\begin{patch}{UnivariatePolynomialXmpPagePatch1}
\begin{paste}{UnivariatePolynomialXmpPageFull1}{UnivariatePolynomialXmpPageEmpty1}
\pastebutton{UnivariatePolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{(p,q) : UP(x,INT)\bound{pdec }\bound{qdec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty1}
\begin{paste}{UnivariatePolynomialXmpPageEmpty1}{UnivariatePolynomialXmpPagePatch1}
\pastebutton{UnivariatePolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{(p,q) : UP(x,INT)\bound{pdec }\bound{qdec }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch2}
\begin{paste}{UnivariatePolynomialXmpPageFull2}{UnivariatePolynomialXmpPageEmpty2}
\pastebutton{UnivariatePolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{p := (3*x-1)**2 * (2*x + 8)\free{pdec }\bound{p }}
\indentrel{3}\begin{verbatim}
           3      2
   (2)  18x  + 60x  - 46x + 8
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty2}
\begin{paste}{UnivariatePolynomialXmpPageEmpty2}{UnivariatePolynomialXmpPagePatch2}
\pastebutton{UnivariatePolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{p := (3*x-1)**2 * (2*x + 8)\free{pdec }\bound{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch3}
\begin{paste}{UnivariatePolynomialXmpPageFull3}{UnivariatePolynomialXmpPageEmpty3}
\pastebutton{UnivariatePolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{q := (1 - 6*x + 9*x**2)**2\free{qdec }\bound{q }}
\indentrel{3}\begin{verbatim}
           4       3      2
   (3)  81x  - 108x  + 54x  - 12x + 1
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty3}
\begin{paste}{UnivariatePolynomialXmpPageEmpty3}{UnivariatePolynomialXmpPagePatch3}
\pastebutton{UnivariatePolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{q := (1 - 6*x + 9*x**2)**2\free{qdec }\bound{q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch4}
\begin{paste}{UnivariatePolynomialXmpPageFull4}{UnivariatePolynomialXmpPageEmpty4}
\pastebutton{UnivariatePolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{p**2 + p*q\free{p q }}
\indentrel{3}\begin{verbatim}
   (4)
          7        6        5         4        3        2
     1458x  + 3240x  - 7074x  + 10584x  - 9282x  + 4120x
   + 
     - 878x + 72
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty4}
\begin{paste}{UnivariatePolynomialXmpPageEmpty4}{UnivariatePolynomialXmpPagePatch4}
\pastebutton{UnivariatePolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{p**2 + p*q\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch5}
\begin{paste}{UnivariatePolynomialXmpPageFull5}{UnivariatePolynomialXmpPageEmpty5}
\pastebutton{UnivariatePolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{leadingCoefficient p\free{p }}
\indentrel{3}\begin{verbatim}
   (5)  18
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty5}
\begin{paste}{UnivariatePolynomialXmpPageEmpty5}{UnivariatePolynomialXmpPagePatch5}
\pastebutton{UnivariatePolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{leadingCoefficient p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch6}
\begin{paste}{UnivariatePolynomialXmpPageFull6}{UnivariatePolynomialXmpPageEmpty6}
\pastebutton{UnivariatePolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{degree p\free{p }}
\indentrel{3}\begin{verbatim}
   (6)  3
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty6}
\begin{paste}{UnivariatePolynomialXmpPageEmpty6}{UnivariatePolynomialXmpPagePatch6}
\pastebutton{UnivariatePolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{degree p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch7}
\begin{paste}{UnivariatePolynomialXmpPageFull7}{UnivariatePolynomialXmpPageEmpty7}
\pastebutton{UnivariatePolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{reductum p\free{p }}
\indentrel{3}\begin{verbatim}
           2
   (7)  60x  - 46x + 8
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty7}
\begin{paste}{UnivariatePolynomialXmpPageEmpty7}{UnivariatePolynomialXmpPagePatch7}
\pastebutton{UnivariatePolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{reductum p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch8}
\begin{paste}{UnivariatePolynomialXmpPageFull8}{UnivariatePolynomialXmpPageEmpty8}
\pastebutton{UnivariatePolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{gcd(p,q)\free{p q }}
\indentrel{3}\begin{verbatim}
          2
   (8)  9x  - 6x + 1
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty8}
\begin{paste}{UnivariatePolynomialXmpPageEmpty8}{UnivariatePolynomialXmpPagePatch8}
\pastebutton{UnivariatePolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{gcd(p,q)\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch9}
\begin{paste}{UnivariatePolynomialXmpPageFull9}{UnivariatePolynomialXmpPageEmpty9}
\pastebutton{UnivariatePolynomialXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{lcm(p,q)\free{p q }}
\indentrel{3}\begin{verbatim}
            5       4       3       2
   (9)  162x  + 432x  - 756x  + 408x  - 94x + 8
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty9}
\begin{paste}{UnivariatePolynomialXmpPageEmpty9}{UnivariatePolynomialXmpPagePatch9}
\pastebutton{UnivariatePolynomialXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{lcm(p,q)\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch10}
\begin{paste}{UnivariatePolynomialXmpPageFull10}{UnivariatePolynomialXmpPageEmpty10}
\pastebutton{UnivariatePolynomialXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{resultant(p,q)\free{p q }}
\indentrel{3}\begin{verbatim}
   (10)  0
                               Type: NonNegativeInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty10}
\begin{paste}{UnivariatePolynomialXmpPageEmpty10}{UnivariatePolynomialXmpPagePatch10}
\pastebutton{UnivariatePolynomialXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{resultant(p,q)\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch11}
\begin{paste}{UnivariatePolynomialXmpPageFull11}{UnivariatePolynomialXmpPageEmpty11}
\pastebutton{UnivariatePolynomialXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{D p\free{p }}
\indentrel{3}\begin{verbatim}
            2
   (11)  54x  + 120x - 46
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty11}
\begin{paste}{UnivariatePolynomialXmpPageEmpty11}{UnivariatePolynomialXmpPagePatch11}
\pastebutton{UnivariatePolynomialXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{D p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch12}
\begin{paste}{UnivariatePolynomialXmpPageFull12}{UnivariatePolynomialXmpPageEmpty12}
\pastebutton{UnivariatePolynomialXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{p(2)\free{p }}
\indentrel{3}\begin{verbatim}
   (12)  300
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty12}
\begin{paste}{UnivariatePolynomialXmpPageEmpty12}{UnivariatePolynomialXmpPagePatch12}
\pastebutton{UnivariatePolynomialXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{p(2)\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch13}
\begin{paste}{UnivariatePolynomialXmpPageFull13}{UnivariatePolynomialXmpPageEmpty13}
\pastebutton{UnivariatePolynomialXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{p(q)\free{p q }}
\indentrel{3}\begin{verbatim}
   (13)
             12            11            10            9
     9565938x   - 38263752x   + 70150212x   - 77944680x
   + 
              8            7            6           5
     58852170x  - 32227632x  + 13349448x  - 4280688x
   + 
             4          3         2
     1058184x  - 192672x  + 23328x  - 1536x + 40
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty13}
\begin{paste}{UnivariatePolynomialXmpPageEmpty13}{UnivariatePolynomialXmpPagePatch13}
\pastebutton{UnivariatePolynomialXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{p(q)\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch14}
\begin{paste}{UnivariatePolynomialXmpPageFull14}{UnivariatePolynomialXmpPageEmpty14}
\pastebutton{UnivariatePolynomialXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{q(p)\free{p q }}
\indentrel{3}\begin{verbatim}
   (14)
             12             11             10
     8503056x   + 113374080x   + 479950272x
   + 
               9              8             7
     404997408x  - 1369516896x  - 626146848x
   + 
                6              5              4
     2939858712x  - 2780728704x  + 1364312160x
   + 
                 3            2
     - 396838872x  + 69205896x  - 6716184x + 279841
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty14}
\begin{paste}{UnivariatePolynomialXmpPageEmpty14}{UnivariatePolynomialXmpPagePatch14}
\pastebutton{UnivariatePolynomialXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{q(p)\free{p q }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch15}
\begin{paste}{UnivariatePolynomialXmpPageFull15}{UnivariatePolynomialXmpPageEmpty15}
\pastebutton{UnivariatePolynomialXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{l := coefficients p\free{p }\bound{l }}
\indentrel{3}\begin{verbatim}
   (15)  [18,60,- 46,8]
                                     Type: List Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty15}
\begin{paste}{UnivariatePolynomialXmpPageEmpty15}{UnivariatePolynomialXmpPagePatch15}
\pastebutton{UnivariatePolynomialXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{l := coefficients p\free{p }\bound{l }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch16}
\begin{paste}{UnivariatePolynomialXmpPageFull16}{UnivariatePolynomialXmpPageEmpty16}
\pastebutton{UnivariatePolynomialXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{reduce(gcd,l)\free{l }}
\indentrel{3}\begin{verbatim}
   (16)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty16}
\begin{paste}{UnivariatePolynomialXmpPageEmpty16}{UnivariatePolynomialXmpPagePatch16}
\pastebutton{UnivariatePolynomialXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{reduce(gcd,l)\free{l }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch17}
\begin{paste}{UnivariatePolynomialXmpPageFull17}{UnivariatePolynomialXmpPageEmpty17}
\pastebutton{UnivariatePolynomialXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{content p\free{p }}
\indentrel{3}\begin{verbatim}
   (17)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty17}
\begin{paste}{UnivariatePolynomialXmpPageEmpty17}{UnivariatePolynomialXmpPagePatch17}
\pastebutton{UnivariatePolynomialXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{content p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch18}
\begin{paste}{UnivariatePolynomialXmpPageFull18}{UnivariatePolynomialXmpPageEmpty18}
\pastebutton{UnivariatePolynomialXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{ux := (x**4+2*x+3)::UP(x,INT)\bound{ux }}
\indentrel{3}\begin{verbatim}
          4
   (18)  x  + 2x + 3
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty18}
\begin{paste}{UnivariatePolynomialXmpPageEmpty18}{UnivariatePolynomialXmpPagePatch18}
\pastebutton{UnivariatePolynomialXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{ux := (x**4+2*x+3)::UP(x,INT)\bound{ux }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch19}
\begin{paste}{UnivariatePolynomialXmpPageFull19}{UnivariatePolynomialXmpPageEmpty19}
\pastebutton{UnivariatePolynomialXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{vectorise(ux,5)\free{ux }}
\indentrel{3}\begin{verbatim}
   (19)  [3,2,0,0,1]
                                   Type: Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty19}
\begin{paste}{UnivariatePolynomialXmpPageEmpty19}{UnivariatePolynomialXmpPagePatch19}
\pastebutton{UnivariatePolynomialXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{vectorise(ux,5)\free{ux }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch20}
\begin{paste}{UnivariatePolynomialXmpPageFull20}{UnivariatePolynomialXmpPageEmpty20}
\pastebutton{UnivariatePolynomialXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{squareTerms(p) ==
  reduce(+,[t**2 for t in monomials p])
\bound{squareTerms }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty20}
\begin{paste}{UnivariatePolynomialXmpPageEmpty20}{UnivariatePolynomialXmpPagePatch20}
\pastebutton{UnivariatePolynomialXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{squareTerms(p) ==
  reduce(+,[t**2 for t in monomials p])
\bound{squareTerms }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch21}
\begin{paste}{UnivariatePolynomialXmpPageFull21}{UnivariatePolynomialXmpPageEmpty21}
\pastebutton{UnivariatePolynomialXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{p\free{p }}
\indentrel{3}\begin{verbatim}
            3      2
   (21)  18x  + 60x  - 46x + 8
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty21}
\begin{paste}{UnivariatePolynomialXmpPageEmpty21}{UnivariatePolynomialXmpPagePatch21}
\pastebutton{UnivariatePolynomialXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{p\free{p }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch22}
\begin{paste}{UnivariatePolynomialXmpPageFull22}{UnivariatePolynomialXmpPageEmpty22}
\pastebutton{UnivariatePolynomialXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{squareTerms p\free{p }\free{squareTerms }}
\indentrel{3}\begin{verbatim}
             6        4        2
   (22)  324x  + 3600x  + 2116x  + 64
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty22}
\begin{paste}{UnivariatePolynomialXmpPageEmpty22}{UnivariatePolynomialXmpPagePatch22}
\pastebutton{UnivariatePolynomialXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{squareTerms p\free{p }\free{squareTerms }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch23}
\begin{paste}{UnivariatePolynomialXmpPageFull23}{UnivariatePolynomialXmpPageEmpty23}
\pastebutton{UnivariatePolynomialXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{(r,s) : UP(a1,FRAC INT)\bound{rdec }\bound{sdec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty23}
\begin{paste}{UnivariatePolynomialXmpPageEmpty23}{UnivariatePolynomialXmpPagePatch23}
\pastebutton{UnivariatePolynomialXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{(r,s) : UP(a1,FRAC INT)\bound{rdec }\bound{sdec }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch24}
\begin{paste}{UnivariatePolynomialXmpPageFull24}{UnivariatePolynomialXmpPageEmpty24}
\pastebutton{UnivariatePolynomialXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{r := a1**2 - 2/3\free{rdec }\bound{r }}
\indentrel{3}\begin{verbatim}
           2   2
   (24)  a1  - Ä
               3
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty24}
\begin{paste}{UnivariatePolynomialXmpPageEmpty24}{UnivariatePolynomialXmpPagePatch24}
\pastebutton{UnivariatePolynomialXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{r := a1**2 - 2/3\free{rdec }\bound{r }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch25}
\begin{paste}{UnivariatePolynomialXmpPageFull25}{UnivariatePolynomialXmpPageEmpty25}
\pastebutton{UnivariatePolynomialXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{s := a1 + 4\free{sdec }\bound{s }}
\indentrel{3}\begin{verbatim}
   (25)  a1 + 4
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty25}
\begin{paste}{UnivariatePolynomialXmpPageEmpty25}{UnivariatePolynomialXmpPagePatch25}
\pastebutton{UnivariatePolynomialXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{s := a1 + 4\free{sdec }\bound{s }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch26}
\begin{paste}{UnivariatePolynomialXmpPageFull26}{UnivariatePolynomialXmpPageEmpty26}
\pastebutton{UnivariatePolynomialXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{r quo s\free{r s }}
\indentrel{3}\begin{verbatim}
   (26)  a1 - 4
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty26}
\begin{paste}{UnivariatePolynomialXmpPageEmpty26}{UnivariatePolynomialXmpPagePatch26}
\pastebutton{UnivariatePolynomialXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{r quo s\free{r s }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch27}
\begin{paste}{UnivariatePolynomialXmpPageFull27}{UnivariatePolynomialXmpPageEmpty27}
\pastebutton{UnivariatePolynomialXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{r rem s\free{r s }}
\indentrel{3}\begin{verbatim}
         46
   (27)  ÄÄ
          3
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty27}
\begin{paste}{UnivariatePolynomialXmpPageEmpty27}{UnivariatePolynomialXmpPagePatch27}
\pastebutton{UnivariatePolynomialXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{r rem s\free{r s }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch28}
\begin{paste}{UnivariatePolynomialXmpPageFull28}{UnivariatePolynomialXmpPageEmpty28}
\pastebutton{UnivariatePolynomialXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{d := divide(r, s)\free{r s }\bound{d }}
\indentrel{3}\begin{verbatim}
                                      46
   (28)  [quotient= a1 - 4,remainder= ÄÄ]
                                       3
Type: Record(quotient: UnivariatePolynomial(a1,Fraction Integer),remainder: UnivariatePolynomial(a1,Fraction Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty28}
\begin{paste}{UnivariatePolynomialXmpPageEmpty28}{UnivariatePolynomialXmpPagePatch28}
\pastebutton{UnivariatePolynomialXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{d := divide(r, s)\free{r s }\bound{d }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch29}
\begin{paste}{UnivariatePolynomialXmpPageFull29}{UnivariatePolynomialXmpPageEmpty29}
\pastebutton{UnivariatePolynomialXmpPageFull29}{\hidepaste}
\tab{5}\spadcommand{r - (d.quotient * s + d.remainder)\free{r s d }}
\indentrel{3}\begin{verbatim}
   (29)  0
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty29}
\begin{paste}{UnivariatePolynomialXmpPageEmpty29}{UnivariatePolynomialXmpPagePatch29}
\pastebutton{UnivariatePolynomialXmpPageEmpty29}{\showpaste}
\tab{5}\spadcommand{r - (d.quotient * s + d.remainder)\free{r s d }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch30}
\begin{paste}{UnivariatePolynomialXmpPageFull30}{UnivariatePolynomialXmpPageEmpty30}
\pastebutton{UnivariatePolynomialXmpPageFull30}{\hidepaste}
\tab{5}\spadcommand{integrate r\free{r }}
\indentrel{3}\begin{verbatim}
         1   3   2
   (30)  Ä a1  - Ä a1
         3       3
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty30}
\begin{paste}{UnivariatePolynomialXmpPageEmpty30}{UnivariatePolynomialXmpPagePatch30}
\pastebutton{UnivariatePolynomialXmpPageEmpty30}{\showpaste}
\tab{5}\spadcommand{integrate r\free{r }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch31}
\begin{paste}{UnivariatePolynomialXmpPageFull31}{UnivariatePolynomialXmpPageEmpty31}
\pastebutton{UnivariatePolynomialXmpPageFull31}{\hidepaste}
\tab{5}\spadcommand{integrate s\free{s }}
\indentrel{3}\begin{verbatim}
         1   2
   (31)  Ä a1  + 4a1
         2
        Type: UnivariatePolynomial(a1,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty31}
\begin{paste}{UnivariatePolynomialXmpPageEmpty31}{UnivariatePolynomialXmpPagePatch31}
\pastebutton{UnivariatePolynomialXmpPageEmpty31}{\showpaste}
\tab{5}\spadcommand{integrate s\free{s }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch32}
\begin{paste}{UnivariatePolynomialXmpPageFull32}{UnivariatePolynomialXmpPageEmpty32}
\pastebutton{UnivariatePolynomialXmpPageFull32}{\hidepaste}
\tab{5}\spadcommand{t : UP(a1,FRAC POLY INT)\bound{tdec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty32}
\begin{paste}{UnivariatePolynomialXmpPageEmpty32}{UnivariatePolynomialXmpPagePatch32}
\pastebutton{UnivariatePolynomialXmpPageEmpty32}{\showpaste}
\tab{5}\spadcommand{t : UP(a1,FRAC POLY INT)\bound{tdec }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch33}
\begin{paste}{UnivariatePolynomialXmpPageFull33}{UnivariatePolynomialXmpPageEmpty33}
\pastebutton{UnivariatePolynomialXmpPageFull33}{\hidepaste}
\tab{5}\spadcommand{t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)\free{tdec }\bound{t }}
\indentrel{3}\begin{verbatim}
                         2
           2    1      b1  - b1
   (33)  a1  - ÄÄ a1 + ÄÄÄÄÄÄÄÄ
               b2       b2 + 3
Type: UnivariatePolynomial(a1,Fraction Polynomial Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty33}
\begin{paste}{UnivariatePolynomialXmpPageEmpty33}{UnivariatePolynomialXmpPagePatch33}
\pastebutton{UnivariatePolynomialXmpPageEmpty33}{\showpaste}
\tab{5}\spadcommand{t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)\free{tdec }\bound{t }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch34}
\begin{paste}{UnivariatePolynomialXmpPageFull34}{UnivariatePolynomialXmpPageEmpty34}
\pastebutton{UnivariatePolynomialXmpPageFull34}{\hidepaste}
\tab{5}\spadcommand{u : FRAC POLY INT := t\bound{u }\free{t }}
\indentrel{3}\begin{verbatim}
           2  2      2           2
         a1 b2  + (b1  - b1 + 3a1  - a1)b2 - 3a1
   (34)  ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
                          2
                        b2  + 3b2
                      Type: Fraction Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty34}
\begin{paste}{UnivariatePolynomialXmpPageEmpty34}{UnivariatePolynomialXmpPagePatch34}
\pastebutton{UnivariatePolynomialXmpPageEmpty34}{\showpaste}
\tab{5}\spadcommand{u : FRAC POLY INT := t\bound{u }\free{t }}
\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPagePatch35}
\begin{paste}{UnivariatePolynomialXmpPageFull35}{UnivariatePolynomialXmpPageEmpty35}
\pastebutton{UnivariatePolynomialXmpPageFull35}{\hidepaste}
\tab{5}\spadcommand{u :: UP(b1,?)\free{u }}
\indentrel{3}\begin{verbatim}
                                    2
            1     2      1        a1 b2 - a1
   (35)  ÄÄÄÄÄÄ b1  - ÄÄÄÄÄÄ b1 + ÄÄÄÄÄÄÄÄÄÄ
         b2 + 3       b2 + 3          b2
Type: UnivariatePolynomial(b1,Fraction Polynomial Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{UnivariatePolynomialXmpPageEmpty35}
\begin{paste}{UnivariatePolynomialXmpPageEmpty35}{UnivariatePolynomialXmpPagePatch35}
\pastebutton{UnivariatePolynomialXmpPageEmpty35}{\showpaste}
\tab{5}\spadcommand{u :: UP(b1,?)\free{u }}
\end{paste}\end{patch}

