\begin{patch}{ugGraphTwoDbuildPagePatch1}
\begin{paste}{ugGraphTwoDbuildPageFull1}{ugGraphTwoDbuildPageEmpty1}
\pastebutton{ugGraphTwoDbuildPageFull1}{\hidepaste}
\tab{5}\spadcommand{p1 := point [1,1]$(Point DFLOAT)\bound{p1 }}
\indentrel{3}\begin{verbatim}
   (1)  [1.0, 1.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty1}
\begin{paste}{ugGraphTwoDbuildPageEmpty1}{ugGraphTwoDbuildPagePatch1}
\pastebutton{ugGraphTwoDbuildPageEmpty1}{\showpaste}
\tab{5}\spadcommand{p1 := point [1,1]$(Point DFLOAT)\bound{p1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch2}
\begin{paste}{ugGraphTwoDbuildPageFull2}{ugGraphTwoDbuildPageEmpty2}
\pastebutton{ugGraphTwoDbuildPageFull2}{\hidepaste}
\tab{5}\spadcommand{p2 := point [0,1]$(Point DFLOAT)\bound{p2 }}
\indentrel{3}\begin{verbatim}
   (2)  [0.0, 1.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty2}
\begin{paste}{ugGraphTwoDbuildPageEmpty2}{ugGraphTwoDbuildPagePatch2}
\pastebutton{ugGraphTwoDbuildPageEmpty2}{\showpaste}
\tab{5}\spadcommand{p2 := point [0,1]$(Point DFLOAT)\bound{p2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch3}
\begin{paste}{ugGraphTwoDbuildPageFull3}{ugGraphTwoDbuildPageEmpty3}
\pastebutton{ugGraphTwoDbuildPageFull3}{\hidepaste}
\tab{5}\spadcommand{p3 := point [0,0]$(Point DFLOAT)\bound{p3 }}
\indentrel{3}\begin{verbatim}
   (3)  [0.0, 0.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty3}
\begin{paste}{ugGraphTwoDbuildPageEmpty3}{ugGraphTwoDbuildPagePatch3}
\pastebutton{ugGraphTwoDbuildPageEmpty3}{\showpaste}
\tab{5}\spadcommand{p3 := point [0,0]$(Point DFLOAT)\bound{p3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch4}
\begin{paste}{ugGraphTwoDbuildPageFull4}{ugGraphTwoDbuildPageEmpty4}
\pastebutton{ugGraphTwoDbuildPageFull4}{\hidepaste}
\tab{5}\spadcommand{p4 := point [1,0]$(Point DFLOAT)\bound{p4 }}
\indentrel{3}\begin{verbatim}
   (4)  [1.0, 0.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty4}
\begin{paste}{ugGraphTwoDbuildPageEmpty4}{ugGraphTwoDbuildPagePatch4}
\pastebutton{ugGraphTwoDbuildPageEmpty4}{\showpaste}
\tab{5}\spadcommand{p4 := point [1,0]$(Point DFLOAT)\bound{p4 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch5}
\begin{paste}{ugGraphTwoDbuildPageFull5}{ugGraphTwoDbuildPageEmpty5}
\pastebutton{ugGraphTwoDbuildPageFull5}{\hidepaste}
\tab{5}\spadcommand{p5 := point [1,.5]$(Point DFLOAT)\bound{p5 }}
\indentrel{3}\begin{verbatim}
   (5)  [1.0, 0.5]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty5}
\begin{paste}{ugGraphTwoDbuildPageEmpty5}{ugGraphTwoDbuildPagePatch5}
\pastebutton{ugGraphTwoDbuildPageEmpty5}{\showpaste}
\tab{5}\spadcommand{p5 := point [1,.5]$(Point DFLOAT)\bound{p5 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch6}
\begin{paste}{ugGraphTwoDbuildPageFull6}{ugGraphTwoDbuildPageEmpty6}
\pastebutton{ugGraphTwoDbuildPageFull6}{\hidepaste}
\tab{5}\spadcommand{p6 := point [.5,0]$(Point DFLOAT)\bound{p6 }}
\indentrel{3}\begin{verbatim}
   (6)  [0.5, 0.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty6}
\begin{paste}{ugGraphTwoDbuildPageEmpty6}{ugGraphTwoDbuildPagePatch6}
\pastebutton{ugGraphTwoDbuildPageEmpty6}{\showpaste}
\tab{5}\spadcommand{p6 := point [.5,0]$(Point DFLOAT)\bound{p6 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch7}
\begin{paste}{ugGraphTwoDbuildPageFull7}{ugGraphTwoDbuildPageEmpty7}
\pastebutton{ugGraphTwoDbuildPageFull7}{\hidepaste}
\tab{5}\spadcommand{p7 := point [0,0.5]$(Point DFLOAT)\bound{p7 }}
\indentrel{3}\begin{verbatim}
   (7)  [0.0, 0.5]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty7}
\begin{paste}{ugGraphTwoDbuildPageEmpty7}{ugGraphTwoDbuildPagePatch7}
\pastebutton{ugGraphTwoDbuildPageEmpty7}{\showpaste}
\tab{5}\spadcommand{p7 := point [0,0.5]$(Point DFLOAT)\bound{p7 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch8}
\begin{paste}{ugGraphTwoDbuildPageFull8}{ugGraphTwoDbuildPageEmpty8}
\pastebutton{ugGraphTwoDbuildPageFull8}{\hidepaste}
\tab{5}\spadcommand{p8 := point [.5,1]$(Point DFLOAT)\bound{p8 }}
\indentrel{3}\begin{verbatim}
   (8)  [0.5, 1.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty8}
\begin{paste}{ugGraphTwoDbuildPageEmpty8}{ugGraphTwoDbuildPagePatch8}
\pastebutton{ugGraphTwoDbuildPageEmpty8}{\showpaste}
\tab{5}\spadcommand{p8 := point [.5,1]$(Point DFLOAT)\bound{p8 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch9}
\begin{paste}{ugGraphTwoDbuildPageFull9}{ugGraphTwoDbuildPageEmpty9}
\pastebutton{ugGraphTwoDbuildPageFull9}{\hidepaste}
\tab{5}\spadcommand{p9 := point [.25,.25]$(Point DFLOAT)\bound{p9 }}
\indentrel{3}\begin{verbatim}
   (9)  [0.25, 0.25]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty9}
\begin{paste}{ugGraphTwoDbuildPageEmpty9}{ugGraphTwoDbuildPagePatch9}
\pastebutton{ugGraphTwoDbuildPageEmpty9}{\showpaste}
\tab{5}\spadcommand{p9 := point [.25,.25]$(Point DFLOAT)\bound{p9 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch10}
\begin{paste}{ugGraphTwoDbuildPageFull10}{ugGraphTwoDbuildPageEmpty10}
\pastebutton{ugGraphTwoDbuildPageFull10}{\hidepaste}
\tab{5}\spadcommand{p10 := point [.25,.75]$(Point DFLOAT)\bound{p10 }}
\indentrel{3}\begin{verbatim}
   (10)  [0.25, 0.75]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty10}
\begin{paste}{ugGraphTwoDbuildPageEmpty10}{ugGraphTwoDbuildPagePatch10}
\pastebutton{ugGraphTwoDbuildPageEmpty10}{\showpaste}
\tab{5}\spadcommand{p10 := point [.25,.75]$(Point DFLOAT)\bound{p10 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch11}
\begin{paste}{ugGraphTwoDbuildPageFull11}{ugGraphTwoDbuildPageEmpty11}
\pastebutton{ugGraphTwoDbuildPageFull11}{\hidepaste}
\tab{5}\spadcommand{p11 := point [.75,.75]$(Point DFLOAT)\bound{p11 }}
\indentrel{3}\begin{verbatim}
   (11)  [0.75, 0.75]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty11}
\begin{paste}{ugGraphTwoDbuildPageEmpty11}{ugGraphTwoDbuildPagePatch11}
\pastebutton{ugGraphTwoDbuildPageEmpty11}{\showpaste}
\tab{5}\spadcommand{p11 := point [.75,.75]$(Point DFLOAT)\bound{p11 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch12}
\begin{paste}{ugGraphTwoDbuildPageFull12}{ugGraphTwoDbuildPageEmpty12}
\pastebutton{ugGraphTwoDbuildPageFull12}{\hidepaste}
\tab{5}\spadcommand{p12 := point [.75,.25]$(Point DFLOAT)\bound{p12 }}
\indentrel{3}\begin{verbatim}
   (12)  [0.75, 0.25]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty12}
\begin{paste}{ugGraphTwoDbuildPageEmpty12}{ugGraphTwoDbuildPagePatch12}
\pastebutton{ugGraphTwoDbuildPageEmpty12}{\showpaste}
\tab{5}\spadcommand{p12 := point [.75,.25]$(Point DFLOAT)\bound{p12 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch13}
\begin{paste}{ugGraphTwoDbuildPageFull13}{ugGraphTwoDbuildPageEmpty13}
\pastebutton{ugGraphTwoDbuildPageFull13}{\hidepaste}
\tab{5}\spadcommand{llp := [[p1,p2], [p2,p3], [p3,p4], [p4,p1], [p5,p6], [p6,p7], [p7,p8], [p8,p5], [p9,p10], [p10,p11], [p11,p12], [p12,p9]]\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }\bound{llp }}
\indentrel{3}\begin{verbatim}
   (13)
   [[[1.0, 1.0], [0.0, 1.0]], [[0.0, 1.0], [0.0, 0.0]],
    [[0.0, 0.0], [1.0, 0.0]], [[1.0, 0.0], [1.0, 1.0]],
    [[1.0, 0.5], [0.5, 0.0]], [[0.5, 0.0], [0.0, 0.5]],
    [[0.0, 0.5], [0.5, 1.0]], [[0.5, 1.0], [1.0, 0.5]],
    [[0.25, 0.25], [0.25, 0.75]],
    [[0.25, 0.75], [0.75, 0.75]],
    [[0.75, 0.75], [0.75, 0.25]],
    [[0.75, 0.25], [0.25, 0.25]]]
                   Type: List(List(Point(DoubleFloat)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty13}
\begin{paste}{ugGraphTwoDbuildPageEmpty13}{ugGraphTwoDbuildPagePatch13}
\pastebutton{ugGraphTwoDbuildPageEmpty13}{\showpaste}
\tab{5}\spadcommand{llp := [[p1,p2], [p2,p3], [p3,p4], [p4,p1], [p5,p6], [p6,p7], [p7,p8], [p8,p5], [p9,p10], [p10,p11], [p11,p12], [p12,p9]]\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }\bound{llp }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch14}
\begin{paste}{ugGraphTwoDbuildPageFull14}{ugGraphTwoDbuildPageEmpty14}
\pastebutton{ugGraphTwoDbuildPageFull14}{\hidepaste}
\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }}
\indentrel{3}\begin{verbatim}
   (14)  6
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty14}
\begin{paste}{ugGraphTwoDbuildPageEmpty14}{ugGraphTwoDbuildPagePatch14}
\pastebutton{ugGraphTwoDbuildPageEmpty14}{\showpaste}
\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch15}
\begin{paste}{ugGraphTwoDbuildPageFull15}{ugGraphTwoDbuildPageEmpty15}
\pastebutton{ugGraphTwoDbuildPageFull15}{\hidepaste}
\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }}
\indentrel{3}\begin{verbatim}
   (15)  8
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty15}
\begin{paste}{ugGraphTwoDbuildPageEmpty15}{ugGraphTwoDbuildPagePatch15}
\pastebutton{ugGraphTwoDbuildPageEmpty15}{\showpaste}
\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch16}
\begin{paste}{ugGraphTwoDbuildPageFull16}{ugGraphTwoDbuildPageEmpty16}
\pastebutton{ugGraphTwoDbuildPageFull16}{\hidepaste}
\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }}
\indentrel{3}\begin{verbatim}
   (16)  10
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty16}
\begin{paste}{ugGraphTwoDbuildPageEmpty16}{ugGraphTwoDbuildPagePatch16}
\pastebutton{ugGraphTwoDbuildPageEmpty16}{\showpaste}
\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch17}
\begin{paste}{ugGraphTwoDbuildPageFull17}{ugGraphTwoDbuildPageEmpty17}
\pastebutton{ugGraphTwoDbuildPageFull17}{\hidepaste}
\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }}
\indentrel{3}\begin{verbatim}
   (17)  [6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10]
                            Type: List(PositiveInteger)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty17}
\begin{paste}{ugGraphTwoDbuildPageEmpty17}{ugGraphTwoDbuildPagePatch17}
\pastebutton{ugGraphTwoDbuildPageEmpty17}{\showpaste}
\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch18}
\begin{paste}{ugGraphTwoDbuildPageFull18}{ugGraphTwoDbuildPageEmpty18}
\pastebutton{ugGraphTwoDbuildPageFull18}{\hidepaste}
\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }}
\indentrel{3}\begin{verbatim}
   (18)  [Hue: 1  Weight: 1.0] from the Pastel palette
                                          Type: Palette
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty18}
\begin{paste}{ugGraphTwoDbuildPageEmpty18}{ugGraphTwoDbuildPagePatch18}
\pastebutton{ugGraphTwoDbuildPageEmpty18}{\showpaste}
\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch19}
\begin{paste}{ugGraphTwoDbuildPageFull19}{ugGraphTwoDbuildPageEmpty19}
\pastebutton{ugGraphTwoDbuildPageFull19}{\hidepaste}
\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }}
\indentrel{3}\begin{verbatim}
   (19)  [Hue: 14  Weight: 1.0] from the Dim palette
                                          Type: Palette
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty19}
\begin{paste}{ugGraphTwoDbuildPageEmpty19}{ugGraphTwoDbuildPagePatch19}
\pastebutton{ugGraphTwoDbuildPageEmpty19}{\showpaste}
\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch20}
\begin{paste}{ugGraphTwoDbuildPageFull20}{ugGraphTwoDbuildPageEmpty20}
\pastebutton{ugGraphTwoDbuildPageFull20}{\hidepaste}
\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }}
\indentrel{3}\begin{verbatim}
   (20)  [Hue: 11  Weight: 1.0] from the Pastel palette
                                          Type: Palette
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty20}
\begin{paste}{ugGraphTwoDbuildPageEmpty20}{ugGraphTwoDbuildPagePatch20}
\pastebutton{ugGraphTwoDbuildPageEmpty20}{\showpaste}
\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch21}
\begin{paste}{ugGraphTwoDbuildPageFull21}{ugGraphTwoDbuildPageEmpty21}
\pastebutton{ugGraphTwoDbuildPageFull21}{\hidepaste}
\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\free{pc1 pc2 pc3 }\bound{lpc }}
\indentrel{3}\begin{verbatim}
   (21)
   [[Hue: 1  Weight: 1.0] from the Pastel palette,
    [Hue: 1  Weight: 1.0] from the Pastel palette,
    [Hue: 1  Weight: 1.0] from the Pastel palette,
    [Hue: 1  Weight: 1.0] from the Pastel palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 11  Weight: 1.0] from the Pastel palette,
    [Hue: 11  Weight: 1.0] from the Pastel palette,
    [Hue: 11  Weight: 1.0] from the Pastel palette,
    [Hue: 11  Weight: 1.0] from the Pastel palette]
                                    Type: List(Palette)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty21}
\begin{paste}{ugGraphTwoDbuildPageEmpty21}{ugGraphTwoDbuildPagePatch21}
\pastebutton{ugGraphTwoDbuildPageEmpty21}{\showpaste}
\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\free{pc1 pc2 pc3 }\bound{lpc }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch22}
\begin{paste}{ugGraphTwoDbuildPageFull22}{ugGraphTwoDbuildPageEmpty22}
\pastebutton{ugGraphTwoDbuildPageFull22}{\hidepaste}
\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }}
\indentrel{3}\begin{verbatim}
   (22)
   [[Hue: 22  Weight: 1.0] from the Pastel palette,
    [Hue: 11  Weight: 1.0] from the Light palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 1  Weight: 1.0] from the Bright palette,
    [Hue: 14  Weight: 1.0] from the Light palette,
    [Hue: 11  Weight: 1.0] from the Dim palette,
    [Hue: 22  Weight: 1.0] from the Bright palette,
    [Hue: 1  Weight: 1.0] from the Dark palette,
    [Hue: 1  Weight: 1.0] from the Pastel palette,
    [Hue: 22  Weight: 1.0] from the Light palette,
    [Hue: 14  Weight: 1.0] from the Dim palette,
    [Hue: 11  Weight: 1.0] from the Light palette]
                                    Type: List(Palette)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty22}
\begin{paste}{ugGraphTwoDbuildPageEmpty22}{ugGraphTwoDbuildPagePatch22}
\pastebutton{ugGraphTwoDbuildPageEmpty22}{\showpaste}
\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch23}
\begin{paste}{ugGraphTwoDbuildPageFull23}{ugGraphTwoDbuildPageEmpty23}
\pastebutton{ugGraphTwoDbuildPageFull23}{\hidepaste}
\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }}
\indentrel{3}\begin{verbatim}
   (23)  Graph with 12 point lists
                                       Type: GraphImage
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty23}
\begin{paste}{ugGraphTwoDbuildPageEmpty23}{ugGraphTwoDbuildPagePatch23}
\pastebutton{ugGraphTwoDbuildPageEmpty23}{\showpaste}
\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch24}
\begin{paste}{ugGraphTwoDbuildPageFull24}{ugGraphTwoDbuildPageEmpty24}
\pastebutton{ugGraphTwoDbuildPageFull24}{\hidepaste}
\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDbuildPage24.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDbuildPage24}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty24}
\begin{paste}{ugGraphTwoDbuildPageEmpty24}{ugGraphTwoDbuildPagePatch24}
\pastebutton{ugGraphTwoDbuildPageEmpty24}{\showpaste}
\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch25}
\begin{paste}{ugGraphTwoDbuildPageFull25}{ugGraphTwoDbuildPageEmpty25}
\pastebutton{ugGraphTwoDbuildPageFull25}{\hidepaste}
\tab{5}\spadcommand{)clear all\bound{clearAll }}
\indentrel{3}\begin{verbatim}
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty25}
\begin{paste}{ugGraphTwoDbuildPageEmpty25}{ugGraphTwoDbuildPagePatch25}
\pastebutton{ugGraphTwoDbuildPageEmpty25}{\showpaste}
\tab{5}\spadcommand{)clear all\bound{clearAll }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch26}
\begin{paste}{ugGraphTwoDbuildPageFull26}{ugGraphTwoDbuildPageEmpty26}
\pastebutton{ugGraphTwoDbuildPageFull26}{\hidepaste}
\tab{5}\spadcommand{g := graphImage()$GRIMAGE\bound{Sg }\free{clearAll }}
\indentrel{3}\begin{verbatim}
   (1)  Graph with 0 point lists
                                       Type: GraphImage
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty26}
\begin{paste}{ugGraphTwoDbuildPageEmpty26}{ugGraphTwoDbuildPagePatch26}
\pastebutton{ugGraphTwoDbuildPageEmpty26}{\showpaste}
\tab{5}\spadcommand{g := graphImage()$GRIMAGE\bound{Sg }\free{clearAll }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch27}
\begin{paste}{ugGraphTwoDbuildPageFull27}{ugGraphTwoDbuildPageEmpty27}
\pastebutton{ugGraphTwoDbuildPageFull27}{\hidepaste}
\tab{5}\spadcommand{p1 := point [0,0]$(Point DFLOAT)\bound{Sp1 }}
\indentrel{3}\begin{verbatim}
   (2)  [0.0, 0.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty27}
\begin{paste}{ugGraphTwoDbuildPageEmpty27}{ugGraphTwoDbuildPagePatch27}
\pastebutton{ugGraphTwoDbuildPageEmpty27}{\showpaste}
\tab{5}\spadcommand{p1 := point [0,0]$(Point DFLOAT)\bound{Sp1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch28}
\begin{paste}{ugGraphTwoDbuildPageFull28}{ugGraphTwoDbuildPageEmpty28}
\pastebutton{ugGraphTwoDbuildPageFull28}{\hidepaste}
\tab{5}\spadcommand{p2 := point [.25,.25]$(Point DFLOAT)\bound{Sp2 }}
\indentrel{3}\begin{verbatim}
   (3)  [0.25, 0.25]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty28}
\begin{paste}{ugGraphTwoDbuildPageEmpty28}{ugGraphTwoDbuildPagePatch28}
\pastebutton{ugGraphTwoDbuildPageEmpty28}{\showpaste}
\tab{5}\spadcommand{p2 := point [.25,.25]$(Point DFLOAT)\bound{Sp2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch29}
\begin{paste}{ugGraphTwoDbuildPageFull29}{ugGraphTwoDbuildPageEmpty29}
\pastebutton{ugGraphTwoDbuildPageFull29}{\hidepaste}
\tab{5}\spadcommand{p3 := point [.5,.5]$(Point DFLOAT)\bound{Sp3 }}
\indentrel{3}\begin{verbatim}
   (4)  [0.5, 0.5]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty29}
\begin{paste}{ugGraphTwoDbuildPageEmpty29}{ugGraphTwoDbuildPagePatch29}
\pastebutton{ugGraphTwoDbuildPageEmpty29}{\showpaste}
\tab{5}\spadcommand{p3 := point [.5,.5]$(Point DFLOAT)\bound{Sp3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch30}
\begin{paste}{ugGraphTwoDbuildPageFull30}{ugGraphTwoDbuildPageEmpty30}
\pastebutton{ugGraphTwoDbuildPageFull30}{\hidepaste}
\tab{5}\spadcommand{p4 := point [.75,.75]$(Point DFLOAT)\bound{Sp4 }}
\indentrel{3}\begin{verbatim}
   (5)  [0.75, 0.75]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty30}
\begin{paste}{ugGraphTwoDbuildPageEmpty30}{ugGraphTwoDbuildPagePatch30}
\pastebutton{ugGraphTwoDbuildPageEmpty30}{\showpaste}
\tab{5}\spadcommand{p4 := point [.75,.75]$(Point DFLOAT)\bound{Sp4 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch31}
\begin{paste}{ugGraphTwoDbuildPageFull31}{ugGraphTwoDbuildPageEmpty31}
\pastebutton{ugGraphTwoDbuildPageFull31}{\hidepaste}
\tab{5}\spadcommand{p5 := point [1,1]$(Point DFLOAT)\bound{Sp5 }}
\indentrel{3}\begin{verbatim}
   (6)  [1.0, 1.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty31}
\begin{paste}{ugGraphTwoDbuildPageEmpty31}{ugGraphTwoDbuildPagePatch31}
\pastebutton{ugGraphTwoDbuildPageEmpty31}{\showpaste}
\tab{5}\spadcommand{p5 := point [1,1]$(Point DFLOAT)\bound{Sp5 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch32}
\begin{paste}{ugGraphTwoDbuildPageFull32}{ugGraphTwoDbuildPageEmpty32}
\pastebutton{ugGraphTwoDbuildPageFull32}{\hidepaste}
\tab{5}\spadcommand{component(g,p1)$GRIMAGE\free{Sg Sp1 }\bound{gp1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty32}
\begin{paste}{ugGraphTwoDbuildPageEmpty32}{ugGraphTwoDbuildPagePatch32}
\pastebutton{ugGraphTwoDbuildPageEmpty32}{\showpaste}
\tab{5}\spadcommand{component(g,p1)$GRIMAGE\free{Sg Sp1 }\bound{gp1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch33}
\begin{paste}{ugGraphTwoDbuildPageFull33}{ugGraphTwoDbuildPageEmpty33}
\pastebutton{ugGraphTwoDbuildPageFull33}{\hidepaste}
\tab{5}\spadcommand{component(g,p2)$GRIMAGE\free{Sg Sp2 }\bound{gp2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty33}
\begin{paste}{ugGraphTwoDbuildPageEmpty33}{ugGraphTwoDbuildPagePatch33}
\pastebutton{ugGraphTwoDbuildPageEmpty33}{\showpaste}
\tab{5}\spadcommand{component(g,p2)$GRIMAGE\free{Sg Sp2 }\bound{gp2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch34}
\begin{paste}{ugGraphTwoDbuildPageFull34}{ugGraphTwoDbuildPageEmpty34}
\pastebutton{ugGraphTwoDbuildPageFull34}{\hidepaste}
\tab{5}\spadcommand{appendPoint(g,p3)$GRIMAGE\free{gp1 gp2 Sp3 }\bound{gp3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty34}
\begin{paste}{ugGraphTwoDbuildPageEmpty34}{ugGraphTwoDbuildPagePatch34}
\pastebutton{ugGraphTwoDbuildPageEmpty34}{\showpaste}
\tab{5}\spadcommand{appendPoint(g,p3)$GRIMAGE\free{gp1 gp2 Sp3 }\bound{gp3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch35}
\begin{paste}{ugGraphTwoDbuildPageFull35}{ugGraphTwoDbuildPageEmpty35}
\pastebutton{ugGraphTwoDbuildPageFull35}{\hidepaste}
\tab{5}\spadcommand{appendPoint(g,p4)$GRIMAGE\free{gp3 Sp4 }\bound{gp4 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty35}
\begin{paste}{ugGraphTwoDbuildPageEmpty35}{ugGraphTwoDbuildPagePatch35}
\pastebutton{ugGraphTwoDbuildPageEmpty35}{\showpaste}
\tab{5}\spadcommand{appendPoint(g,p4)$GRIMAGE\free{gp3 Sp4 }\bound{gp4 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch36}
\begin{paste}{ugGraphTwoDbuildPageFull36}{ugGraphTwoDbuildPageEmpty36}
\pastebutton{ugGraphTwoDbuildPageFull36}{\hidepaste}
\tab{5}\spadcommand{appendPoint(g,p5)$GRIMAGE\free{gp4 Sp5 }\bound{gp5 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty36}
\begin{paste}{ugGraphTwoDbuildPageEmpty36}{ugGraphTwoDbuildPagePatch36}
\pastebutton{ugGraphTwoDbuildPageEmpty36}{\showpaste}
\tab{5}\spadcommand{appendPoint(g,p5)$GRIMAGE\free{gp4 Sp5 }\bound{gp5 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch37}
\begin{paste}{ugGraphTwoDbuildPageFull37}{ugGraphTwoDbuildPageEmpty37}
\pastebutton{ugGraphTwoDbuildPageFull37}{\hidepaste}
\tab{5}\spadgraph{makeViewport2D(g,[title("Graph Points")])$VIEW2D\free{Sg gp5 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDbuildPage37.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDbuildPage37}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty37}
\begin{paste}{ugGraphTwoDbuildPageEmpty37}{ugGraphTwoDbuildPagePatch37}
\pastebutton{ugGraphTwoDbuildPageEmpty37}{\showpaste}
\tab{5}\spadgraph{makeViewport2D(g,[title("Graph Points")])$VIEW2D\free{Sg gp5 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch38}
\begin{paste}{ugGraphTwoDbuildPageFull38}{ugGraphTwoDbuildPageEmpty38}
\pastebutton{ugGraphTwoDbuildPageFull38}{\hidepaste}
\tab{5}\spadcommand{g2 := coerce([[p1],[p2],[p3],[p4],[p5]])$GRIMAGE\free{Sp1 Sp2 Sp3 Sp4 Sp5 }\bound{Sg2 }}
\indentrel{3}\begin{verbatim}
   (13)  Graph with 5 point lists
                                       Type: GraphImage
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty38}
\begin{paste}{ugGraphTwoDbuildPageEmpty38}{ugGraphTwoDbuildPagePatch38}
\pastebutton{ugGraphTwoDbuildPageEmpty38}{\showpaste}
\tab{5}\spadcommand{g2 := coerce([[p1],[p2],[p3],[p4],[p5]])$GRIMAGE\free{Sp1 Sp2 Sp3 Sp4 Sp5 }\bound{Sg2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch39}
\begin{paste}{ugGraphTwoDbuildPageFull39}{ugGraphTwoDbuildPageEmpty39}
\pastebutton{ugGraphTwoDbuildPageFull39}{\hidepaste}
\tab{5}\spadcommand{v := viewport2D()$VIEW2D\bound{Sv }}
\indentrel{3}\begin{verbatim}
   (14)
   Closed or Undefined TwoDimensionalViewport: "FriCAS2D"
                           Type: TwoDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty39}
\begin{paste}{ugGraphTwoDbuildPageEmpty39}{ugGraphTwoDbuildPagePatch39}
\pastebutton{ugGraphTwoDbuildPageEmpty39}{\showpaste}
\tab{5}\spadcommand{v := viewport2D()$VIEW2D\bound{Sv }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch40}
\begin{paste}{ugGraphTwoDbuildPageFull40}{ugGraphTwoDbuildPageEmpty40}
\pastebutton{ugGraphTwoDbuildPageFull40}{\hidepaste}
\tab{5}\spadcommand{options(v,[title("Just Points")])$VIEW2D\free{Sv }\bound{Svo }}
\indentrel{3}\begin{verbatim}
   (15)
   Closed or Undefined TwoDimensionalViewport: "FriCAS2D"
                           Type: TwoDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty40}
\begin{paste}{ugGraphTwoDbuildPageEmpty40}{ugGraphTwoDbuildPagePatch40}
\pastebutton{ugGraphTwoDbuildPageEmpty40}{\showpaste}
\tab{5}\spadcommand{options(v,[title("Just Points")])$VIEW2D\free{Sv }\bound{Svo }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch41}
\begin{paste}{ugGraphTwoDbuildPageFull41}{ugGraphTwoDbuildPageEmpty41}
\pastebutton{ugGraphTwoDbuildPageFull41}{\hidepaste}
\tab{5}\spadcommand{putGraph(v,g2,1)$VIEW2D\free{Sg2 Svo }\bound{Svog2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty41}
\begin{paste}{ugGraphTwoDbuildPageEmpty41}{ugGraphTwoDbuildPagePatch41}
\pastebutton{ugGraphTwoDbuildPageEmpty41}{\showpaste}
\tab{5}\spadcommand{putGraph(v,g2,1)$VIEW2D\free{Sg2 Svo }\bound{Svog2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPagePatch42}
\begin{paste}{ugGraphTwoDbuildPageFull42}{ugGraphTwoDbuildPageEmpty42}
\pastebutton{ugGraphTwoDbuildPageFull42}{\hidepaste}
\tab{5}\spadgraph{makeViewport2D(v)$VIEW2D\free{Svog2 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDbuildPage42.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDbuildPage42}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDbuildPageEmpty42}
\begin{paste}{ugGraphTwoDbuildPageEmpty42}{ugGraphTwoDbuildPagePatch42}
\pastebutton{ugGraphTwoDbuildPageEmpty42}{\showpaste}
\tab{5}\spadgraph{makeViewport2D(v)$VIEW2D\free{Svog2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPagePatch1}
\begin{paste}{ugGraphThreeDParmPageFull1}{ugGraphThreeDParmPageEmpty1}
\pastebutton{ugGraphThreeDParmPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(curve(5*cos(t), 5*sin(t),t), t=-12..12)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDParmPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDParmPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPageEmpty1}
\begin{paste}{ugGraphThreeDParmPageEmpty1}{ugGraphThreeDParmPagePatch1}
\pastebutton{ugGraphThreeDParmPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(curve(5*cos(t), 5*sin(t),t), t=-12..12)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPagePatch2}
\begin{paste}{ugGraphThreeDParmPageFull2}{ugGraphThreeDParmPageEmpty2}
\pastebutton{ugGraphThreeDParmPageFull2}{\hidepaste}
\tab{5}\spadcommand{i1(t:DFLOAT):DFLOAT == sin(t)*cos(3*t/5)\bound{i1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPageEmpty2}
\begin{paste}{ugGraphThreeDParmPageEmpty2}{ugGraphThreeDParmPagePatch2}
\pastebutton{ugGraphThreeDParmPageEmpty2}{\showpaste}
\tab{5}\spadcommand{i1(t:DFLOAT):DFLOAT == sin(t)*cos(3*t/5)\bound{i1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPagePatch3}
\begin{paste}{ugGraphThreeDParmPageFull3}{ugGraphThreeDParmPageEmpty3}
\pastebutton{ugGraphThreeDParmPageFull3}{\hidepaste}
\tab{5}\spadcommand{i2(t:DFLOAT):DFLOAT == cos(t)*cos(3*t/5)\bound{i2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPageEmpty3}
\begin{paste}{ugGraphThreeDParmPageEmpty3}{ugGraphThreeDParmPagePatch3}
\pastebutton{ugGraphThreeDParmPageEmpty3}{\showpaste}
\tab{5}\spadcommand{i2(t:DFLOAT):DFLOAT == cos(t)*cos(3*t/5)\bound{i2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPagePatch4}
\begin{paste}{ugGraphThreeDParmPageFull4}{ugGraphThreeDParmPageEmpty4}
\pastebutton{ugGraphThreeDParmPageFull4}{\hidepaste}
\tab{5}\spadcommand{i3(t:DFLOAT):DFLOAT == cos(t)*sin(3*t/5)\bound{i3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPageEmpty4}
\begin{paste}{ugGraphThreeDParmPageEmpty4}{ugGraphThreeDParmPagePatch4}
\pastebutton{ugGraphThreeDParmPageEmpty4}{\showpaste}
\tab{5}\spadcommand{i3(t:DFLOAT):DFLOAT == cos(t)*sin(3*t/5)\bound{i3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPagePatch5}
\begin{paste}{ugGraphThreeDParmPageFull5}{ugGraphThreeDParmPageEmpty5}
\pastebutton{ugGraphThreeDParmPageFull5}{\hidepaste}
\tab{5}\spadgraph{draw(curve(i1,i2,i3),0..15*\%pi)\free{i1 i2 i3 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDParmPage5.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDParmPage5}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParmPageEmpty5}
\begin{paste}{ugGraphThreeDParmPageEmpty5}{ugGraphThreeDParmPagePatch5}
\pastebutton{ugGraphThreeDParmPageEmpty5}{\showpaste}
\tab{5}\spadgraph{draw(curve(i1,i2,i3),0..15*\%pi)\free{i1 i2 i3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPagePatch1}
\begin{paste}{ugGraphMakeObjectPageFull1}{ugGraphMakeObjectPageEmpty1}
\pastebutton{ugGraphMakeObjectPageFull1}{\hidepaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPageEmpty1}
\begin{paste}{ugGraphMakeObjectPageEmpty1}{ugGraphMakeObjectPagePatch1}
\pastebutton{ugGraphMakeObjectPageEmpty1}{\showpaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPagePatch2}
\begin{paste}{ugGraphMakeObjectPageFull2}{ugGraphMakeObjectPageEmpty2}
\pastebutton{ugGraphMakeObjectPageFull2}{\hidepaste}
\tab{5}\spadcommand{sph := makeObject(m, 0..\%pi, 0..2*\%pi, coordinates==spherical)\bound{sph }\free{m }}
\indentrel{3}\begin{verbatim}
   (2)  3-Space with 1 component
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPageEmpty2}
\begin{paste}{ugGraphMakeObjectPageEmpty2}{ugGraphMakeObjectPagePatch2}
\pastebutton{ugGraphMakeObjectPageEmpty2}{\showpaste}
\tab{5}\spadcommand{sph := makeObject(m, 0..\%pi, 0..2*\%pi, coordinates==spherical)\bound{sph }\free{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPagePatch3}
\begin{paste}{ugGraphMakeObjectPageFull3}{ugGraphMakeObjectPageEmpty3}
\pastebutton{ugGraphMakeObjectPageFull3}{\hidepaste}
\tab{5}\spadcommand{makeObject(curve(1.5*sin(t), 1.5*cos(t), 0), t=0..2*\%pi, space == sph, tubeRadius == .25)\free{sph }\bound{v1 }}
\indentrel{3}\begin{verbatim}
   (3)  3-Space with 2 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPageEmpty3}
\begin{paste}{ugGraphMakeObjectPageEmpty3}{ugGraphMakeObjectPagePatch3}
\pastebutton{ugGraphMakeObjectPageEmpty3}{\showpaste}
\tab{5}\spadcommand{makeObject(curve(1.5*sin(t), 1.5*cos(t), 0), t=0..2*\%pi, space == sph, tubeRadius == .25)\free{sph }\bound{v1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPagePatch4}
\begin{paste}{ugGraphMakeObjectPageFull4}{ugGraphMakeObjectPageEmpty4}
\pastebutton{ugGraphMakeObjectPageFull4}{\hidepaste}
\tab{5}\spadgraph{makeViewport3D(sph,"Multiple Objects")\free{v1 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphMakeObjectPage4.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphMakeObjectPage4}}
\end{paste}\end{patch}

\begin{patch}{ugGraphMakeObjectPageEmpty4}
\begin{paste}{ugGraphMakeObjectPageEmpty4}{ugGraphMakeObjectPagePatch4}
\pastebutton{ugGraphMakeObjectPageEmpty4}{\showpaste}
\tab{5}\spadgraph{makeViewport3D(sph,"Multiple Objects")\free{v1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPagePatch1}
\begin{paste}{ugGraphThreeDPlotPageFull1}{ugGraphThreeDPlotPageEmpty1}
\pastebutton{ugGraphThreeDPlotPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDPlotPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDPlotPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPageEmpty1}
\begin{paste}{ugGraphThreeDPlotPageEmpty1}{ugGraphThreeDPlotPagePatch1}
\pastebutton{ugGraphThreeDPlotPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPagePatch2}
\begin{paste}{ugGraphThreeDPlotPageFull2}{ugGraphThreeDPlotPageEmpty2}
\pastebutton{ugGraphThreeDPlotPageFull2}{\hidepaste}
\tab{5}\spadcommand{f(x,y) == sin(x)*cos(y)\bound{f }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPageEmpty2}
\begin{paste}{ugGraphThreeDPlotPageEmpty2}{ugGraphThreeDPlotPagePatch2}
\pastebutton{ugGraphThreeDPlotPageEmpty2}{\showpaste}
\tab{5}\spadcommand{f(x,y) == sin(x)*cos(y)\bound{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPagePatch3}
\begin{paste}{ugGraphThreeDPlotPageFull3}{ugGraphThreeDPlotPageEmpty3}
\pastebutton{ugGraphThreeDPlotPageFull3}{\hidepaste}
\tab{5}\spadgraph{draw(f,-\%pi..\%pi,-\%pi..\%pi)\free{f }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDPlotPage3.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDPlotPage3}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDPlotPageEmpty3}
\begin{paste}{ugGraphThreeDPlotPageEmpty3}{ugGraphThreeDPlotPagePatch3}
\pastebutton{ugGraphThreeDPlotPageEmpty3}{\showpaste}
\tab{5}\spadgraph{draw(f,-\%pi..\%pi,-\%pi..\%pi)\free{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch1}
\begin{paste}{ugGraphTwoDappendPageFull1}{ugGraphTwoDappendPageEmpty1}
\pastebutton{ugGraphTwoDappendPageFull1}{\hidepaste}
\tab{5}\spadcommand{v1 := draw(sin(x),x=0..2*\%pi)\bound{v1 }}
\indentrel{3}\begin{verbatim}
   (1)  TwoDimensionalViewport: "sin(x)"
                           Type: TwoDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty1}
\begin{paste}{ugGraphTwoDappendPageEmpty1}{ugGraphTwoDappendPagePatch1}
\pastebutton{ugGraphTwoDappendPageEmpty1}{\showpaste}
\tab{5}\spadcommand{v1 := draw(sin(x),x=0..2*\%pi)\bound{v1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch2}
\begin{paste}{ugGraphTwoDappendPageFull2}{ugGraphTwoDappendPageEmpty2}
\pastebutton{ugGraphTwoDappendPageFull2}{\hidepaste}
\tab{5}\spadcommand{v2 := draw(cos(x),x=0..2*\%pi, curveColor==light red())\bound{v2 }}
\indentrel{3}\begin{verbatim}
   (2)  TwoDimensionalViewport: "cos(x)"
                           Type: TwoDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty2}
\begin{paste}{ugGraphTwoDappendPageEmpty2}{ugGraphTwoDappendPagePatch2}
\pastebutton{ugGraphTwoDappendPageEmpty2}{\showpaste}
\tab{5}\spadcommand{v2 := draw(cos(x),x=0..2*\%pi, curveColor==light red())\bound{v2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch3}
\begin{paste}{ugGraphTwoDappendPageFull3}{ugGraphTwoDappendPageEmpty3}
\pastebutton{ugGraphTwoDappendPageFull3}{\hidepaste}
\tab{5}\spadcommand{g1 := getGraph(v1,1)\bound{g1 }\free{v1 }}
\indentrel{3}\begin{verbatim}
   (3)  Graph with 1 point list
                                       Type: GraphImage
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty3}
\begin{paste}{ugGraphTwoDappendPageEmpty3}{ugGraphTwoDappendPagePatch3}
\pastebutton{ugGraphTwoDappendPageEmpty3}{\showpaste}
\tab{5}\spadcommand{g1 := getGraph(v1,1)\bound{g1 }\free{v1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch4}
\begin{paste}{ugGraphTwoDappendPageFull4}{ugGraphTwoDappendPageEmpty4}
\pastebutton{ugGraphTwoDappendPageFull4}{\hidepaste}
\tab{5}\spadcommand{putGraph(v2,g1,2)\bound{v22 }\free{g1 v2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty4}
\begin{paste}{ugGraphTwoDappendPageEmpty4}{ugGraphTwoDappendPagePatch4}
\pastebutton{ugGraphTwoDappendPageEmpty4}{\showpaste}
\tab{5}\spadcommand{putGraph(v2,g1,2)\bound{v22 }\free{g1 v2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch5}
\begin{paste}{ugGraphTwoDappendPageFull5}{ugGraphTwoDappendPageEmpty5}
\pastebutton{ugGraphTwoDappendPageFull5}{\hidepaste}
\tab{5}\spadgraph{makeViewport2D(v2)\free{v22 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDappendPage5.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDappendPage5}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty5}
\begin{paste}{ugGraphTwoDappendPageEmpty5}{ugGraphTwoDappendPagePatch5}
\pastebutton{ugGraphTwoDappendPageEmpty5}{\showpaste}
\tab{5}\spadgraph{makeViewport2D(v2)\free{v22 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch6}
\begin{paste}{ugGraphTwoDappendPageFull6}{ugGraphTwoDappendPageEmpty6}
\pastebutton{ugGraphTwoDappendPageFull6}{\hidepaste}
\tab{5}\spadcommand{g3 := makeObject(sin(x),x=-1..\%pi,[])\bound{g3 }}
\indentrel{3}\begin{verbatim}
   (6)  Graph with 1 point list
                                       Type: GraphImage
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty6}
\begin{paste}{ugGraphTwoDappendPageEmpty6}{ugGraphTwoDappendPagePatch6}
\pastebutton{ugGraphTwoDappendPageEmpty6}{\showpaste}
\tab{5}\spadcommand{g3 := makeObject(sin(x),x=-1..\%pi,[])\bound{g3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch7}
\begin{paste}{ugGraphTwoDappendPageFull7}{ugGraphTwoDappendPageEmpty7}
\pastebutton{ugGraphTwoDappendPageFull7}{\hidepaste}
\tab{5}\spadcommand{v3 := draw(cos(x),x=-1..\%pi, curveColor==light red())\bound{v3 }}
\indentrel{3}\begin{verbatim}
   (7)  TwoDimensionalViewport: "cos(x)"
                           Type: TwoDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty7}
\begin{paste}{ugGraphTwoDappendPageEmpty7}{ugGraphTwoDappendPagePatch7}
\pastebutton{ugGraphTwoDappendPageEmpty7}{\showpaste}
\tab{5}\spadcommand{v3 := draw(cos(x),x=-1..\%pi, curveColor==light red())\bound{v3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch8}
\begin{paste}{ugGraphTwoDappendPageFull8}{ugGraphTwoDappendPageEmpty8}
\pastebutton{ugGraphTwoDappendPageFull8}{\hidepaste}
\tab{5}\spadcommand{putGraph(v3,g3,2)\bound{v33 }\free{g3 v3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty8}
\begin{paste}{ugGraphTwoDappendPageEmpty8}{ugGraphTwoDappendPagePatch8}
\pastebutton{ugGraphTwoDappendPageEmpty8}{\showpaste}
\tab{5}\spadcommand{putGraph(v3,g3,2)\bound{v33 }\free{g3 v3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch9}
\begin{paste}{ugGraphTwoDappendPageFull9}{ugGraphTwoDappendPageEmpty9}
\pastebutton{ugGraphTwoDappendPageFull9}{\hidepaste}
\tab{5}\spadgraph{makeViewport2D(v3)\free{v33 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDappendPage9.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDappendPage9}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty9}
\begin{paste}{ugGraphTwoDappendPageEmpty9}{ugGraphTwoDappendPagePatch9}
\pastebutton{ugGraphTwoDappendPageEmpty9}{\showpaste}
\tab{5}\spadgraph{makeViewport2D(v3)\free{v33 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPagePatch10}
\begin{paste}{ugGraphTwoDappendPageFull10}{ugGraphTwoDappendPageEmpty10}
\pastebutton{ugGraphTwoDappendPageFull10}{\hidepaste}
\tab{5}\spadcommand{close(v1); close(v2); close(v3)\free{v1 v2 v3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDappendPageEmpty10}
\begin{paste}{ugGraphTwoDappendPageEmpty10}{ugGraphTwoDappendPagePatch10}
\pastebutton{ugGraphTwoDappendPageEmpty10}{\showpaste}
\tab{5}\spadcommand{close(v1); close(v2); close(v3)\free{v1 v2 v3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch1}
\begin{paste}{ugGraphThreeDBuildPageFull1}{ugGraphThreeDBuildPageEmpty1}
\pastebutton{ugGraphThreeDBuildPageFull1}{\hidepaste}
\tab{5}\spadcommand{space := create3Space()$(ThreeSpace DFLOAT)\bound{space }}
\indentrel{3}\begin{verbatim}
   (1)  3-Space with 0 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty1}
\begin{paste}{ugGraphThreeDBuildPageEmpty1}{ugGraphThreeDBuildPagePatch1}
\pastebutton{ugGraphThreeDBuildPageEmpty1}{\showpaste}
\tab{5}\spadcommand{space := create3Space()$(ThreeSpace DFLOAT)\bound{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch2}
\begin{paste}{ugGraphThreeDBuildPageFull2}{ugGraphThreeDBuildPageEmpty2}
\pastebutton{ugGraphThreeDBuildPageFull2}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[0,30,20], [0,30,30], [0,40,30], [0,40,100], [0,30,100],[0,30,110], [0,60,110], [0,60,100], [0,50,100], [0,50,30], [0,60,30], [0,60,20]])\bound{curve1 }\free{space }}
\indentrel{3}\begin{verbatim}
   (2)  3-Space with 1 component
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty2}
\begin{paste}{ugGraphThreeDBuildPageEmpty2}{ugGraphThreeDBuildPagePatch2}
\pastebutton{ugGraphThreeDBuildPageEmpty2}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[0,30,20], [0,30,30], [0,40,30], [0,40,100], [0,30,100],[0,30,110], [0,60,110], [0,60,100], [0,50,100], [0,50,30], [0,60,30], [0,60,20]])\bound{curve1 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch3}
\begin{paste}{ugGraphThreeDBuildPageFull3}{ugGraphThreeDBuildPageEmpty3}
\pastebutton{ugGraphThreeDBuildPageFull3}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[80,0,30], [80,0,100], [70,0,110], [40,0,110], [30,0,100], [30,0,90], [40,0,90], [40,0,95], [45,0,100], [65,0,100], [70,0,95], [70,0,35]])\bound{curve2 }\free{space }}
\indentrel{3}\begin{verbatim}
   (3)  3-Space with 2 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty3}
\begin{paste}{ugGraphThreeDBuildPageEmpty3}{ugGraphThreeDBuildPagePatch3}
\pastebutton{ugGraphThreeDBuildPageEmpty3}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[80,0,30], [80,0,100], [70,0,110], [40,0,110], [30,0,100], [30,0,90], [40,0,90], [40,0,95], [45,0,100], [65,0,100], [70,0,95], [70,0,35]])\bound{curve2 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch4}
\begin{paste}{ugGraphThreeDBuildPageFull4}{ugGraphThreeDBuildPageEmpty4}
\pastebutton{ugGraphThreeDBuildPageFull4}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[70,0,35], [65,0,30], [45,0,30], [40,0,35], [40,0,60], [50,0,60], [50,0,70], [30,0,70], [30,0,30], [40,0,20], [70,0,20], [80,0,30]])\bound{curve3 }\free{space }}
\indentrel{3}\begin{verbatim}
   (4)  3-Space with 3 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty4}
\begin{paste}{ugGraphThreeDBuildPageEmpty4}{ugGraphThreeDBuildPagePatch4}
\pastebutton{ugGraphThreeDBuildPageEmpty4}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[70,0,35], [65,0,30], [45,0,30], [40,0,35], [40,0,60], [50,0,60], [50,0,70], [30,0,70], [30,0,30], [40,0,20], [70,0,20], [80,0,30]])\bound{curve3 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch5}
\begin{paste}{ugGraphThreeDBuildPageFull5}{ugGraphThreeDBuildPageEmpty5}
\pastebutton{ugGraphThreeDBuildPageFull5}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[0,70,20], [0,70,110], [0,110,110], [0,120,100], [0,120,70], [0,115,65], [0,120,60], [0,120,30], [0,110,20], [0,80,20], [0,80,30], [0,80,20]])\bound{curve4 }\free{space }}
\indentrel{3}\begin{verbatim}
   (5)  3-Space with 4 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty5}
\begin{paste}{ugGraphThreeDBuildPageEmpty5}{ugGraphThreeDBuildPagePatch5}
\pastebutton{ugGraphThreeDBuildPageEmpty5}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[0,70,20], [0,70,110], [0,110,110], [0,120,100], [0,120,70], [0,115,65], [0,120,60], [0,120,30], [0,110,20], [0,80,20], [0,80,30], [0,80,20]])\bound{curve4 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch6}
\begin{paste}{ugGraphThreeDBuildPageFull6}{ugGraphThreeDBuildPageEmpty6}
\pastebutton{ugGraphThreeDBuildPageFull6}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[0,105,30], [0,110,35], [0,110,55], [0,105,60], [0,80,60], [0,80,70], [0,105,70], [0,110,75], [0,110,95], [0,105,100], [0,80,100], [0,80,20], [0,80,30]])\bound{curve5 }\free{space }}
\indentrel{3}\begin{verbatim}
   (6)  3-Space with 5 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty6}
\begin{paste}{ugGraphThreeDBuildPageEmpty6}{ugGraphThreeDBuildPagePatch6}
\pastebutton{ugGraphThreeDBuildPageEmpty6}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[0,105,30], [0,110,35], [0,110,55], [0,105,60], [0,80,60], [0,80,70], [0,105,70], [0,110,75], [0,110,95], [0,105,100], [0,80,100], [0,80,20], [0,80,30]])\bound{curve5 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch7}
\begin{paste}{ugGraphThreeDBuildPageFull7}{ugGraphThreeDBuildPageEmpty7}
\pastebutton{ugGraphThreeDBuildPageFull7}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[140,0,20], [140,0,110], [130,0,110], [90,0,20], [101,0,20],[114,0,50], [130,0,50], [130,0,60], [119,0,60], [130,0,85], [130,0,20]])\bound{curve6 }\free{space }}
\indentrel{3}\begin{verbatim}
   (7)  3-Space with 6 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty7}
\begin{paste}{ugGraphThreeDBuildPageEmpty7}{ugGraphThreeDBuildPagePatch7}
\pastebutton{ugGraphThreeDBuildPageEmpty7}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[140,0,20], [140,0,110], [130,0,110], [90,0,20], [101,0,20],[114,0,50], [130,0,50], [130,0,60], [119,0,60], [130,0,85], [130,0,20]])\bound{curve6 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch8}
\begin{paste}{ugGraphThreeDBuildPageFull8}{ugGraphThreeDBuildPageEmpty8}
\pastebutton{ugGraphThreeDBuildPageFull8}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[0,140,20], [0,140,110], [0,150,110], [0,170,50], [0,190,110], [0,200,110], [0,200,20], [0,190,20], [0,190,75], [0,175,35], [0,165,35],[0,150,75], [0,150,20]])\bound{curve7 }\free{space }}
\indentrel{3}\begin{verbatim}
   (8)  3-Space with 7 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty8}
\begin{paste}{ugGraphThreeDBuildPageEmpty8}{ugGraphThreeDBuildPagePatch8}
\pastebutton{ugGraphThreeDBuildPageEmpty8}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[0,140,20], [0,140,110], [0,150,110], [0,170,50], [0,190,110], [0,200,110], [0,200,20], [0,190,20], [0,190,75], [0,175,35], [0,165,35],[0,150,75], [0,150,20]])\bound{curve7 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch9}
\begin{paste}{ugGraphThreeDBuildPageFull9}{ugGraphThreeDBuildPageEmpty9}
\pastebutton{ugGraphThreeDBuildPageFull9}{\hidepaste}
\tab{5}\spadcommand{closedCurve(space,[[200,0,20], [200,0,110], [189,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [161,0,20], [190,0,85], [190,0,20]])\bound{curve8 }\free{space }}
\indentrel{3}\begin{verbatim}
   (9)  3-Space with 8 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty9}
\begin{paste}{ugGraphThreeDBuildPageEmpty9}{ugGraphThreeDBuildPagePatch9}
\pastebutton{ugGraphThreeDBuildPageEmpty9}{\showpaste}
\tab{5}\spadcommand{closedCurve(space,[[200,0,20], [200,0,110], [189,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [161,0,20], [190,0,85], [190,0,20]])\bound{curve8 }\free{space }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch10}
\begin{paste}{ugGraphThreeDBuildPageFull10}{ugGraphThreeDBuildPageEmpty10}
\pastebutton{ugGraphThreeDBuildPageFull10}{\hidepaste}
\tab{5}\spadgraph{makeViewport3D(space, title == "Letters")\free{space curve1 curve2 curve3 curve4 curve5 curve6 curve7 curve8 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDBuildPage10.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDBuildPage10}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty10}
\begin{paste}{ugGraphThreeDBuildPageEmpty10}{ugGraphThreeDBuildPagePatch10}
\pastebutton{ugGraphThreeDBuildPageEmpty10}{\showpaste}
\tab{5}\spadgraph{makeViewport3D(space, title == "Letters")\free{space curve1 curve2 curve3 curve4 curve5 curve6 curve7 curve8 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch11}
\begin{paste}{ugGraphThreeDBuildPageFull11}{ugGraphThreeDBuildPageEmpty11}
\pastebutton{ugGraphThreeDBuildPageFull11}{\hidepaste}
\tab{5}\spadcommand{spaceC := create3Space()$(ThreeSpace DFLOAT)\bound{spaceC }}
\indentrel{3}\begin{verbatim}
   (11)  3-Space with 0 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty11}
\begin{paste}{ugGraphThreeDBuildPageEmpty11}{ugGraphThreeDBuildPagePatch11}
\pastebutton{ugGraphThreeDBuildPageEmpty11}{\showpaste}
\tab{5}\spadcommand{spaceC := create3Space()$(ThreeSpace DFLOAT)\bound{spaceC }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch12}
\begin{paste}{ugGraphThreeDBuildPageFull12}{ugGraphThreeDBuildPageEmpty12}
\pastebutton{ugGraphThreeDBuildPageFull12}{\hidepaste}
\tab{5}\spadcommand{x: DFLOAT := 1\bound{x }}
\indentrel{3}\begin{verbatim}
   (12)  1.0
                                      Type: DoubleFloat
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty12}
\begin{paste}{ugGraphThreeDBuildPageEmpty12}{ugGraphThreeDBuildPagePatch12}
\pastebutton{ugGraphThreeDBuildPageEmpty12}{\showpaste}
\tab{5}\spadcommand{x: DFLOAT := 1\bound{x }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch13}
\begin{paste}{ugGraphThreeDBuildPageFull13}{ugGraphThreeDBuildPageEmpty13}
\pastebutton{ugGraphThreeDBuildPageFull13}{\hidepaste}
\tab{5}\spadcommand{y: DFLOAT := -1\bound{y }}
\indentrel{3}\begin{verbatim}
   (13)  - 1.0
                                      Type: DoubleFloat
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty13}
\begin{paste}{ugGraphThreeDBuildPageEmpty13}{ugGraphThreeDBuildPagePatch13}
\pastebutton{ugGraphThreeDBuildPageEmpty13}{\showpaste}
\tab{5}\spadcommand{y: DFLOAT := -1\bound{y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch14}
\begin{paste}{ugGraphThreeDBuildPageFull14}{ugGraphThreeDBuildPageEmpty14}
\pastebutton{ugGraphThreeDBuildPageFull14}{\hidepaste}
\tab{5}\spadcommand{a := point [x,x,y,1::DFLOAT]$(Point DFLOAT)\bound{a }\free{x y }}
\indentrel{3}\begin{verbatim}
   (14)  [1.0, 1.0, - 1.0, 1.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty14}
\begin{paste}{ugGraphThreeDBuildPageEmpty14}{ugGraphThreeDBuildPagePatch14}
\pastebutton{ugGraphThreeDBuildPageEmpty14}{\showpaste}
\tab{5}\spadcommand{a := point [x,x,y,1::DFLOAT]$(Point DFLOAT)\bound{a }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch15}
\begin{paste}{ugGraphThreeDBuildPageFull15}{ugGraphThreeDBuildPageEmpty15}
\pastebutton{ugGraphThreeDBuildPageFull15}{\hidepaste}
\tab{5}\spadcommand{b := point [y,x,y,4::DFLOAT]$(Point DFLOAT)\bound{b }\free{x y }}
\indentrel{3}\begin{verbatim}
   (15)  [- 1.0, 1.0, - 1.0, 4.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty15}
\begin{paste}{ugGraphThreeDBuildPageEmpty15}{ugGraphThreeDBuildPagePatch15}
\pastebutton{ugGraphThreeDBuildPageEmpty15}{\showpaste}
\tab{5}\spadcommand{b := point [y,x,y,4::DFLOAT]$(Point DFLOAT)\bound{b }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch16}
\begin{paste}{ugGraphThreeDBuildPageFull16}{ugGraphThreeDBuildPageEmpty16}
\pastebutton{ugGraphThreeDBuildPageFull16}{\hidepaste}
\tab{5}\spadcommand{c := point [y,x,x,8::DFLOAT]$(Point DFLOAT)\bound{c }\free{x y }}
\indentrel{3}\begin{verbatim}
   (16)  [- 1.0, 1.0, 1.0, 8.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty16}
\begin{paste}{ugGraphThreeDBuildPageEmpty16}{ugGraphThreeDBuildPagePatch16}
\pastebutton{ugGraphThreeDBuildPageEmpty16}{\showpaste}
\tab{5}\spadcommand{c := point [y,x,x,8::DFLOAT]$(Point DFLOAT)\bound{c }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch17}
\begin{paste}{ugGraphThreeDBuildPageFull17}{ugGraphThreeDBuildPageEmpty17}
\pastebutton{ugGraphThreeDBuildPageFull17}{\hidepaste}
\tab{5}\spadcommand{d := point [x,x,x,12::DFLOAT]$(Point DFLOAT)\bound{d }\free{x y }}
\indentrel{3}\begin{verbatim}
   (17)  [1.0, 1.0, 1.0, 12.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty17}
\begin{paste}{ugGraphThreeDBuildPageEmpty17}{ugGraphThreeDBuildPagePatch17}
\pastebutton{ugGraphThreeDBuildPageEmpty17}{\showpaste}
\tab{5}\spadcommand{d := point [x,x,x,12::DFLOAT]$(Point DFLOAT)\bound{d }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch18}
\begin{paste}{ugGraphThreeDBuildPageFull18}{ugGraphThreeDBuildPageEmpty18}
\pastebutton{ugGraphThreeDBuildPageFull18}{\hidepaste}
\tab{5}\spadcommand{e := point [x,y,y,16::DFLOAT]$(Point DFLOAT)\bound{e }\free{x y }}
\indentrel{3}\begin{verbatim}
   (18)  [1.0, - 1.0, - 1.0, 16.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty18}
\begin{paste}{ugGraphThreeDBuildPageEmpty18}{ugGraphThreeDBuildPagePatch18}
\pastebutton{ugGraphThreeDBuildPageEmpty18}{\showpaste}
\tab{5}\spadcommand{e := point [x,y,y,16::DFLOAT]$(Point DFLOAT)\bound{e }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch19}
\begin{paste}{ugGraphThreeDBuildPageFull19}{ugGraphThreeDBuildPageEmpty19}
\pastebutton{ugGraphThreeDBuildPageFull19}{\hidepaste}
\tab{5}\spadcommand{f := point [y,y,y,20::DFLOAT]$(Point DFLOAT)\bound{f }\free{x y }}
\indentrel{3}\begin{verbatim}
   (19)  [- 1.0, - 1.0, - 1.0, 20.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty19}
\begin{paste}{ugGraphThreeDBuildPageEmpty19}{ugGraphThreeDBuildPagePatch19}
\pastebutton{ugGraphThreeDBuildPageEmpty19}{\showpaste}
\tab{5}\spadcommand{f := point [y,y,y,20::DFLOAT]$(Point DFLOAT)\bound{f }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch20}
\begin{paste}{ugGraphThreeDBuildPageFull20}{ugGraphThreeDBuildPageEmpty20}
\pastebutton{ugGraphThreeDBuildPageFull20}{\hidepaste}
\tab{5}\spadcommand{g := point [y,y,x,24::DFLOAT]$(Point DFLOAT)\bound{g }\free{x y }}
\indentrel{3}\begin{verbatim}
   (20)  [- 1.0, - 1.0, 1.0, 24.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty20}
\begin{paste}{ugGraphThreeDBuildPageEmpty20}{ugGraphThreeDBuildPagePatch20}
\pastebutton{ugGraphThreeDBuildPageEmpty20}{\showpaste}
\tab{5}\spadcommand{g := point [y,y,x,24::DFLOAT]$(Point DFLOAT)\bound{g }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch21}
\begin{paste}{ugGraphThreeDBuildPageFull21}{ugGraphThreeDBuildPageEmpty21}
\pastebutton{ugGraphThreeDBuildPageFull21}{\hidepaste}
\tab{5}\spadcommand{h := point [x,y,x,27::DFLOAT]$(Point DFLOAT)\bound{h }\free{x y }}
\indentrel{3}\begin{verbatim}
   (21)  [1.0, - 1.0, 1.0, 27.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty21}
\begin{paste}{ugGraphThreeDBuildPageEmpty21}{ugGraphThreeDBuildPagePatch21}
\pastebutton{ugGraphThreeDBuildPageEmpty21}{\showpaste}
\tab{5}\spadcommand{h := point [x,y,x,27::DFLOAT]$(Point DFLOAT)\bound{h }\free{x y }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch22}
\begin{paste}{ugGraphThreeDBuildPageFull22}{ugGraphThreeDBuildPageEmpty22}
\pastebutton{ugGraphThreeDBuildPageFull22}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[d,c,g,h])\free{d c g h spaceC }\bound{pol1 }}
\indentrel{3}\begin{verbatim}
   (22)  3-Space with 1 component
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty22}
\begin{paste}{ugGraphThreeDBuildPageEmpty22}{ugGraphThreeDBuildPagePatch22}
\pastebutton{ugGraphThreeDBuildPageEmpty22}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[d,c,g,h])\free{d c g h spaceC }\bound{pol1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch23}
\begin{paste}{ugGraphThreeDBuildPageFull23}{ugGraphThreeDBuildPageEmpty23}
\pastebutton{ugGraphThreeDBuildPageFull23}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[d,h,e,a])\free{d h e a spaceC }\bound{pol2 }}
\indentrel{3}\begin{verbatim}
   (23)  3-Space with 2 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty23}
\begin{paste}{ugGraphThreeDBuildPageEmpty23}{ugGraphThreeDBuildPagePatch23}
\pastebutton{ugGraphThreeDBuildPageEmpty23}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[d,h,e,a])\free{d h e a spaceC }\bound{pol2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch24}
\begin{paste}{ugGraphThreeDBuildPageFull24}{ugGraphThreeDBuildPageEmpty24}
\pastebutton{ugGraphThreeDBuildPageFull24}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[c,d,a,b])\free{c d a b spaceC }\bound{pol3 }}
\indentrel{3}\begin{verbatim}
   (24)  3-Space with 3 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty24}
\begin{paste}{ugGraphThreeDBuildPageEmpty24}{ugGraphThreeDBuildPagePatch24}
\pastebutton{ugGraphThreeDBuildPageEmpty24}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[c,d,a,b])\free{c d a b spaceC }\bound{pol3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch25}
\begin{paste}{ugGraphThreeDBuildPageFull25}{ugGraphThreeDBuildPageEmpty25}
\pastebutton{ugGraphThreeDBuildPageFull25}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[g,c,b,f])\free{g c b f spaceC }\bound{pol4 }}
\indentrel{3}\begin{verbatim}
   (25)  3-Space with 4 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty25}
\begin{paste}{ugGraphThreeDBuildPageEmpty25}{ugGraphThreeDBuildPagePatch25}
\pastebutton{ugGraphThreeDBuildPageEmpty25}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[g,c,b,f])\free{g c b f spaceC }\bound{pol4 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch26}
\begin{paste}{ugGraphThreeDBuildPageFull26}{ugGraphThreeDBuildPageEmpty26}
\pastebutton{ugGraphThreeDBuildPageFull26}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[h,g,f,e])\free{h g f e spaceC }\bound{pol5 }}
\indentrel{3}\begin{verbatim}
   (26)  3-Space with 5 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty26}
\begin{paste}{ugGraphThreeDBuildPageEmpty26}{ugGraphThreeDBuildPagePatch26}
\pastebutton{ugGraphThreeDBuildPageEmpty26}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[h,g,f,e])\free{h g f e spaceC }\bound{pol5 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch27}
\begin{paste}{ugGraphThreeDBuildPageFull27}{ugGraphThreeDBuildPageEmpty27}
\pastebutton{ugGraphThreeDBuildPageFull27}{\hidepaste}
\tab{5}\spadcommand{polygon(spaceC,[e,f,b,a])\free{e f b a spaceC }\bound{pol6 }}
\indentrel{3}\begin{verbatim}
   (27)  3-Space with 6 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty27}
\begin{paste}{ugGraphThreeDBuildPageEmpty27}{ugGraphThreeDBuildPagePatch27}
\pastebutton{ugGraphThreeDBuildPageEmpty27}{\showpaste}
\tab{5}\spadcommand{polygon(spaceC,[e,f,b,a])\free{e f b a spaceC }\bound{pol6 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPagePatch28}
\begin{paste}{ugGraphThreeDBuildPageFull28}{ugGraphThreeDBuildPageEmpty28}
\pastebutton{ugGraphThreeDBuildPageFull28}{\hidepaste}
\tab{5}\spadgraph{makeViewport3D(spaceC, title == "Cube")\free{pol1 pol2 pol3 pol4 pol5 pol6 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDBuildPage28.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDBuildPage28}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDBuildPageEmpty28}
\begin{paste}{ugGraphThreeDBuildPageEmpty28}{ugGraphThreeDBuildPagePatch28}
\pastebutton{ugGraphThreeDBuildPageEmpty28}{\showpaste}
\tab{5}\spadgraph{makeViewport3D(spaceC, title == "Cube")\free{pol1 pol2 pol3 pol4 pol5 pol6 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch1}
\begin{paste}{ugGraphTwoDOptionsPageFull1}{ugGraphTwoDOptionsPageEmpty1}
\pastebutton{ugGraphTwoDOptionsPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(sin(1/x),x=-2*\%pi..2*\%pi, adaptive == false)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty1}
\begin{paste}{ugGraphTwoDOptionsPageEmpty1}{ugGraphTwoDOptionsPagePatch1}
\pastebutton{ugGraphTwoDOptionsPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(sin(1/x),x=-2*\%pi..2*\%pi, adaptive == false)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch2}
\begin{paste}{ugGraphTwoDOptionsPageFull2}{ugGraphTwoDOptionsPageEmpty2}
\pastebutton{ugGraphTwoDOptionsPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(tan(x),x=-2*\%pi..2*\%pi, clip == true)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty2}
\begin{paste}{ugGraphTwoDOptionsPageEmpty2}{ugGraphTwoDOptionsPagePatch2}
\pastebutton{ugGraphTwoDOptionsPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(tan(x),x=-2*\%pi..2*\%pi, clip == true)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch3}
\begin{paste}{ugGraphTwoDOptionsPageFull3}{ugGraphTwoDOptionsPageEmpty3}
\pastebutton{ugGraphTwoDOptionsPageFull3}{\hidepaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, toScale == true, unit == [1.0,1.0])}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage3.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage3}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty3}
\begin{paste}{ugGraphTwoDOptionsPageEmpty3}{ugGraphTwoDOptionsPagePatch3}
\pastebutton{ugGraphTwoDOptionsPageEmpty3}{\showpaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, toScale == true, unit == [1.0,1.0])}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch4}
\begin{paste}{ugGraphTwoDOptionsPageFull4}{ugGraphTwoDOptionsPageEmpty4}
\pastebutton{ugGraphTwoDOptionsPageFull4}{\hidepaste}
\tab{5}\spadgraph{draw(sec(x),x=-2*\%pi..2*\%pi, clip == [-2*\%pi..2*\%pi,-\%pi..\%pi], unit == [1.0,1.0])}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage4.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage4}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty4}
\begin{paste}{ugGraphTwoDOptionsPageEmpty4}{ugGraphTwoDOptionsPagePatch4}
\pastebutton{ugGraphTwoDOptionsPageEmpty4}{\showpaste}
\tab{5}\spadgraph{draw(sec(x),x=-2*\%pi..2*\%pi, clip == [-2*\%pi..2*\%pi,-\%pi..\%pi], unit == [1.0,1.0])}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch5}
\begin{paste}{ugGraphTwoDOptionsPageFull5}{ugGraphTwoDOptionsPageEmpty5}
\pastebutton{ugGraphTwoDOptionsPageFull5}{\hidepaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, curveColor == bright red())}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage5.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage5}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty5}
\begin{paste}{ugGraphTwoDOptionsPageEmpty5}{ugGraphTwoDOptionsPagePatch5}
\pastebutton{ugGraphTwoDOptionsPageEmpty5}{\showpaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, curveColor == bright red())}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch6}
\begin{paste}{ugGraphTwoDOptionsPageFull6}{ugGraphTwoDOptionsPageEmpty6}
\pastebutton{ugGraphTwoDOptionsPageFull6}{\hidepaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, pointColor == pastel yellow())}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage6.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage6}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty6}
\begin{paste}{ugGraphTwoDOptionsPageEmpty6}{ugGraphTwoDOptionsPagePatch6}
\pastebutton{ugGraphTwoDOptionsPageEmpty6}{\showpaste}
\tab{5}\spadgraph{draw(sin(x),x=-\%pi..\%pi, pointColor == pastel yellow())}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch7}
\begin{paste}{ugGraphTwoDOptionsPageFull7}{ugGraphTwoDOptionsPageEmpty7}
\pastebutton{ugGraphTwoDOptionsPageFull7}{\hidepaste}
\tab{5}\spadgraph{draw(curve(9*sin(3*t/4),8*sin(t)), t = -4*\%pi..4*\%pi, unit == [2.0,1.0])}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage7.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage7}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty7}
\begin{paste}{ugGraphTwoDOptionsPageEmpty7}{ugGraphTwoDOptionsPagePatch7}
\pastebutton{ugGraphTwoDOptionsPageEmpty7}{\showpaste}
\tab{5}\spadgraph{draw(curve(9*sin(3*t/4),8*sin(t)), t = -4*\%pi..4*\%pi, unit == [2.0,1.0])}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch8}
\begin{paste}{ugGraphTwoDOptionsPageFull8}{ugGraphTwoDOptionsPageEmpty8}
\pastebutton{ugGraphTwoDOptionsPageFull8}{\hidepaste}
\tab{5}\spadgraph{draw(y^2 + y - (x^3 - x) = 0, x, y, range == [-2..2,-2..1], unit==[1.0,1.0])}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage8.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage8}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty8}
\begin{paste}{ugGraphTwoDOptionsPageEmpty8}{ugGraphTwoDOptionsPagePatch8}
\pastebutton{ugGraphTwoDOptionsPageEmpty8}{\showpaste}
\tab{5}\spadgraph{draw(y^2 + y - (x^3 - x) = 0, x, y, range == [-2..2,-2..1], unit==[1.0,1.0])}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch9}
\begin{paste}{ugGraphTwoDOptionsPageFull9}{ugGraphTwoDOptionsPageEmpty9}
\pastebutton{ugGraphTwoDOptionsPageFull9}{\hidepaste}
\tab{5}\spadgraph{draw(x^2 + y^2 = 1, x, y, range == [-3/2..3/2,-3/2..3/2], unit==[0.5,0.5])}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage9.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage9}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty9}
\begin{paste}{ugGraphTwoDOptionsPageEmpty9}{ugGraphTwoDOptionsPagePatch9}
\pastebutton{ugGraphTwoDOptionsPageEmpty9}{\showpaste}
\tab{5}\spadgraph{draw(x^2 + y^2 = 1, x, y, range == [-3/2..3/2,-3/2..3/2], unit==[0.5,0.5])}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPagePatch10}
\begin{paste}{ugGraphTwoDOptionsPageFull10}{ugGraphTwoDOptionsPageEmpty10}
\pastebutton{ugGraphTwoDOptionsPageFull10}{\hidepaste}
\tab{5}\spadgraph{draw(curve(sin(5*t),t),t=0..2*\%pi, coordinates == polar)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage10.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDOptionsPage10}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDOptionsPageEmpty10}
\begin{paste}{ugGraphTwoDOptionsPageEmpty10}{ugGraphTwoDOptionsPagePatch10}
\pastebutton{ugGraphTwoDOptionsPageEmpty10}{\showpaste}
\tab{5}\spadgraph{draw(curve(sin(5*t),t),t=0..2*\%pi, coordinates == polar)}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePagePatch1}
\begin{paste}{ugGraphColorPalettePageFull1}{ugGraphColorPalettePageEmpty1}
\pastebutton{ugGraphColorPalettePageFull1}{\hidepaste}
\tab{5}\spadcommand{shade red()}
\indentrel{3}\begin{verbatim}
   (1)  3
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePageEmpty1}
\begin{paste}{ugGraphColorPalettePageEmpty1}{ugGraphColorPalettePagePatch1}
\pastebutton{ugGraphColorPalettePageEmpty1}{\showpaste}
\tab{5}\spadcommand{shade red()}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePagePatch2}
\begin{paste}{ugGraphColorPalettePageFull2}{ugGraphColorPalettePageEmpty2}
\pastebutton{ugGraphColorPalettePageFull2}{\hidepaste}
\tab{5}\spadcommand{myFavoriteColor := dark blue()\bound{mfc }}
\indentrel{3}\begin{verbatim}
   (2)  [Hue: 22  Weight: 1.0] from the Dark palette
                                          Type: Palette
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePageEmpty2}
\begin{paste}{ugGraphColorPalettePageEmpty2}{ugGraphColorPalettePagePatch2}
\pastebutton{ugGraphColorPalettePageEmpty2}{\showpaste}
\tab{5}\spadcommand{myFavoriteColor := dark blue()\bound{mfc }}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePagePatch3}
\begin{paste}{ugGraphColorPalettePageFull3}{ugGraphColorPalettePageEmpty3}
\pastebutton{ugGraphColorPalettePageFull3}{\hidepaste}
\tab{5}\spadcommand{shade myFavoriteColor\free{mfc }}
\indentrel{3}\begin{verbatim}
   (3)  1
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePageEmpty3}
\begin{paste}{ugGraphColorPalettePageEmpty3}{ugGraphColorPalettePagePatch3}
\pastebutton{ugGraphColorPalettePageEmpty3}{\showpaste}
\tab{5}\spadcommand{shade myFavoriteColor\free{mfc }}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePagePatch4}
\begin{paste}{ugGraphColorPalettePageFull4}{ugGraphColorPalettePageEmpty4}
\pastebutton{ugGraphColorPalettePageFull4}{\hidepaste}
\tab{5}\spadcommand{hue myFavoriteColor\free{mfc }}
\indentrel{3}\begin{verbatim}
   (4)  Hue: 22  Weight: 1.0
                                            Type: Color
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePageEmpty4}
\begin{paste}{ugGraphColorPalettePageEmpty4}{ugGraphColorPalettePagePatch4}
\pastebutton{ugGraphColorPalettePageEmpty4}{\showpaste}
\tab{5}\spadcommand{hue myFavoriteColor\free{mfc }}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePagePatch5}
\begin{paste}{ugGraphColorPalettePageFull5}{ugGraphColorPalettePageEmpty5}
\pastebutton{ugGraphColorPalettePageFull5}{\hidepaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,curveColor == dark blue())}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphColorPalettePage5.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphColorPalettePage5}}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPalettePageEmpty5}
\begin{paste}{ugGraphColorPalettePageEmpty5}{ugGraphColorPalettePagePatch5}
\pastebutton{ugGraphColorPalettePageEmpty5}{\showpaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,curveColor == dark blue())}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch1}
\begin{paste}{ugGraphThreeDOptionsPageFull1}{ugGraphThreeDOptionsPageEmpty1}
\pastebutton{ugGraphThreeDOptionsPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(cos(x*y),x=0..2*\%pi,y=0..\%pi,title == "Title of Graph")}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty1}
\begin{paste}{ugGraphThreeDOptionsPageEmpty1}{ugGraphThreeDOptionsPagePatch1}
\pastebutton{ugGraphThreeDOptionsPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(cos(x*y),x=0..2*\%pi,y=0..\%pi,title == "Title of Graph")}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch2}
\begin{paste}{ugGraphThreeDOptionsPageFull2}{ugGraphThreeDOptionsPageEmpty2}
\pastebutton{ugGraphThreeDOptionsPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="smooth", title=="Smooth Option")}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty2}
\begin{paste}{ugGraphThreeDOptionsPageEmpty2}{ugGraphThreeDOptionsPagePatch2}
\pastebutton{ugGraphThreeDOptionsPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="smooth", title=="Smooth Option")}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch3}
\begin{paste}{ugGraphThreeDOptionsPageFull3}{ugGraphThreeDOptionsPageEmpty3}
\pastebutton{ugGraphThreeDOptionsPageFull3}{\hidepaste}
\tab{5}\spadcommand{color1(t) == t\bound{colorFxn1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty3}
\begin{paste}{ugGraphThreeDOptionsPageEmpty3}{ugGraphThreeDOptionsPagePatch3}
\pastebutton{ugGraphThreeDOptionsPageEmpty3}{\showpaste}
\tab{5}\spadcommand{color1(t) == t\bound{colorFxn1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch4}
\begin{paste}{ugGraphThreeDOptionsPageFull4}{ugGraphThreeDOptionsPageEmpty4}
\pastebutton{ugGraphThreeDOptionsPageFull4}{\hidepaste}
\tab{5}\spadgraph{draw(curve(sin(t), cos(t),0), t=0..2*\%pi, tubeRadius == .3, colorFunction == color1)\free{colorFxn1 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage4.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage4}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty4}
\begin{paste}{ugGraphThreeDOptionsPageEmpty4}{ugGraphThreeDOptionsPagePatch4}
\pastebutton{ugGraphThreeDOptionsPageEmpty4}{\showpaste}
\tab{5}\spadgraph{draw(curve(sin(t), cos(t),0), t=0..2*\%pi, tubeRadius == .3, colorFunction == color1)\free{colorFxn1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch5}
\begin{paste}{ugGraphThreeDOptionsPageFull5}{ugGraphThreeDOptionsPageEmpty5}
\pastebutton{ugGraphThreeDOptionsPageFull5}{\hidepaste}
\tab{5}\spadcommand{color2(u,v) == u^2 - v^2\bound{colorFxn2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty5}
\begin{paste}{ugGraphThreeDOptionsPageEmpty5}{ugGraphThreeDOptionsPagePatch5}
\pastebutton{ugGraphThreeDOptionsPageEmpty5}{\showpaste}
\tab{5}\spadcommand{color2(u,v) == u^2 - v^2\bound{colorFxn2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch6}
\begin{paste}{ugGraphThreeDOptionsPageFull6}{ugGraphThreeDOptionsPageEmpty6}
\pastebutton{ugGraphThreeDOptionsPageFull6}{\hidepaste}
\tab{5}\spadgraph{draw(cos(u*v), u=-3..3, v=-3..3, colorFunction == color2)\free{colorFxn2 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage6.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage6}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty6}
\begin{paste}{ugGraphThreeDOptionsPageEmpty6}{ugGraphThreeDOptionsPagePatch6}
\pastebutton{ugGraphThreeDOptionsPageEmpty6}{\showpaste}
\tab{5}\spadgraph{draw(cos(u*v), u=-3..3, v=-3..3, colorFunction == color2)\free{colorFxn2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch7}
\begin{paste}{ugGraphThreeDOptionsPageFull7}{ugGraphThreeDOptionsPageEmpty7}
\pastebutton{ugGraphThreeDOptionsPageFull7}{\hidepaste}
\tab{5}\spadcommand{color3(x,y,fxy) == sin(x*fxy) + cos(y*fxy)\bound{colorFxn3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty7}
\begin{paste}{ugGraphThreeDOptionsPageEmpty7}{ugGraphThreeDOptionsPagePatch7}
\pastebutton{ugGraphThreeDOptionsPageEmpty7}{\showpaste}
\tab{5}\spadcommand{color3(x,y,fxy) == sin(x*fxy) + cos(y*fxy)\bound{colorFxn3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch8}
\begin{paste}{ugGraphThreeDOptionsPageFull8}{ugGraphThreeDOptionsPageEmpty8}
\pastebutton{ugGraphThreeDOptionsPageFull8}{\hidepaste}
\tab{5}\spadgraph{draw(cos(x*y), x=-3..3, y=-3..3, colorFunction == color3)\free{colorFxn3 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage8.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage8}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty8}
\begin{paste}{ugGraphThreeDOptionsPageEmpty8}{ugGraphThreeDOptionsPagePatch8}
\pastebutton{ugGraphThreeDOptionsPageEmpty8}{\showpaste}
\tab{5}\spadgraph{draw(cos(x*y), x=-3..3, y=-3..3, colorFunction == color3)\free{colorFxn3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch9}
\begin{paste}{ugGraphThreeDOptionsPageFull9}{ugGraphThreeDOptionsPageEmpty9}
\pastebutton{ugGraphThreeDOptionsPageFull9}{\hidepaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty9}
\begin{paste}{ugGraphThreeDOptionsPageEmpty9}{ugGraphThreeDOptionsPagePatch9}
\pastebutton{ugGraphThreeDOptionsPageEmpty9}{\showpaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch10}
\begin{paste}{ugGraphThreeDOptionsPageFull10}{ugGraphThreeDOptionsPageEmpty10}
\pastebutton{ugGraphThreeDOptionsPageFull10}{\hidepaste}
\tab{5}\spadgraph{draw(m, 0..2*\%pi,0..\%pi, coordinates == spherical, style=="shade")\free{m }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage10.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage10}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty10}
\begin{paste}{ugGraphThreeDOptionsPageEmpty10}{ugGraphThreeDOptionsPagePatch10}
\pastebutton{ugGraphThreeDOptionsPageEmpty10}{\showpaste}
\tab{5}\spadgraph{draw(m, 0..2*\%pi,0..\%pi, coordinates == spherical, style=="shade")\free{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch11}
\begin{paste}{ugGraphThreeDOptionsPageFull11}{ugGraphThreeDOptionsPageEmpty11}
\pastebutton{ugGraphThreeDOptionsPageFull11}{\hidepaste}
\tab{5}\spadgraph{draw(curve(sin(t),cos(t),0),t=0..2*\%pi, style=="shade", tubeRadius == .3)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage11.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage11}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty11}
\begin{paste}{ugGraphThreeDOptionsPageEmpty11}{ugGraphThreeDOptionsPagePatch11}
\pastebutton{ugGraphThreeDOptionsPageEmpty11}{\showpaste}
\tab{5}\spadgraph{draw(curve(sin(t),cos(t),0),t=0..2*\%pi, style=="shade", tubeRadius == .3)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch12}
\begin{paste}{ugGraphThreeDOptionsPageFull12}{ugGraphThreeDOptionsPageEmpty12}
\pastebutton{ugGraphThreeDOptionsPageFull12}{\hidepaste}
\tab{5}\spadgraph{draw(curve(sin(t), cos(t), 0), t=0..2*\%pi, style=="shade", tubeRadius == .25, tubePoints == 3)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage12.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage12}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty12}
\begin{paste}{ugGraphThreeDOptionsPageEmpty12}{ugGraphThreeDOptionsPagePatch12}
\pastebutton{ugGraphThreeDOptionsPageEmpty12}{\showpaste}
\tab{5}\spadgraph{draw(curve(sin(t), cos(t), 0), t=0..2*\%pi, style=="shade", tubeRadius == .25, tubePoints == 3)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch13}
\begin{paste}{ugGraphThreeDOptionsPageFull13}{ugGraphThreeDOptionsPageEmpty13}
\pastebutton{ugGraphThreeDOptionsPageFull13}{\hidepaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="shade", var1Steps == 30, var2Steps == 30)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage13.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage13}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty13}
\begin{paste}{ugGraphThreeDOptionsPageEmpty13}{ugGraphThreeDOptionsPagePatch13}
\pastebutton{ugGraphThreeDOptionsPageEmpty13}{\showpaste}
\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="shade", var1Steps == 30, var2Steps == 30)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch14}
\begin{paste}{ugGraphThreeDOptionsPageFull14}{ugGraphThreeDOptionsPageEmpty14}
\pastebutton{ugGraphThreeDOptionsPageFull14}{\hidepaste}
\tab{5}\spadcommand{s := create3Space()$(ThreeSpace DFLOAT)\bound{s }}
\indentrel{3}\begin{verbatim}
   (14)  3-Space with 0 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty14}
\begin{paste}{ugGraphThreeDOptionsPageEmpty14}{ugGraphThreeDOptionsPagePatch14}
\pastebutton{ugGraphThreeDOptionsPageEmpty14}{\showpaste}
\tab{5}\spadcommand{s := create3Space()$(ThreeSpace DFLOAT)\bound{s }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch15}
\begin{paste}{ugGraphThreeDOptionsPageFull15}{ugGraphThreeDOptionsPageEmpty15}
\pastebutton{ugGraphThreeDOptionsPageFull15}{\hidepaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty15}
\begin{paste}{ugGraphThreeDOptionsPageEmpty15}{ugGraphThreeDOptionsPagePatch15}
\pastebutton{ugGraphThreeDOptionsPageEmpty15}{\showpaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch16}
\begin{paste}{ugGraphThreeDOptionsPageFull16}{ugGraphThreeDOptionsPageEmpty16}
\pastebutton{ugGraphThreeDOptionsPageFull16}{\hidepaste}
\tab{5}\spadgraph{draw(m,0..\%pi,0..2*\%pi, coordinates == spherical, space == s)\free{s m }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage16.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage16}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty16}
\begin{paste}{ugGraphThreeDOptionsPageEmpty16}{ugGraphThreeDOptionsPagePatch16}
\pastebutton{ugGraphThreeDOptionsPageEmpty16}{\showpaste}
\tab{5}\spadgraph{draw(m,0..\%pi,0..2*\%pi, coordinates == spherical, space == s)\free{s m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch17}
\begin{paste}{ugGraphThreeDOptionsPageFull17}{ugGraphThreeDOptionsPageEmpty17}
\pastebutton{ugGraphThreeDOptionsPageFull17}{\hidepaste}
\tab{5}\spadgraph{v := draw(curve(1.5*sin(t), 1.5*cos(t),0), t=0..2*\%pi, tubeRadius == .25, space == s)\free{s }\bound{v }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage17.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage17}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty17}
\begin{paste}{ugGraphThreeDOptionsPageEmpty17}{ugGraphThreeDOptionsPagePatch17}
\pastebutton{ugGraphThreeDOptionsPageEmpty17}{\showpaste}
\tab{5}\spadgraph{v := draw(curve(1.5*sin(t), 1.5*cos(t),0), t=0..2*\%pi, tubeRadius == .25, space == s)\free{s }\bound{v }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch18}
\begin{paste}{ugGraphThreeDOptionsPageFull18}{ugGraphThreeDOptionsPageEmpty18}
\pastebutton{ugGraphThreeDOptionsPageFull18}{\hidepaste}
\tab{5}\spadcommand{subsp := subspace v\free{v }\bound{su }}
\indentrel{3}\begin{verbatim}
   (18)  3-Space with 2 components
                          Type: ThreeSpace(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty18}
\begin{paste}{ugGraphThreeDOptionsPageEmpty18}{ugGraphThreeDOptionsPagePatch18}
\pastebutton{ugGraphThreeDOptionsPageEmpty18}{\showpaste}
\tab{5}\spadcommand{subsp := subspace v\free{v }\bound{su }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch19}
\begin{paste}{ugGraphThreeDOptionsPageFull19}{ugGraphThreeDOptionsPageEmpty19}
\pastebutton{ugGraphThreeDOptionsPageFull19}{\hidepaste}
\tab{5}\spadcommand{subspace(v, subsp)\bound{sp }\free{su }}
\indentrel{3}\begin{verbatim}
   (19)
   Closed or Undefined ThreeDimensionalViewport:
     "FriCAS3D"
                         Type: ThreeDimensionalViewport
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty19}
\begin{paste}{ugGraphThreeDOptionsPageEmpty19}{ugGraphThreeDOptionsPagePatch19}
\pastebutton{ugGraphThreeDOptionsPageEmpty19}{\showpaste}
\tab{5}\spadcommand{subspace(v, subsp)\bound{sp }\free{su }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPagePatch20}
\begin{paste}{ugGraphThreeDOptionsPageFull20}{ugGraphThreeDOptionsPageEmpty20}
\pastebutton{ugGraphThreeDOptionsPageFull20}{\hidepaste}
\tab{5}\spadgraph{makeViewport3D(subsp,"Graphs")\free{sp }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage20.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDOptionsPage20}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDOptionsPageEmpty20}
\begin{paste}{ugGraphThreeDOptionsPageEmpty20}{ugGraphThreeDOptionsPagePatch20}
\pastebutton{ugGraphThreeDOptionsPageEmpty20}{\showpaste}
\tab{5}\spadgraph{makeViewport3D(subsp,"Graphs")\free{sp }}
\end{paste}\end{patch}

\begin{patch}{ugGraphClipPagePatch1}
\begin{paste}{ugGraphClipPageFull1}{ugGraphClipPageEmpty1}
\pastebutton{ugGraphClipPageFull1}{\hidepaste}
\tab{5}\spadcommand{gamma(x,y) ==
  g := Gamma complex(x,y)
  point [x, y, max( min(real g, 4), -4), argument g]
\bound{g }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphClipPageEmpty1}
\begin{paste}{ugGraphClipPageEmpty1}{ugGraphClipPagePatch1}
\pastebutton{ugGraphClipPageEmpty1}{\showpaste}
\tab{5}\spadcommand{gamma(x,y) ==
  g := Gamma complex(x,y)
  point [x, y, max( min(real g, 4), -4), argument g]
\bound{g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphClipPagePatch2}
\begin{paste}{ugGraphClipPageFull2}{ugGraphClipPageEmpty2}
\pastebutton{ugGraphClipPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(gamma,-\%pi..\%pi,-\%pi..\%pi,var1Steps==50,var2Steps==50)\free{g }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphClipPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphClipPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphClipPageEmpty2}
\begin{paste}{ugGraphClipPageEmpty2}{ugGraphClipPagePatch2}
\pastebutton{ugGraphClipPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(gamma,-\%pi..\%pi,-\%pi..\%pi,var1Steps==50,var2Steps==50)\free{g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch1}
\begin{paste}{ugGraphCoordPageFull1}{ugGraphCoordPageEmpty1}
\pastebutton{ugGraphCoordPageFull1}{\hidepaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == u^2\bound{m }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty1}
\begin{paste}{ugGraphCoordPageEmpty1}{ugGraphCoordPagePatch1}
\pastebutton{ugGraphCoordPageEmpty1}{\showpaste}
\tab{5}\spadcommand{m(u:DFLOAT,v:DFLOAT):DFLOAT == u^2\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch2}
\begin{paste}{ugGraphCoordPageFull2}{ugGraphCoordPageEmpty2}
\pastebutton{ugGraphCoordPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(m,0..3,0..5)\free{m }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphCoordPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphCoordPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty2}
\begin{paste}{ugGraphCoordPageEmpty2}{ugGraphCoordPagePatch2}
\pastebutton{ugGraphCoordPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(m,0..3,0..5)\free{m }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch3}
\begin{paste}{ugGraphCoordPageFull3}{ugGraphCoordPageEmpty3}
\pastebutton{ugGraphCoordPageFull3}{\hidepaste}
\tab{5}\spadcommand{cartesian(point:Point DFLOAT):Point DFLOAT == point\bound{cart }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty3}
\begin{paste}{ugGraphCoordPageEmpty3}{ugGraphCoordPagePatch3}
\pastebutton{ugGraphCoordPageEmpty3}{\showpaste}
\tab{5}\spadcommand{cartesian(point:Point DFLOAT):Point DFLOAT == point\bound{cart }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch4}
\begin{paste}{ugGraphCoordPageFull4}{ugGraphCoordPageEmpty4}
\pastebutton{ugGraphCoordPageFull4}{\hidepaste}
\tab{5}\spadgraph{draw(m,0..3,0..5,coordinates==cartesian)\free{m cart }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphCoordPage4.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphCoordPage4}}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty4}
\begin{paste}{ugGraphCoordPageEmpty4}{ugGraphCoordPagePatch4}
\pastebutton{ugGraphCoordPageEmpty4}{\showpaste}
\tab{5}\spadgraph{draw(m,0..3,0..5,coordinates==cartesian)\free{m cart }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch5}
\begin{paste}{ugGraphCoordPageFull5}{ugGraphCoordPageEmpty5}
\pastebutton{ugGraphCoordPageFull5}{\hidepaste}
\tab{5}\spadcommand{f(u:DFLOAT,v:DFLOAT):DFLOAT == 3\bound{f }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty5}
\begin{paste}{ugGraphCoordPageEmpty5}{ugGraphCoordPagePatch5}
\pastebutton{ugGraphCoordPageEmpty5}{\showpaste}
\tab{5}\spadcommand{f(u:DFLOAT,v:DFLOAT):DFLOAT == 3\bound{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch6}
\begin{paste}{ugGraphCoordPageFull6}{ugGraphCoordPageEmpty6}
\pastebutton{ugGraphCoordPageFull6}{\hidepaste}
\tab{5}\spadgraph{draw(f,0..\%pi,0..6,coordinates==cylindrical)\free{f }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphCoordPage6.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphCoordPage6}}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty6}
\begin{paste}{ugGraphCoordPageEmpty6}{ugGraphCoordPagePatch6}
\pastebutton{ugGraphCoordPageEmpty6}{\showpaste}
\tab{5}\spadgraph{draw(f,0..\%pi,0..6,coordinates==cylindrical)\free{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch7}
\begin{paste}{ugGraphCoordPageFull7}{ugGraphCoordPageEmpty7}
\pastebutton{ugGraphCoordPageFull7}{\hidepaste}
\tab{5}\spadcommand{col := 5\bound{c }}
\indentrel{3}\begin{verbatim}
   (7)  5
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty7}
\begin{paste}{ugGraphCoordPageEmpty7}{ugGraphCoordPagePatch7}
\pastebutton{ugGraphCoordPageEmpty7}{\showpaste}
\tab{5}\spadcommand{col := 5\bound{c }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch8}
\begin{paste}{ugGraphCoordPageFull8}{ugGraphCoordPageEmpty8}
\pastebutton{ugGraphCoordPageFull8}{\hidepaste}
\tab{5}\spadcommand{pt := point[1,2,3,col]$(Point DFLOAT)\free{c }\bound{pt }}
\indentrel{3}\begin{verbatim}
   (8)  [1.0, 2.0, 3.0, 5.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty8}
\begin{paste}{ugGraphCoordPageEmpty8}{ugGraphCoordPagePatch8}
\pastebutton{ugGraphCoordPageEmpty8}{\showpaste}
\tab{5}\spadcommand{pt := point[1,2,3,col]$(Point DFLOAT)\free{c }\bound{pt }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch9}
\begin{paste}{ugGraphCoordPageFull9}{ugGraphCoordPageEmpty9}
\pastebutton{ugGraphCoordPageFull9}{\hidepaste}
\tab{5}\spadcommand{reorder(p:Point DFLOAT):Point DFLOAT == point[p.2, p.3, p.1, p.4]\bound{freo }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty9}
\begin{paste}{ugGraphCoordPageEmpty9}{ugGraphCoordPagePatch9}
\pastebutton{ugGraphCoordPageEmpty9}{\showpaste}
\tab{5}\spadcommand{reorder(p:Point DFLOAT):Point DFLOAT == point[p.2, p.3, p.1, p.4]\bound{freo }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch10}
\begin{paste}{ugGraphCoordPageFull10}{ugGraphCoordPageEmpty10}
\pastebutton{ugGraphCoordPageFull10}{\hidepaste}
\tab{5}\spadcommand{reorder pt\free{pt freo }}
\indentrel{3}\begin{verbatim}
   (10)  [2.0, 3.0, 1.0, 5.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty10}
\begin{paste}{ugGraphCoordPageEmpty10}{ugGraphCoordPagePatch10}
\pastebutton{ugGraphCoordPageEmpty10}{\showpaste}
\tab{5}\spadcommand{reorder pt\free{pt freo }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch11}
\begin{paste}{ugGraphCoordPageFull11}{ugGraphCoordPageEmpty11}
\pastebutton{ugGraphCoordPageFull11}{\hidepaste}
\tab{5}\spadcommand{newmap(pt:Point DFLOAT):Point DFLOAT == cylindrical(reorder pt)\free{freo }\bound{fnewmap }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty11}
\begin{paste}{ugGraphCoordPageEmpty11}{ugGraphCoordPagePatch11}
\pastebutton{ugGraphCoordPageEmpty11}{\showpaste}
\tab{5}\spadcommand{newmap(pt:Point DFLOAT):Point DFLOAT == cylindrical(reorder pt)\free{freo }\bound{fnewmap }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch12}
\begin{paste}{ugGraphCoordPageFull12}{ugGraphCoordPageEmpty12}
\pastebutton{ugGraphCoordPageFull12}{\hidepaste}
\tab{5}\spadcommand{newmap pt\free{fnewmap pt }\bound{new }}
\indentrel{3}\begin{verbatim}
   (12)
   [- 1.9799849932008908, 0.2822400161197344, 1.0, 5.0]
                               Type: Point(DoubleFloat)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty12}
\begin{paste}{ugGraphCoordPageEmpty12}{ugGraphCoordPagePatch12}
\pastebutton{ugGraphCoordPageEmpty12}{\showpaste}
\tab{5}\spadcommand{newmap pt\free{fnewmap pt }\bound{new }}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPagePatch13}
\begin{paste}{ugGraphCoordPageFull13}{ugGraphCoordPageEmpty13}
\pastebutton{ugGraphCoordPageFull13}{\hidepaste}
\tab{5}\spadgraph{draw(f,0..3,0..2*\%pi,coordinates==newmap)\free{f new }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphCoordPage13.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphCoordPage13}}
\end{paste}\end{patch}

\begin{patch}{ugGraphCoordPageEmpty13}
\begin{paste}{ugGraphCoordPageEmpty13}{ugGraphCoordPagePatch13}
\pastebutton{ugGraphCoordPageEmpty13}{\showpaste}
\tab{5}\spadgraph{draw(f,0..3,0..2*\%pi,coordinates==newmap)\free{f new }}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPagePatch1}
\begin{paste}{ugGraphColorPageFull1}{ugGraphColorPageEmpty1}
\pastebutton{ugGraphColorPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,pointColor == green())}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphColorPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphColorPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPageEmpty1}
\begin{paste}{ugGraphColorPageEmpty1}{ugGraphColorPagePatch1}
\pastebutton{ugGraphColorPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,pointColor == green())}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPagePatch2}
\begin{paste}{ugGraphColorPageFull2}{ugGraphColorPageEmpty2}
\pastebutton{ugGraphColorPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,curveColor == color(13) + 2*blue())}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphColorPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphColorPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphColorPageEmpty2}
\begin{paste}{ugGraphColorPageEmpty2}{ugGraphColorPagePatch2}
\pastebutton{ugGraphColorPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(x^2,x=-1..1,curveColor == color(13) + 2*blue())}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch1}
\begin{paste}{ugGraphTwoDParPageFull1}{ugGraphTwoDParPageEmpty1}
\pastebutton{ugGraphTwoDParPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDParPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDParPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty1}
\begin{paste}{ugGraphTwoDParPageEmpty1}{ugGraphTwoDParPagePatch1}
\pastebutton{ugGraphTwoDParPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch2}
\begin{paste}{ugGraphTwoDParPageFull2}{ugGraphTwoDParPageEmpty2}
\pastebutton{ugGraphTwoDParPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDParPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDParPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty2}
\begin{paste}{ugGraphTwoDParPageEmpty2}{ugGraphTwoDParPagePatch2}
\pastebutton{ugGraphTwoDParPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch3}
\begin{paste}{ugGraphTwoDParPageFull3}{ugGraphTwoDParPageEmpty3}
\pastebutton{ugGraphTwoDParPageFull3}{\hidepaste}
\tab{5}\spadcommand{f(t:DFLOAT):DFLOAT == sin(3*t/4)\bound{f }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty3}
\begin{paste}{ugGraphTwoDParPageEmpty3}{ugGraphTwoDParPagePatch3}
\pastebutton{ugGraphTwoDParPageEmpty3}{\showpaste}
\tab{5}\spadcommand{f(t:DFLOAT):DFLOAT == sin(3*t/4)\bound{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch4}
\begin{paste}{ugGraphTwoDParPageFull4}{ugGraphTwoDParPageEmpty4}
\pastebutton{ugGraphTwoDParPageFull4}{\hidepaste}
\tab{5}\spadcommand{g(t:DFLOAT):DFLOAT == sin(t)\bound{g }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty4}
\begin{paste}{ugGraphTwoDParPageEmpty4}{ugGraphTwoDParPagePatch4}
\pastebutton{ugGraphTwoDParPageEmpty4}{\showpaste}
\tab{5}\spadcommand{g(t:DFLOAT):DFLOAT == sin(t)\bound{g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch5}
\begin{paste}{ugGraphTwoDParPageFull5}{ugGraphTwoDParPageEmpty5}
\pastebutton{ugGraphTwoDParPageFull5}{\hidepaste}
\tab{5}\spadgraph{draw(curve(f,g),0..\%pi)\free{f g }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDParPage5.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDParPage5}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty5}
\begin{paste}{ugGraphTwoDParPageEmpty5}{ugGraphTwoDParPagePatch5}
\pastebutton{ugGraphTwoDParPageEmpty5}{\showpaste}
\tab{5}\spadgraph{draw(curve(f,g),0..\%pi)\free{f g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPagePatch6}
\begin{paste}{ugGraphTwoDParPageFull6}{ugGraphTwoDParPageEmpty6}
\pastebutton{ugGraphTwoDParPageFull6}{\hidepaste}
\tab{5}\spadgraph{draw(curve(f,g),-4*\%pi..4*\%pi)\free{f g }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDParPage6.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDParPage6}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDParPageEmpty6}
\begin{paste}{ugGraphTwoDParPageEmpty6}{ugGraphTwoDParPagePatch6}
\pastebutton{ugGraphTwoDParPageEmpty6}{\showpaste}
\tab{5}\spadgraph{draw(curve(f,g),-4*\%pi..4*\%pi)\free{f g }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPagePatch1}
\begin{paste}{ugGraphTwoDPlotPageFull1}{ugGraphTwoDPlotPageEmpty1}
\pastebutton{ugGraphTwoDPlotPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDPlotPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDPlotPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPageEmpty1}
\begin{paste}{ugGraphTwoDPlotPageEmpty1}{ugGraphTwoDPlotPagePatch1}
\pastebutton{ugGraphTwoDPlotPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPagePatch2}
\begin{paste}{ugGraphTwoDPlotPageFull2}{ugGraphTwoDPlotPageEmpty2}
\pastebutton{ugGraphTwoDPlotPageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDPlotPage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDPlotPage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPageEmpty2}
\begin{paste}{ugGraphTwoDPlotPageEmpty2}{ugGraphTwoDPlotPagePatch2}
\pastebutton{ugGraphTwoDPlotPageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPagePatch3}
\begin{paste}{ugGraphTwoDPlotPageFull3}{ugGraphTwoDPlotPageEmpty3}
\pastebutton{ugGraphTwoDPlotPageFull3}{\hidepaste}
\tab{5}\spadcommand{f(x) == (x-1)*(x-2)*(x-3)\bound{f }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPageEmpty3}
\begin{paste}{ugGraphTwoDPlotPageEmpty3}{ugGraphTwoDPlotPagePatch3}
\pastebutton{ugGraphTwoDPlotPageEmpty3}{\showpaste}
\tab{5}\spadcommand{f(x) == (x-1)*(x-2)*(x-3)\bound{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPagePatch4}
\begin{paste}{ugGraphTwoDPlotPageFull4}{ugGraphTwoDPlotPageEmpty4}
\pastebutton{ugGraphTwoDPlotPageFull4}{\hidepaste}
\tab{5}\spadgraph{draw(f, 0..4)\free{f }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDPlotPage4.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDPlotPage4}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlotPageEmpty4}
\begin{paste}{ugGraphTwoDPlotPageEmpty4}{ugGraphTwoDPlotPagePatch4}
\pastebutton{ugGraphTwoDPlotPageEmpty4}{\showpaste}
\tab{5}\spadgraph{draw(f, 0..4)\free{f }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch1}
\begin{paste}{ugGraphThreeDParPageFull1}{ugGraphThreeDParPageEmpty1}
\pastebutton{ugGraphThreeDParPageFull1}{\hidepaste}
\tab{5}\spadgraph{draw(surface(u*cos(v), u*sin(v), v*cos(u)), u=-4..4, v=0..\%pi, coordinates== parabolicCylindrical)}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDParPage1.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDParPage1}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty1}
\begin{paste}{ugGraphThreeDParPageEmpty1}{ugGraphThreeDParPagePatch1}
\pastebutton{ugGraphThreeDParPageEmpty1}{\showpaste}
\tab{5}\spadgraph{draw(surface(u*cos(v), u*sin(v), v*cos(u)), u=-4..4, v=0..\%pi, coordinates== parabolicCylindrical)}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch2}
\begin{paste}{ugGraphThreeDParPageFull2}{ugGraphThreeDParPageEmpty2}
\pastebutton{ugGraphThreeDParPageFull2}{\hidepaste}
\tab{5}\spadcommand{n1(u:DFLOAT,v:DFLOAT):DFLOAT == u*cos(v)\bound{n1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty2}
\begin{paste}{ugGraphThreeDParPageEmpty2}{ugGraphThreeDParPagePatch2}
\pastebutton{ugGraphThreeDParPageEmpty2}{\showpaste}
\tab{5}\spadcommand{n1(u:DFLOAT,v:DFLOAT):DFLOAT == u*cos(v)\bound{n1 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch3}
\begin{paste}{ugGraphThreeDParPageFull3}{ugGraphThreeDParPageEmpty3}
\pastebutton{ugGraphThreeDParPageFull3}{\hidepaste}
\tab{5}\spadcommand{n2(u:DFLOAT,v:DFLOAT):DFLOAT == u*sin(v)\bound{n2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty3}
\begin{paste}{ugGraphThreeDParPageEmpty3}{ugGraphThreeDParPagePatch3}
\pastebutton{ugGraphThreeDParPageEmpty3}{\showpaste}
\tab{5}\spadcommand{n2(u:DFLOAT,v:DFLOAT):DFLOAT == u*sin(v)\bound{n2 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch4}
\begin{paste}{ugGraphThreeDParPageFull4}{ugGraphThreeDParPageEmpty4}
\pastebutton{ugGraphThreeDParPageFull4}{\hidepaste}
\tab{5}\spadcommand{n3(u:DFLOAT,v:DFLOAT):DFLOAT == u\bound{n3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty4}
\begin{paste}{ugGraphThreeDParPageEmpty4}{ugGraphThreeDParPagePatch4}
\pastebutton{ugGraphThreeDParPageEmpty4}{\showpaste}
\tab{5}\spadcommand{n3(u:DFLOAT,v:DFLOAT):DFLOAT == u\bound{n3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch5}
\begin{paste}{ugGraphThreeDParPageFull5}{ugGraphThreeDParPageEmpty5}
\pastebutton{ugGraphThreeDParPageFull5}{\hidepaste}
\tab{5}\spadcommand{n3(0.5,1.0)\free{n3 }}
\indentrel{3}\begin{verbatim}
   (5)  0.5
                                      Type: DoubleFloat
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty5}
\begin{paste}{ugGraphThreeDParPageEmpty5}{ugGraphThreeDParPagePatch5}
\pastebutton{ugGraphThreeDParPageEmpty5}{\showpaste}
\tab{5}\spadcommand{n3(0.5,1.0)\free{n3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPagePatch6}
\begin{paste}{ugGraphThreeDParPageFull6}{ugGraphThreeDParPageEmpty6}
\pastebutton{ugGraphThreeDParPageFull6}{\hidepaste}
\tab{5}\spadgraph{draw(surface(n1,n2,n3), 1..4, 1..2*\%pi, coordinates == toroidal(1$DFLOAT))\free{n1 n2 n3 }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphThreeDParPage6.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphThreeDParPage6}}
\end{paste}\end{patch}

\begin{patch}{ugGraphThreeDParPageEmpty6}
\begin{paste}{ugGraphThreeDParPageEmpty6}{ugGraphThreeDParPagePatch6}
\pastebutton{ugGraphThreeDParPageEmpty6}{\showpaste}
\tab{5}\spadgraph{draw(surface(n1,n2,n3), 1..4, 1..2*\%pi, coordinates == toroidal(1$DFLOAT))\free{n1 n2 n3 }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlanePagePatch1}
\begin{paste}{ugGraphTwoDPlanePageFull1}{ugGraphTwoDPlanePageEmpty1}
\pastebutton{ugGraphTwoDPlanePageFull1}{\hidepaste}
\tab{5}\spadcommand{p := ((x^2 + y^2 + 1) - 8*x)^2 - (8*(x^2 + y^2 + 1)-4*x-1)\bound{p }}
\indentrel{3}\begin{verbatim}
   (1)
      4       2             2    4       3       2
     y  + (2 x  - 16 x - 6)y  + x  - 16 x  + 58 x  - 12 x
   + 
     - 6
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlanePageEmpty1}
\begin{paste}{ugGraphTwoDPlanePageEmpty1}{ugGraphTwoDPlanePagePatch1}
\pastebutton{ugGraphTwoDPlanePageEmpty1}{\showpaste}
\tab{5}\spadcommand{p := ((x^2 + y^2 + 1) - 8*x)^2 - (8*(x^2 + y^2 + 1)-4*x-1)\bound{p }}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlanePagePatch2}
\begin{paste}{ugGraphTwoDPlanePageFull2}{ugGraphTwoDPlanePageEmpty2}
\pastebutton{ugGraphTwoDPlanePageFull2}{\hidepaste}
\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7])\free{p }}
\center{\unixcommand{\inputimage{\env{AXIOM}/share/viewports/ugGraphTwoDPlanePage2.VIEW/image}}{\env{AXIOM}/bin/viewAlone\space{1} \env{AXIOM}/share/viewports/ugGraphTwoDPlanePage2}}
\end{paste}\end{patch}

\begin{patch}{ugGraphTwoDPlanePageEmpty2}
\begin{paste}{ugGraphTwoDPlanePageEmpty2}{ugGraphTwoDPlanePagePatch2}
\pastebutton{ugGraphTwoDPlanePageEmpty2}{\showpaste}
\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7])\free{p }}
\end{paste}\end{patch}

