\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 - 컴컴 x - 컴컴 x + 컴� x + 컴� x - 컴컴 x 2745 305 305 549 610 + 103 2857 - 컴컴 x - 컴컴� 2745 10980 , 2 112 6 84 5 1264 4 13 3 84 2 y + 컴컴 x - 컴� x - 컴컴 x - 컴� x + 컴� x 2745 305 305 549 305 + 1772 2 컴컴 x + 컴컴 2745 2745 , 7 29 6 17 4 11 3 1 2 15 1 x + 컴 x - 컴 x - 컴 x + 컴 x + 컴 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 + 컴 x - � y - � z x - 컴 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}