\begin{patch}{MultivariatePolynomialXmpPagePatch1}
\begin{paste}{MultivariatePolynomialXmpPageFull1}{MultivariatePolynomialXmpPageEmpty1}
\pastebutton{MultivariatePolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2\bound{m }}
\indentrel{3}\begin{verbatim}
         4      3 3     6        2      4       2
   (1)  x  - 2 y x  + (y  + 6 y)x  - 6 y x + 9 y
            Type: MultivariatePolynomial([x,y],Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty1}
\begin{paste}{MultivariatePolynomialXmpPageEmpty1}{MultivariatePolynomialXmpPagePatch1}
\pastebutton{MultivariatePolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2\bound{m }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch2}
\begin{paste}{MultivariatePolynomialXmpPageFull2}{MultivariatePolynomialXmpPageEmpty2}
\pastebutton{MultivariatePolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{m :: MPOLY([y,x],INT)\free{m }}
\indentrel{3}\begin{verbatim}
         2 6        4      3 3      2      2     4
   (2)  x y  - 6 x y  - 2 x y  + 9 y  + 6 x y + x
            Type: MultivariatePolynomial([y,x],Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty2}
\begin{paste}{MultivariatePolynomialXmpPageEmpty2}{MultivariatePolynomialXmpPagePatch2}
\pastebutton{MultivariatePolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{m :: MPOLY([y,x],INT)\free{m }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch3}
\begin{paste}{MultivariatePolynomialXmpPageFull3}{MultivariatePolynomialXmpPageEmpty3}
\pastebutton{MultivariatePolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{p : MPOLY([x,y],POLY INT)\bound{pdec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty3}
\begin{paste}{MultivariatePolynomialXmpPageEmpty3}{MultivariatePolynomialXmpPagePatch3}
\pastebutton{MultivariatePolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{p : MPOLY([x,y],POLY INT)\bound{pdec }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch4}
\begin{paste}{MultivariatePolynomialXmpPageFull4}{MultivariatePolynomialXmpPageEmpty4}
\pastebutton{MultivariatePolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{p := (a^2*x - b*y^2 + 1)^2\free{pdec }\bound{p }}
\indentrel{3}\begin{verbatim}
         4 2         2   2      2      2 4        2
   (4)  a x  + (- 2 a b y  + 2 a )x + b y  - 2 b y  + 1
Type: MultivariatePolynomial([x,y],Polynomial(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty4}
\begin{paste}{MultivariatePolynomialXmpPageEmpty4}{MultivariatePolynomialXmpPagePatch4}
\pastebutton{MultivariatePolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{p := (a^2*x - b*y^2 + 1)^2\free{pdec }\bound{p }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch5}
\begin{paste}{MultivariatePolynomialXmpPageFull5}{MultivariatePolynomialXmpPageEmpty5}
\pastebutton{MultivariatePolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{p :: POLY INT\free{p }\bound{prev }}
\indentrel{3}\begin{verbatim}
         2 4         2           2    4 2      2
   (5)  b y  + (- 2 a b x - 2 b)y  + a x  + 2 a x + 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty5}
\begin{paste}{MultivariatePolynomialXmpPageEmpty5}{MultivariatePolynomialXmpPagePatch5}
\pastebutton{MultivariatePolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{p :: POLY INT\free{p }\bound{prev }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch6}
\begin{paste}{MultivariatePolynomialXmpPageFull6}{MultivariatePolynomialXmpPageEmpty6}
\pastebutton{MultivariatePolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{\% :: MPOLY([a,b],POLY INT)\free{prev }}
\indentrel{3}\begin{verbatim}
         2 4           2         2    4 2      2
   (6)  x a  + (- 2 x y b + 2 x)a  + y b  - 2 y b + 1
Type: MultivariatePolynomial([a,b],Polynomial(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty6}
\begin{paste}{MultivariatePolynomialXmpPageEmpty6}{MultivariatePolynomialXmpPagePatch6}
\pastebutton{MultivariatePolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{\% :: MPOLY([a,b],POLY INT)\free{prev }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch7}
\begin{paste}{MultivariatePolynomialXmpPageFull7}{MultivariatePolynomialXmpPageEmpty7}
\pastebutton{MultivariatePolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{q : UP(x, FRAC MPOLY([y,z],INT))\bound{qdec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty7}
\begin{paste}{MultivariatePolynomialXmpPageEmpty7}{MultivariatePolynomialXmpPagePatch7}
\pastebutton{MultivariatePolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{q : UP(x, FRAC MPOLY([y,z],INT))\bound{qdec }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch8}
\begin{paste}{MultivariatePolynomialXmpPageFull8}{MultivariatePolynomialXmpPageEmpty8}
\pastebutton{MultivariatePolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{q := (x^2 - x*(z+1)/y +2)^2\free{qdec }\bound{q }}
\indentrel{3}\begin{verbatim}
   (8)
                            2    2
      4   - 2 z - 2  3   4 y  + z  + 2 z + 1  2
     x  + --------- x  + ------------------- x
              y                    2
                                  y
   + 
     - 4 z - 4
     --------- x + 4
         y
Type: UnivariatePolynomial(x,Fraction(MultivariatePolynomial([y,z],Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty8}
\begin{paste}{MultivariatePolynomialXmpPageEmpty8}{MultivariatePolynomialXmpPagePatch8}
\pastebutton{MultivariatePolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{q := (x^2 - x*(z+1)/y +2)^2\free{qdec }\bound{q }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch9}
\begin{paste}{MultivariatePolynomialXmpPageFull9}{MultivariatePolynomialXmpPageEmpty9}
\pastebutton{MultivariatePolynomialXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{q :: UP(z, FRAC MPOLY([x,y],INT))\free{q }}
\indentrel{3}\begin{verbatim}
   (9)
      2             3      2
     x   2   - 2 y x  + 2 x  - 4 y x
     -- z  + ----------------------- z
      2                  2
     y                  y
   + 
      2 4        3       2      2              2
     y x  - 2 y x  + (4 y  + 1)x  - 4 y x + 4 y
     -------------------------------------------
                           2
                          y
Type: UnivariatePolynomial(z,Fraction(MultivariatePolynomial([x,y],Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty9}
\begin{paste}{MultivariatePolynomialXmpPageEmpty9}{MultivariatePolynomialXmpPagePatch9}
\pastebutton{MultivariatePolynomialXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{q :: UP(z, FRAC MPOLY([x,y],INT))\free{q }}
\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPagePatch10}
\begin{paste}{MultivariatePolynomialXmpPageFull10}{MultivariatePolynomialXmpPageEmpty10}
\pastebutton{MultivariatePolynomialXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{q :: MPOLY([x,z], FRAC UP(y,INT))\free{q }}
\indentrel{3}\begin{verbatim}
   (10)
                                             2
      4      2     2  3     1  2    2     4 y  + 1  2
     x  + (- - z - -)x  + (-- z  + -- z + --------)x
             y     y        2       2         2
                           y       y         y
   + 
        4     4
     (- - z - -)x + 4
        y     y
Type: MultivariatePolynomial([x,z],Fraction(UnivariatePolynomial(y,Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{MultivariatePolynomialXmpPageEmpty10}
\begin{paste}{MultivariatePolynomialXmpPageEmpty10}{MultivariatePolynomialXmpPagePatch10}
\pastebutton{MultivariatePolynomialXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{q :: MPOLY([x,z], FRAC UP(y,INT))\free{q }}
\end{paste}\end{patch}

