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\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 - 2y x + (y + 6y)x - 6y x + 9y
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 - 6x y - 2x y + 9y + 6x 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 + (- 2a b y + 2a )x + b y - 2b 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 + (- 2a b x - 2b)y + a x + 2a 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 + (- 2x y b + 2x)a + y b - 2y 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 - 2z - 2 3 4y + z + 2z + 1 2 - 4z - 4
x + �������� x + ����������������� x + �������� x
y 2 y
y
+
4
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 - 2y x + 2x - 4y x
�� z + �������������������� z
2 2
y y
+
2 4 3 2 2 2
y x - 2y x + (4y + 1)x - 4y x + 4y
���������������������������������������
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 4y + 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}
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