may not be supported on all system
-platforms.
-
-For a detailed description you should read the GNUPLOT
-system documentation, available together with the GNUPLOT
-installation material from several servers by anonymous FTP.
-
-The REDUCE developers thank the GNUPLOT people for their permission
-to distribute GNUPLOT together with REDUCE.
-\end{Introduction}
-
-\begin{Concept}{Axes names}
-Inside REDUCE the choice of variable names for a graph is completely
-free. For referring to the GNUPLOT axes the names
-X and Y for 2 dimensions, X,Y and Z for 3 dimensions are used
-in the usual schoolbook sense independent from the variables of
-the REDUCE expression.
-
-\begin{Examples}
-  plot(w=sin(a),a=(0 .. 10),xlabel="angle",ylabel="sine");
-\end{Examples}
-
-\end{Concept}
-
-\begin{Type}{Pointset}
-\index{plot}
-A curve can be give as set of precomputed points (a polygon)
-in 2 or 3 dimensions. Such a point set is a \nameref{list}
-of points, where each point is a \nameref{list} 2 (or 3)
-numbers. These numbers are interpreted as \name{(x,y)}
-(or \name{x,y,z}) coordinates. All points of one set must have
-the same dimension.
-
-\begin{Examples}
- for i:=2:10 collect{i,factorial(i)};
-
-\end{Examples}
-
-Also a surface in 3d can be given by precomputed points,
-but only on a logically orthogonal mesh: the surface is defined
-by a list of curves (in 3d) which must have a uniform length.
-GNUPLOT then will draw an orthogonal mesh by first drawing the
-given lines, and second connecting the 1st point of the 1st curve
-with the 1st point of the 2nd curve, that one with the 1st point
-of the 3rd curve and so on for all curves and for all indexes.
-
-
-\end{Type}
-
-
-\begin{Command}{PLOT}
-\index{graphics}\index{plot}
-The command \name{plot} is the main entry for drawing a
-picture from inside REDUCE.
-
-\begin{Syntax}
-\name{plot}\(\meta{spec},\meta{spec},...\)
-\end{Syntax}
-
-where \meta{spec} is a \meta{function}, a \meta{range} or an \meta{option}.
-
-\meta{function}:
-
-- an expression depending
-on one unknown (e.g. \name{sin(x)} or two unknowns (e.g.
-\name{sin(x+y)},
-
-- an equation with a function on its right-hand
-side and a single name on its left-hand side (e.g.
-\name{z=sin(x+y)} where the name on the left-hand side specifies
-the dependent variable.
-
-- a list of functions:
-if in 2 dimensions the picture should have more than one
-curve the expressions can be given as list (e.g. \name{\{sin(x),cos(x)\}}).
-
-- an equation with zero left or right hand side describing
-   an implicit curve in two dimensions (e.g. \name{x**3+x*y**3-9x=0}).
-
-- a point set: the graph can be given
-as point set in 2 dimensions or a \nameref{pointset}  or pointset list
-in 3 dimensions.
-
-\meta{range}:
-
-Each dependent and independent variable can be limited
-to an interval by an equation where the left-hand side specifies
-the variable and the right-hand side defines the \nameref{interval},
-e.g. \name{x=( -3 .. 5)}.
-
-If omitted the independent variables
-range from -10 to 10 and the dependent variable is limited only
-by the precision of the IEEE floating point arithmetic.
-
-\meta{option}:
-
-An option can be an equation equating a variable
-and a value (in general a string), or a keyword(GNUPLOT switch).
-These have to be included in the gnuplot command arguments directly.
-Strings have to be enclosed in
-string quotes (see \nameref{string}). Available options are:
-
-\nameref{title}: assign a heading (default: empty)
-
-\nameref{xlabel}: set label for the x axis
-
-\nameref{ylabel}: set label for the y axis
-
-\nameref{zlabel}: set label for the z axis
-
-\nameref{terminal}: select an output device
-
-\nameref{size}: rescale the picture
-
-\nameref{view}: set a viewpoint
-
-\name{(no)}\nameref{contour}: 3d: add contour lines
-
-\name{(no)}\nameref{surface}: 3d: draw surface (default: yes)
-
-\name{(no)}\nameref{hidden3d}: 3d: remove hidden lines (default: no)
-
-\begin{Examples}
-plot(cos x);\\
-plot(s=sin phi,phi=(-3 .. 3));\\
-plot(sin phi,cos phi,phi=(-3 .. 3));\\
-plot (cos sqrt(x**2 + y**2),x=(-3 .. 3),y=(-3 .. 3),hidden3d);\\
-plot {{0,0},{0,1},{1,1},{0,0},{1,0},{0,1},{0.5,1.5},{1,1},{1,0}};\\
-\\
-on rounded;\\
-w:=for j:=1:200 collect {1/j*sin j,1/j*cos j,j/200}$\\
-plot w; \\
-\end{Examples}
-
-Additional control of the \name{plot} operation:
-\nameref{plotrefine},
-\nameref{plot_xmesh}, \nameref{plot_ymesh}, \nameref{trplot},
-\nameref{plotkeep}, \nameref{show_grid}.
-
-\end{Command}
-
-\begin{Command}{PLOTRESET}
-The command \name{plotreset} closes the current GNUPLOT windows.
-The next call to \nameref{plot} will create a new one. \name{plotreset}
-can also be used to reset the system status after technical problems.
-
-\begin{Syntax}
-\name{plotreset};
-\end{Syntax}
-\end{Command}
-
-
-\begin{Variable}{title}
-\index{plot}
-\nameref{plot} option:
-Assign a title to the GNUPLOT graph.
-
-\begin{Syntax}
-\name{title} = \meta{string}
-\end{Syntax}
-\begin{Examples}
-title="annual revenue in 1993"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{xlabel}
-\index{plot}
-\nameref{plot} option:
-Assign a name to to the x axis (see \nameref{axes names}).
-
-\begin{Syntax}
-\name{xlabel} = \meta{string}
-\end{Syntax}
-\begin{Examples}
-xlabel="month"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{ylabel}
-\index{plot}
-\nameref{plot} option:
-Assign a name to to the x axis (see \nameref{axes names}).
-
-\begin{Syntax}
-\name{ylabel} = \meta{string}
-\end{Syntax}
-\begin{Examples}
-ylabel="million forint"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{zlabel}
-\index{plot}
-\nameref{plot} option:
-Assign a name to to the z axis (see \nameref{axes names}).
-
-\begin{Syntax}
-\name{zlabel} = \meta{string}
-\end{Syntax}
-\begin{Examples}
-zlabel="local weight"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{terminal}
-\index{plot}
-\nameref{plot} option:
-Select a different output device. The possible values here
-depend highly on the facilities installed for your GNUPLOT
-software.
-
-\begin{Syntax}
-\name{terminal} = \meta{string}
-\end{Syntax}
-\begin{Examples}
-terminal="x11"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{size}
-\index{plot}
-\nameref{plot} option:
-Rescale the graph (not the window!) in x and y direction.
-Default is 1.0 (no rescaling).
-
-\begin{Syntax}
-\name{size} = "\meta{sx},\meta{sy}"
-\end{Syntax}
-where \meta{sx},\meta{sy} are floating point number not too
-far from 1.0.
-\begin{Examples}
-size="0.7,1"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Variable}{view}
-\index{plot}
-\nameref{plot} option:
-Set a new viewpoint by turning the object around the x and then
-around the z axis (see \nameref{axes names}).
-
-\begin{Syntax}
-\name{view} = "\meta{sx},\meta{sz}"
-\end{Syntax}
-where \meta{sx},\meta{sz} are floating point number representing
-angles in degrees.
-\begin{Examples}
-view="30,130"\\
-\end{Examples}
-\end{Variable}
-
-\begin{Switch}{contour}
-\index{plot}
-\nameref{plot} option:
-If \name{contour} is member of the options for a 3d \nameref{plot}
-contour lines are projected to the z=0 plane
-(see \nameref{axes names}). The absence of contour lines
-can be selected explicitly by including \name{nocontour}. Default
-is \name{nocontour}.
-\end{Switch}
-
-
-\begin{Switch}{surface}
-\index{plot}
-\nameref{plot} option:
-If \name{surface} is member of the options for a 3d \nameref{plot}
-the surface is drawn. The absence of the surface plotting
-can be selected by including \name{nosurface}, e.g. if
-only the \nameref{contour} should be visualized. Default is \name{surface}.
-\end{Switch}
-
-
-\begin{Switch}{hidden3d}
-\index{plot}
-\nameref{plot} option:
-If \name{hidden3d} is member of the options for a 3d \nameref{plot}
-hidden lines are removed from the picture. Otherwise a
-surface is drawn as transparent object. Default is
-\name{nohidden3d}. Selecting \name{hidden3d} increases the
-computing time substantially.
-\end{Switch}
-
-\begin{Switch}{PLOTKEEP}
-\index{plot}
-Normally all intermediate data sets are deleted after terminating
-a plot session. If the switch \name{plotkeep} is set \nameref{on},
-the data sets are kept for eventual post processing independent
-of REDUCE.
-\end{Switch}
-
-\begin{Switch}{PLOTREFINE}
-\index{plot}
-In general \nameref{plot} tries to generate smooth pictures by evaluating
-the functions at interior points until the distances are fine
-enough. This can require a lot of computing time if the
-single function evaluation is expensive. The refinement is
-controlled by the switch \name{plotrefine} which is \nameref{on}
-by default. When you turn it \nameref{off} the functions will
-be evaluated only at the basic points (see \nameref{plot_xmesh},
-\nameref{plot_ymesh}).
-\end{Switch}
-
-\begin{Variable}{plot_xmesh}
-\index{plot}
-The integer value of the global variable \name{plot_xmesh}
-defines the number of initial function evaluations in x
-direction (see \nameref{axes names}) for \nameref{plot}. For 2d graphs additional
-points will be used as long as \nameref{plotrefine} is \name{on}.
-For 3d graphs this number defines also the number of mesh lines
-orthogonal to the x axis.
-\end{Variable}
-
-\begin{Variable}{plot_ymesh}
-\index{plot}
-The integer value of the global variable \name{plot_ymesh}
-defines for 3d  \nameref{plot} calls the number of function evaluations in y
-direction (see \nameref{axes names}) and the number of mesh lines
-orthogonal to the y axis.
-\end{Variable}
-
-\begin{Switch}{SHOW_GRID}
-\index{plot}
-The grid for localizing an implicitly defined curve in \nameref{plot}
-consists of triangles. These are computed initially equally distributed
-over the x-y plane controlled by \nameref{plot_xmesh}. The grid is
-refined adaptively in several levels. The final grid can be visualized
-by setting on the switch \name{show_grid}.
-\end{Switch}
-
-
-\begin{Switch}{TRPLOT}
-\index{plot}
-In general the interaction between REDUCE and GNUPLOT is performed
-as silently as possible. However, sometimes it might be useful
-to see the GNUPLOT commands generated by REDUCE, e.g. for a
-postprocessing of generated data sets independent of REDUCE.
-When the switch \name{trplot} is set on all GNUPLOT commands will
-be printed to the standard output additionally.
-\end{Switch}
+\section{Gnuplot package}
+
+\begin{Introduction}{GNUPLOT and REDUCE}
+
+The GNUPLOT system provides easy to use graphics output
+for curves or surfaces which are defined by
+formulas and/or data sets. GNUPLOT supports
+a great variety of output devices
+such as X-windows, VGA screen, postscript, picTeX.
+The REDUCE GNUPLOT package lets one use the GNUPLOT
+graphical output directly from inside REDUCE, either for
+the interactive display of curves/surfaces or for the production
+of pictures on paper.
+
+Note that this package may not be supported on all system
+platforms.
+
+For a detailed description you should read the GNUPLOT
+system documentation, available together with the GNUPLOT
+installation material from several servers by anonymous FTP.
+
+The REDUCE developers thank the GNUPLOT people for their permission
+to distribute GNUPLOT together with REDUCE.
+\end{Introduction}
+
+\begin{Concept}{Axes names}
+Inside REDUCE the choice of variable names for a graph is completely
+free. For referring to the GNUPLOT axes the names
+X and Y for 2 dimensions, X,Y and Z for 3 dimensions are used
+in the usual schoolbook sense independent from the variables of
+the REDUCE expression.
+
+\begin{Examples}
+  plot(w=sin(a),a=(0 .. 10),xlabel="angle",ylabel="sine");
+\end{Examples}
+
+\end{Concept}
+
+\begin{Type}{Pointset}
+\index{plot}
+A curve can be give as set of precomputed points (a polygon)
+in 2 or 3 dimensions. Such a point set is a \nameref{list}
+of points, where each point is a \nameref{list} 2 (or 3)
+numbers. These numbers are interpreted as \name{(x,y)}
+(or \name{x,y,z}) coordinates. All points of one set must have
+the same dimension.
+
+\begin{Examples}
+ for i:=2:10 collect{i,factorial(i)};
+
+\end{Examples}
+
+Also a surface in 3d can be given by precomputed points,
+but only on a logically orthogonal mesh: the surface is defined
+by a list of curves (in 3d) which must have a uniform length.
+GNUPLOT then will draw an orthogonal mesh by first drawing the
+given lines, and second connecting the 1st point of the 1st curve
+with the 1st point of the 2nd curve, that one with the 1st point
+of the 3rd curve and so on for all curves and for all indexes.
+
+
+\end{Type}
+
+
+\begin{Command}{PLOT}
+\index{graphics}\index{plot}
+The command \name{plot} is the main entry for drawing a
+picture from inside REDUCE.
+
+\begin{Syntax}
+\name{plot}\(\meta{spec},\meta{spec},...\)
+\end{Syntax}
+
+where \meta{spec} is a \meta{function}, a \meta{range} or an \meta{option}.
+
+\meta{function}:
+
+- an expression depending
+on one unknown (e.g. \name{sin(x)} or two unknowns (e.g.
+\name{sin(x+y)},
+
+- an equation with a function on its right-hand
+side and a single name on its left-hand side (e.g.
+\name{z=sin(x+y)} where the name on the left-hand side specifies
+the dependent variable.
+
+- a list of functions:
+if in 2 dimensions the picture should have more than one
+curve the expressions can be given as list (e.g. \name{\{sin(x),cos(x)\}}).
+
+- an equation with zero left or right hand side describing
+   an implicit curve in two dimensions (e.g. \name{x**3+x*y**3-9x=0}).
+
+- a point set: the graph can be given
+as point set in 2 dimensions or a \nameref{pointset}  or pointset list
+in 3 dimensions.
+
+\meta{range}:
+
+Each dependent and independent variable can be limited
+to an interval by an equation where the left-hand side specifies
+the variable and the right-hand side defines the \nameref{interval},
+e.g. \name{x=( -3 .. 5)}.
+
+If omitted the independent variables
+range from -10 to 10 and the dependent variable is limited only
+by the precision of the IEEE floating point arithmetic.
+
+\meta{option}:
+
+An option can be an equation equating a variable
+and a value (in general a string), or a keyword(GNUPLOT switch).
+These have to be included in the gnuplot command arguments directly.
+Strings have to be enclosed in
+string quotes (see \nameref{string}). Available options are:
+
+\nameref{title}: assign a heading (default: empty)
+
+\nameref{xlabel}: set label for the x axis
+
+\nameref{ylabel}: set label for the y axis
+
+\nameref{zlabel}: set label for the z axis
+
+\nameref{terminal}: select an output device
+
+\nameref{size}: rescale the picture
+
+\nameref{view}: set a viewpoint
+
+\name{(no)}\nameref{contour}: 3d: add contour lines
+
+\name{(no)}\nameref{surface}: 3d: draw surface (default: yes)
+
+\name{(no)}\nameref{hidden3d}: 3d: remove hidden lines (default: no)
+
+\begin{Examples}
+plot(cos x);\\
+plot(s=sin phi,phi=(-3 .. 3));\\
+plot(sin phi,cos phi,phi=(-3 .. 3));\\
+plot (cos sqrt(x**2 + y**2),x=(-3 .. 3),y=(-3 .. 3),hidden3d);\\
+plot {{0,0},{0,1},{1,1},{0,0},{1,0},{0,1},{0.5,1.5},{1,1},{1,0}};\\
+\\
+on rounded;\\
+w:=for j:=1:200 collect {1/j*sin j,1/j*cos j,j/200}$\\
+plot w; \\
+\end{Examples}
+
+Additional control of the \name{plot} operation:
+\nameref{plotrefine},
+\nameref{plot_xmesh}, \nameref{plot_ymesh}, \nameref{trplot},
+\nameref{plotkeep}, \nameref{show_grid}.
+
+\end{Command}
+
+\begin{Command}{PLOTRESET}
+The command \name{plotreset} closes the current GNUPLOT windows.
+The next call to \nameref{plot} will create a new one. \name{plotreset}
+can also be used to reset the system status after technical problems.
+
+\begin{Syntax}
+\name{plotreset};
+\end{Syntax}
+\end{Command}
+
+
+\begin{Variable}{title}
+\index{plot}
+\nameref{plot} option:
+Assign a title to the GNUPLOT graph.
+
+\begin{Syntax}
+\name{title} = \meta{string}
+\end{Syntax}
+\begin{Examples}
+title="annual revenue in 1993"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{xlabel}
+\index{plot}
+\nameref{plot} option:
+Assign a name to to the x axis (see \nameref{axes names}).
+
+\begin{Syntax}
+\name{xlabel} = \meta{string}
+\end{Syntax}
+\begin{Examples}
+xlabel="month"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{ylabel}
+\index{plot}
+\nameref{plot} option:
+Assign a name to to the x axis (see \nameref{axes names}).
+
+\begin{Syntax}
+\name{ylabel} = \meta{string}
+\end{Syntax}
+\begin{Examples}
+ylabel="million forint"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{zlabel}
+\index{plot}
+\nameref{plot} option:
+Assign a name to to the z axis (see \nameref{axes names}).
+
+\begin{Syntax}
+\name{zlabel} = \meta{string}
+\end{Syntax}
+\begin{Examples}
+zlabel="local weight"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{terminal}
+\index{plot}
+\nameref{plot} option:
+Select a different output device. The possible values here
+depend highly on the facilities installed for your GNUPLOT
+software.
+
+\begin{Syntax}
+\name{terminal} = \meta{string}
+\end{Syntax}
+\begin{Examples}
+terminal="x11"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{size}
+\index{plot}
+\nameref{plot} option:
+Rescale the graph (not the window!) in x and y direction.
+Default is 1.0 (no rescaling).
+
+\begin{Syntax}
+\name{size} = "\meta{sx},\meta{sy}"
+\end{Syntax}
+where \meta{sx},\meta{sy} are floating point number not too
+far from 1.0.
+\begin{Examples}
+size="0.7,1"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Variable}{view}
+\index{plot}
+\nameref{plot} option:
+Set a new viewpoint by turning the object around the x and then
+around the z axis (see \nameref{axes names}).
+
+\begin{Syntax}
+\name{view} = "\meta{sx},\meta{sz}"
+\end{Syntax}
+where \meta{sx},\meta{sz} are floating point number representing
+angles in degrees.
+\begin{Examples}
+view="30,130"\\
+\end{Examples}
+\end{Variable}
+
+\begin{Switch}{contour}
+\index{plot}
+\nameref{plot} option:
+If \name{contour} is member of the options for a 3d \nameref{plot}
+contour lines are projected to the z=0 plane
+(see \nameref{axes names}). The absence of contour lines
+can be selected explicitly by including \name{nocontour}. Default
+is \name{nocontour}.
+\end{Switch}
+
+
+\begin{Switch}{surface}
+\index{plot}
+\nameref{plot} option:
+If \name{surface} is member of the options for a 3d \nameref{plot}
+the surface is drawn. The absence of the surface plotting
+can be selected by including \name{nosurface}, e.g. if
+only the \nameref{contour} should be visualized. Default is \name{surface}.
+\end{Switch}
+
+
+\begin{Switch}{hidden3d}
+\index{plot}
+\nameref{plot} option:
+If \name{hidden3d} is member of the options for a 3d \nameref{plot}
+hidden lines are removed from the picture. Otherwise a
+surface is drawn as transparent object. Default is
+\name{nohidden3d}. Selecting \name{hidden3d} increases the
+computing time substantially.
+\end{Switch}
+
+\begin{Switch}{PLOTKEEP}
+\index{plot}
+Normally all intermediate data sets are deleted after terminating
+a plot session. If the switch \name{plotkeep} is set \nameref{on},
+the data sets are kept for eventual post processing independent
+of REDUCE.
+\end{Switch}
+
+\begin{Switch}{PLOTREFINE}
+\index{plot}
+In general \nameref{plot} tries to generate smooth pictures by evaluating
+the functions at interior points until the distances are fine
+enough. This can require a lot of computing time if the
+single function evaluation is expensive. The refinement is
+controlled by the switch \name{plotrefine} which is \nameref{on}
+by default. When you turn it \nameref{off} the functions will
+be evaluated only at the basic points (see \nameref{plot_xmesh},
+\nameref{plot_ymesh}).
+\end{Switch}
+
+\begin{Variable}{plot_xmesh}
+\index{plot}
+The integer value of the global variable \name{plot_xmesh}
+defines the number of initial function evaluations in x
+direction (see \nameref{axes names}) for \nameref{plot}. For 2d graphs additional
+points will be used as long as \nameref{plotrefine} is \name{on}.
+For 3d graphs this number defines also the number of mesh lines
+orthogonal to the x axis.
+\end{Variable}
+
+\begin{Variable}{plot_ymesh}
+\index{plot}
+The integer value of the global variable \name{plot_ymesh}
+defines for 3d  \nameref{plot} calls the number of function evaluations in y
+direction (see \nameref{axes names}) and the number of mesh lines
+orthogonal to the y axis.
+\end{Variable}
+
+\begin{Switch}{SHOW_GRID}
+\index{plot}
+The grid for localizing an implicitly defined curve in \nameref{plot}
+consists of triangles. These are computed initially equally distributed
+over the x-y plane controlled by \nameref{plot_xmesh}. The grid is
+refined adaptively in several levels. The final grid can be visualized
+by setting on the switch \name{show_grid}.
+\end{Switch}
+
+
+\begin{Switch}{TRPLOT}
+\index{plot}
+In general the interaction between REDUCE and GNUPLOT is performed
+as silently as possible. However, sometimes it might be useful
+to see the GNUPLOT commands generated by REDUCE, e.g. for a
+postprocessing of generated data sets independent of REDUCE.
+When the switch \name{trplot} is set on all GNUPLOT commands will
+be printed to the standard output additionally.
+\end{Switch}