\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)  - 4 z + 4 y x + 16 x  + 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)  2 z y  + 4 x + 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)  2 z x  - 2 y  - 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)  2 z x  - 2 y  - 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  + 2 x  - - x  + - z - -,
                2      2     8
     4   29  3   1  2   7        9     1     2         1
    x  + -- x  - - y  - - z x - -- x - -, z y  + 2 x + -,
          4      8      4       16     4               2
     2       2       1     2    2   1
    y x + 4 x  - z + -, z x  - y  - - x,
                     4              2
     2      2      2   1     3
    z  - 4 y  + 2 x  - - 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}

