\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: Domain
\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 + x 2 + y 3
                              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 + x(- 20 + x 4 + y 6) + y(- 30 + x 6 + y 9)
                              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 + 2x + 3y
           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 - 20x - 30y + 4x  + 6x y + 6y x + 9y
           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
   + 
     x(150 + x(- 60 + x 8 + y 12) + y(- 90 + x 12 + y 18))
   + 
   y(225 + x(- 90 + x 12 + y 18) + y(- 135 + x 18 + y 27))
                              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                       2
     - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y
   + 
       3      2                   2        2
     8x  + 12x y + 12x y x + 18x y  + 12y x  + 18y x y
   + 
        2       3
     18y x + 27y
           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                       2
   - 125 + 150x + 225y - 60x  - 90x y - 90y x - 135y
           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 + x(150 + x(- 60) + y(- 90))
   + 
     y(225 + x(- 90) + y(- 135))
                              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 := OrderedFreeMonoid Symbol\bound{Word }}
\indentrel{3}\begin{verbatim}
   (11)  OrderedFreeMonoid Symbol
                                           Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{XPolynomialXmpPageEmpty11}
\begin{paste}{XPolynomialXmpPageEmpty11}{XPolynomialXmpPagePatch11}
\pastebutton{XPolynomialXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{Word := OrderedFreeMonoid 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: OrderedFreeMonoid 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)
   x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3
                              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}