\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch1}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull1}{DistributedMultivariatePolynomialXmpPageEmpty1}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty1}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty1}{DistributedMultivariatePolynomialXmpPagePatch1}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch2}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull2}{DistributedMultivariatePolynomialXmpPageEmpty2}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }}
\indentrel{3}\begin{verbatim}
                 2       2
   (2)  - 4z + 4y x + 16x  + 1
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty2}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty2}{DistributedMultivariatePolynomialXmpPagePatch2}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch3}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull3}{DistributedMultivariatePolynomialXmpPageEmpty3}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }}
\indentrel{3}\begin{verbatim}
            2
   (3)  2z y  + 4x + 1
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty3}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty3}{DistributedMultivariatePolynomialXmpPagePatch3}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch4}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull4}{DistributedMultivariatePolynomialXmpPageEmpty4}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }}
\indentrel{3}\begin{verbatim}
            2     2
   (4)  2z x  - 2y  - x
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty4}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty4}{DistributedMultivariatePolynomialXmpPagePatch4}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch5}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull5}{DistributedMultivariatePolynomialXmpPageEmpty5}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }}
\indentrel{3}\begin{verbatim}
   (5)
   [
           1568  6   1264  5    6   4   182  3   2047  2
       z - ���� x  - ���� x  + ��� x  + ��� x  - ���� x
           2745       305      305      549       610
     + 
          103      2857
       - ���� x - �����
         2745     10980
     ,

        2    112  6    84  5   1264  4    13  3    84  2
       y  + ���� x  - ��� x  - ���� x  - ��� x  + ��� x
            2745      305       305      549      305
     + 
       1772       2
       ���� x + ����
       2745     2745
     ,
     7   29  6   17  4   11  3    1  2   15     1
    x  + �� x  - �� x  - �� x  + �� x  + �� x + �]
          4      16       8      32      16     4
Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty5}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty5}{DistributedMultivariatePolynomialXmpPagePatch5}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch6}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull6}{DistributedMultivariatePolynomialXmpPageEmpty6}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty6}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty6}{DistributedMultivariatePolynomialXmpPagePatch6}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch7}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull7}{DistributedMultivariatePolynomialXmpPageEmpty7}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }}
\indentrel{3}\begin{verbatim}
            2     2
   (7)  2z x  - 2y  - x
Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty7}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty7}{DistributedMultivariatePolynomialXmpPagePatch7}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }}
\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch8}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull8}{DistributedMultivariatePolynomialXmpPageEmpty8}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }}
\indentrel{3}\begin{verbatim}
   (8)
     4     3   3  2   1     1
   [y  + 2x  - � x  + � z - �,
               2      2     8
     4   29  3   1  2   7        9     1     2        1
    x  + �� x  - � y  - � z x - �� x - �, z y  + 2x + �,
          4      8      4       16     4              2
     2      2       1     2    2   1
    y x + 4x  - z + �, z x  - y  - � x,
                    4              2
     2     2     2   1     3
    z  - 4y  + 2x  - � z - � x]
                     4     2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty8}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty8}{DistributedMultivariatePolynomialXmpPagePatch8}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }}
\end{paste}\end{patch}