\begin{patch}{XPolynomialXmpPagePatch1}
\begin{paste}{XPolynomialXmpPageFull1}{XPolynomialXmpPageEmpty1}
\pastebutton{XPolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{poly := XPolynomial(Integer)\bound{poly }}
\indentrel{3}\begin{verbatim}
   (1)  XPolynomial(Integer)
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty1}
\begin{paste}{XPolynomialXmpPageEmpty1}{XPolynomialXmpPagePatch1}
\pastebutton{XPolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{poly := XPolynomial(Integer)\bound{poly }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch2}
\begin{paste}{XPolynomialXmpPageFull2}{XPolynomialXmpPageEmpty2}
\pastebutton{XPolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{pr: poly := 2*x + 3*y-5\free{poly }\bound{pr }}
\indentrel{3}\begin{verbatim}
   (2)  - 5 + 2 x + 3 y
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty2}
\begin{paste}{XPolynomialXmpPageEmpty2}{XPolynomialXmpPagePatch2}
\pastebutton{XPolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{pr: poly := 2*x + 3*y-5\free{poly }\bound{pr }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch3}
\begin{paste}{XPolynomialXmpPageFull3}{XPolynomialXmpPageEmpty3}
\pastebutton{XPolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{pr2: poly := pr*pr\free{poly }\bound{pr2 }}
\indentrel{3}\begin{verbatim}
   (3)  25 + (- 20 + 4 x + 6 y)x + (- 30 + 6 x + 9 y)y
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty3}
\begin{paste}{XPolynomialXmpPageEmpty3}{XPolynomialXmpPagePatch3}
\pastebutton{XPolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{pr2: poly := pr*pr\free{poly }\bound{pr2 }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch4}
\begin{paste}{XPolynomialXmpPageFull4}{XPolynomialXmpPageEmpty4}
\pastebutton{XPolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{pd := expand pr\free{pr }\bound{pd }}
\indentrel{3}\begin{verbatim}
   (4)  - 5 + 2 x + 3 y
           Type: XDistributedPolynomial(Symbol,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty4}
\begin{paste}{XPolynomialXmpPageEmpty4}{XPolynomialXmpPagePatch4}
\pastebutton{XPolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{pd := expand pr\free{pr }\bound{pd }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch5}
\begin{paste}{XPolynomialXmpPageFull5}{XPolynomialXmpPageEmpty5}
\pastebutton{XPolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{pd2 := pd*pd\free{pd }\bound{pd2 }}
\indentrel{3}\begin{verbatim}
                              2                      2
   (5)  25 - 20 x - 30 y + 4 x  + 6 x y + 6 y x + 9 y
           Type: XDistributedPolynomial(Symbol,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty5}
\begin{paste}{XPolynomialXmpPageEmpty5}{XPolynomialXmpPagePatch5}
\pastebutton{XPolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{pd2 := pd*pd\free{pd }\bound{pd2 }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch6}
\begin{paste}{XPolynomialXmpPageFull6}{XPolynomialXmpPageEmpty6}
\pastebutton{XPolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{expand(pr2) - pd2\free{pr2 }\free{pd2 }}
\indentrel{3}\begin{verbatim}
   (6)  0
           Type: XDistributedPolynomial(Symbol,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty6}
\begin{paste}{XPolynomialXmpPageEmpty6}{XPolynomialXmpPagePatch6}
\pastebutton{XPolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{expand(pr2) - pd2\free{pr2 }\free{pd2 }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch7}
\begin{paste}{XPolynomialXmpPageFull7}{XPolynomialXmpPageEmpty7}
\pastebutton{XPolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{qr := pr^3\free{pr }\bound{qr }}
\indentrel{3}\begin{verbatim}
   (7)
     - 125
   + 
     (150 + (- 60 + 8 x + 12 y)x + (- 90 + 12 x + 18 y)y)x
   + 
   (225 + (- 90 + 12 x + 18 y)x + (- 135 + 18 x + 27 y)y)y
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty7}
\begin{paste}{XPolynomialXmpPageEmpty7}{XPolynomialXmpPagePatch7}
\pastebutton{XPolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{qr := pr^3\free{pr }\bound{qr }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch8}
\begin{paste}{XPolynomialXmpPageFull8}{XPolynomialXmpPageEmpty8}
\pastebutton{XPolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{qd := pd^3\free{pd }\bound{qd }}
\indentrel{3}\begin{verbatim}
   (8)
                                 2
     - 125 + 150 x + 225 y - 60 x  - 90 x y - 90 y x
   + 
            2      3       2                     2
     - 135 y  + 8 x  + 12 x y + 12 x y x + 18 x y
   + 
           2                  2        3
     12 y x  + 18 y x y + 18 y x + 27 y
           Type: XDistributedPolynomial(Symbol,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty8}
\begin{paste}{XPolynomialXmpPageEmpty8}{XPolynomialXmpPagePatch8}
\pastebutton{XPolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{qd := pd^3\free{pd }\bound{qd }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch9}
\begin{paste}{XPolynomialXmpPageFull9}{XPolynomialXmpPageEmpty9}
\pastebutton{XPolynomialXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{trunc(qd,2)\free{qd }}
\indentrel{3}\begin{verbatim}
   (9)
                                 2
     - 125 + 150 x + 225 y - 60 x  - 90 x y - 90 y x
   + 
            2
     - 135 y
           Type: XDistributedPolynomial(Symbol,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty9}
\begin{paste}{XPolynomialXmpPageEmpty9}{XPolynomialXmpPagePatch9}
\pastebutton{XPolynomialXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{trunc(qd,2)\free{qd }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch10}
\begin{paste}{XPolynomialXmpPageFull10}{XPolynomialXmpPageEmpty10}
\pastebutton{XPolynomialXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{trunc(qr,2)\free{qr }}
\indentrel{3}\begin{verbatim}
   (10)
   - 125 + (150 - 60 x - 90 y)x + (225 - 90 x - 135 y)y
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty10}
\begin{paste}{XPolynomialXmpPageEmpty10}{XPolynomialXmpPagePatch10}
\pastebutton{XPolynomialXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{trunc(qr,2)\free{qr }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch11}
\begin{paste}{XPolynomialXmpPageFull11}{XPolynomialXmpPageEmpty11}
\pastebutton{XPolynomialXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{Word := FreeMonoid Symbol\bound{Word }}
\indentrel{3}\begin{verbatim}
   (11)  FreeMonoid(Symbol)
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty11}
\begin{paste}{XPolynomialXmpPageEmpty11}{XPolynomialXmpPagePatch11}
\pastebutton{XPolynomialXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{Word := FreeMonoid Symbol\bound{Word }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch12}
\begin{paste}{XPolynomialXmpPageFull12}{XPolynomialXmpPageEmpty12}
\pastebutton{XPolynomialXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{w: Word := x*y^2\free{Word }\bound{w }}
\indentrel{3}\begin{verbatim}
            2
   (12)  x y
                               Type: FreeMonoid(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty12}
\begin{paste}{XPolynomialXmpPageEmpty12}{XPolynomialXmpPagePatch12}
\pastebutton{XPolynomialXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{w: Word := x*y^2\free{Word }\bound{w }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch13}
\begin{paste}{XPolynomialXmpPageFull13}{XPolynomialXmpPageEmpty13}
\pastebutton{XPolynomialXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{rquo(qr,w)\free{qr }\free{w }}
\indentrel{3}\begin{verbatim}
   (13)  18
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty13}
\begin{paste}{XPolynomialXmpPageEmpty13}{XPolynomialXmpPagePatch13}
\pastebutton{XPolynomialXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{rquo(qr,w)\free{qr }\free{w }}
\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPagePatch14}
\begin{paste}{XPolynomialXmpPageFull14}{XPolynomialXmpPageEmpty14}
\pastebutton{XPolynomialXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{sh(pr,w::poly)\free{pr }\free{w }}
\indentrel{3}\begin{verbatim}
   (14)
   2 x y y x + (2 x y x + ((- 5 + 4 x + 3 y)x + 9 x y)y)y
                             Type: XPolynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty14}
\begin{paste}{XPolynomialXmpPageEmpty14}{XPolynomialXmpPagePatch14}
\pastebutton{XPolynomialXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{sh(pr,w::poly)\free{pr }\free{w }}
\end{paste}\end{patch}

