\begin{patch}{LazardSetSolvingPackageXmpPagePatch1}
\begin{paste}{LazardSetSolvingPackageXmpPageFull1}{LazardSetSolvingPackageXmpPageEmpty1}
\pastebutton{LazardSetSolvingPackageXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\indentrel{3}\begin{verbatim}
   (1)  Integer
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty1}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty1}{LazardSetSolvingPackageXmpPagePatch1}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch2}
\begin{paste}{LazardSetSolvingPackageXmpPageFull2}{LazardSetSolvingPackageXmpPageEmpty2}
\pastebutton{LazardSetSolvingPackageXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{ls : List Symbol := [b1,x,y,z,t,v,u,w]\bound{ls }}
\indentrel{3}\begin{verbatim}
   (2)  [b1, x, y, z, t, v, u, w]
                                     Type: List(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty2}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty2}{LazardSetSolvingPackageXmpPagePatch2}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{ls : List Symbol := [b1,x,y,z,t,v,u,w]\bound{ls }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch3}
\begin{paste}{LazardSetSolvingPackageXmpPageFull3}{LazardSetSolvingPackageXmpPageEmpty3}
\pastebutton{LazardSetSolvingPackageXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\indentrel{3}\begin{verbatim}
   (3)  OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty3}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty3}{LazardSetSolvingPackageXmpPagePatch3}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch4}
\begin{paste}{LazardSetSolvingPackageXmpPageFull4}{LazardSetSolvingPackageXmpPageEmpty4}
\pastebutton{LazardSetSolvingPackageXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\indentrel{3}\begin{verbatim}
   (4)
   IndexedExponents
      OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty4}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty4}{LazardSetSolvingPackageXmpPagePatch4}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch5}
\begin{paste}{LazardSetSolvingPackageXmpPageFull5}{LazardSetSolvingPackageXmpPageEmpty5}
\pastebutton{LazardSetSolvingPackageXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
\indentrel{3}\begin{verbatim}
   (5)
   NewSparseMultivariatePolynomial
      Integer
  ,
      OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty5}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty5}{LazardSetSolvingPackageXmpPagePatch5}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch6}
\begin{paste}{LazardSetSolvingPackageXmpPageFull6}{LazardSetSolvingPackageXmpPageEmpty6}
\pastebutton{LazardSetSolvingPackageXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{b1: P := 'b1\free{P }\bound{b1 }}
\indentrel{3}\begin{verbatim}
   (6)  b1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty6}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty6}{LazardSetSolvingPackageXmpPagePatch6}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{b1: P := 'b1\free{P }\bound{b1 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch7}
\begin{paste}{LazardSetSolvingPackageXmpPageFull7}{LazardSetSolvingPackageXmpPageEmpty7}
\pastebutton{LazardSetSolvingPackageXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }}
\indentrel{3}\begin{verbatim}
   (7)  x
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty7}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty7}{LazardSetSolvingPackageXmpPagePatch7}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch8}
\begin{paste}{LazardSetSolvingPackageXmpPageFull8}{LazardSetSolvingPackageXmpPageEmpty8}
\pastebutton{LazardSetSolvingPackageXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }}
\indentrel{3}\begin{verbatim}
   (8)  y
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty8}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty8}{LazardSetSolvingPackageXmpPagePatch8}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch9}
\begin{paste}{LazardSetSolvingPackageXmpPageFull9}{LazardSetSolvingPackageXmpPageEmpty9}
\pastebutton{LazardSetSolvingPackageXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }}
\indentrel{3}\begin{verbatim}
   (9)  z
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty9}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty9}{LazardSetSolvingPackageXmpPagePatch9}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch10}
\begin{paste}{LazardSetSolvingPackageXmpPageFull10}{LazardSetSolvingPackageXmpPageEmpty10}
\pastebutton{LazardSetSolvingPackageXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }}
\indentrel{3}\begin{verbatim}
   (10)  t
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty10}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty10}{LazardSetSolvingPackageXmpPagePatch10}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch11}
\begin{paste}{LazardSetSolvingPackageXmpPageFull11}{LazardSetSolvingPackageXmpPageEmpty11}
\pastebutton{LazardSetSolvingPackageXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{u: P := 'u\free{P }\bound{u }}
\indentrel{3}\begin{verbatim}
   (11)  u
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty11}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty11}{LazardSetSolvingPackageXmpPagePatch11}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{u: P := 'u\free{P }\bound{u }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch12}
\begin{paste}{LazardSetSolvingPackageXmpPageFull12}{LazardSetSolvingPackageXmpPageEmpty12}
\pastebutton{LazardSetSolvingPackageXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{v: P := 'v\free{P }\bound{v }}
\indentrel{3}\begin{verbatim}
   (12)  v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty12}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty12}{LazardSetSolvingPackageXmpPagePatch12}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{v: P := 'v\free{P }\bound{v }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch13}
\begin{paste}{LazardSetSolvingPackageXmpPageFull13}{LazardSetSolvingPackageXmpPageEmpty13}
\pastebutton{LazardSetSolvingPackageXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{w: P := 'w\free{P }\bound{w }}
\indentrel{3}\begin{verbatim}
   (13)  w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty13}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty13}{LazardSetSolvingPackageXmpPagePatch13}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{w: P := 'w\free{P }\bound{w }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch14}
\begin{paste}{LazardSetSolvingPackageXmpPageFull14}{LazardSetSolvingPackageXmpPageEmpty14}
\pastebutton{LazardSetSolvingPackageXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{T := REGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }}
\indentrel{3}\begin{verbatim}
   (14)
   RegularTriangularSet
      Integer
  ,
      IndexedExponents
         OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      NewSparseMultivariatePolynomial
         Integer
     ,
         OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty14}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty14}{LazardSetSolvingPackageXmpPagePatch14}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{T := REGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch15}
\begin{paste}{LazardSetSolvingPackageXmpPageFull15}{LazardSetSolvingPackageXmpPageEmpty15}
\pastebutton{LazardSetSolvingPackageXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{p0 := b1 + y + z - t - w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p0 }}
\indentrel{3}\begin{verbatim}
   (15)  b1 + y + z - t - w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty15}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty15}{LazardSetSolvingPackageXmpPagePatch15}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{p0 := b1 + y + z - t - w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p0 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch16}
\begin{paste}{LazardSetSolvingPackageXmpPageFull16}{LazardSetSolvingPackageXmpPageEmpty16}
\pastebutton{LazardSetSolvingPackageXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{p1 := 2*z*u + 2*y*v + 2*t*w - 2*w^2 - w - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p1 }}
\indentrel{3}\begin{verbatim}
                                    2
   (16)  2 v y + 2 u z + 2 w t - 2 w  - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty16}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty16}{LazardSetSolvingPackageXmpPagePatch16}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{p1 := 2*z*u + 2*y*v + 2*t*w - 2*w^2 - w - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p1 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch17}
\begin{paste}{LazardSetSolvingPackageXmpPageFull17}{LazardSetSolvingPackageXmpPageEmpty17}
\pastebutton{LazardSetSolvingPackageXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{p2 := 3*z*u^2 + 3*y*v^2 - 3*t*w^2 + 3*w^3 + 3*w^2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p2 }}
\indentrel{3}\begin{verbatim}
   (17)
      2       2          2            3      2
   3 v y + 3 u z + (- 3 w  - 1)t + 3 w  + 3 w  + 4 w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty17}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty17}{LazardSetSolvingPackageXmpPagePatch17}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{p2 := 3*z*u^2 + 3*y*v^2 - 3*t*w^2 + 3*w^3 + 3*w^2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p2 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch18}
\begin{paste}{LazardSetSolvingPackageXmpPageFull18}{LazardSetSolvingPackageXmpPageEmpty18}
\pastebutton{LazardSetSolvingPackageXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{p3 := 6*x*z*v - 6*t*w^2 + 6*w^3 - 3*t*w + 6*w^2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p3 }}
\indentrel{3}\begin{verbatim}
   (18)
                   2                  3      2
   6 v z x + (- 6 w  - 3 w - 1)t + 6 w  + 6 w  + 4 w
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty18}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty18}{LazardSetSolvingPackageXmpPagePatch18}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{p3 := 6*x*z*v - 6*t*w^2 + 6*w^3 - 3*t*w + 6*w^2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p3 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch19}
\begin{paste}{LazardSetSolvingPackageXmpPageFull19}{LazardSetSolvingPackageXmpPageEmpty19}
\pastebutton{LazardSetSolvingPackageXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{p4 := 4*z*u^3+ 4*y*v^3+ 4*t*w^3- 4*w^4 - 6*w^3+ 4*t*w- 10*w^2- w- 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p4 }}
\indentrel{3}\begin{verbatim}
   (19)
        3       3        3              4      3       2
     4 v y + 4 u z + (4 w  + 4 w)t - 4 w  - 6 w  - 10 w
   + 
     - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty19}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty19}{LazardSetSolvingPackageXmpPagePatch19}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{p4 := 4*z*u^3+ 4*y*v^3+ 4*t*w^3- 4*w^4 - 6*w^3+ 4*t*w- 10*w^2- w- 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p4 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch20}
\begin{paste}{LazardSetSolvingPackageXmpPageFull20}{LazardSetSolvingPackageXmpPageEmpty20}
\pastebutton{LazardSetSolvingPackageXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{p5 := 8*x*z*u*v +8*t*w^3 -8*w^4 +4*t*w^2 -12*w^3 +4*t*w -14*w^2 -3*w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p5 }}
\indentrel{3}\begin{verbatim}
   (20)
                     3      2              4       3
     8 u v z x + (8 w  + 4 w  + 4 w)t - 8 w  - 12 w
   + 
           2
     - 14 w  - 3 w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty20}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty20}{LazardSetSolvingPackageXmpPagePatch20}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{p5 := 8*x*z*u*v +8*t*w^3 -8*w^4 +4*t*w^2 -12*w^3 +4*t*w -14*w^2 -3*w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p5 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch21}
\begin{paste}{LazardSetSolvingPackageXmpPageFull21}{LazardSetSolvingPackageXmpPageEmpty21}
\pastebutton{LazardSetSolvingPackageXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{p6 := 12*x*z*v^2+12*t*w^3 -12*w^4 +12*t*w^2 -18*w^3 +8*t*w -14*w^2 -w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p6 }}
\indentrel{3}\begin{verbatim}
   (21)
         2           3       2               4       3
     12 v z x + (12 w  + 12 w  + 8 w)t - 12 w  - 18 w
   + 
           2
     - 14 w  - w - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty21}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty21}{LazardSetSolvingPackageXmpPagePatch21}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{p6 := 12*x*z*v^2+12*t*w^3 -12*w^4 +12*t*w^2 -18*w^3 +8*t*w -14*w^2 -w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p6 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch22}
\begin{paste}{LazardSetSolvingPackageXmpPageFull22}{LazardSetSolvingPackageXmpPageEmpty22}
\pastebutton{LazardSetSolvingPackageXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{p7 := -24*t*w^3 + 24*w^4 - 24*t*w^2 + 36*w^3 - 8*t*w + 26*w^2 + 7*w + 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p7 }}
\indentrel{3}\begin{verbatim}
   (22)
            3       2               4       3       2
     (- 24 w  - 24 w  - 8 w)t + 24 w  + 36 w  + 26 w
   + 
     7 w + 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty22}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty22}{LazardSetSolvingPackageXmpPagePatch22}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{p7 := -24*t*w^3 + 24*w^4 - 24*t*w^2 + 36*w^3 - 8*t*w + 26*w^2 + 7*w + 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p7 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch23}
\begin{paste}{LazardSetSolvingPackageXmpPageFull23}{LazardSetSolvingPackageXmpPageEmpty23}
\pastebutton{LazardSetSolvingPackageXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{lp := [p0, p1, p2, p3, p4, p5, p6, p7]\free{p0 }\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\free{p7 }\bound{lp }}
\indentrel{3}\begin{verbatim}
   (23)
   [b1 + y + z - t - w,
                               2
    2 v y + 2 u z + 2 w t - 2 w  - w - 1,
       2       2          2            3      2
    3 v y + 3 u z + (- 3 w  - 1)t + 3 w  + 3 w  + 4 w,
                    2                  3      2
    6 v z x + (- 6 w  - 3 w - 1)t + 6 w  + 6 w  + 4 w,

          3       3        3              4      3       2
       4 v y + 4 u z + (4 w  + 4 w)t - 4 w  - 6 w  - 10 w
     + 
       - w - 1
     ,

                       3      2              4       3
       8 u v z x + (8 w  + 4 w  + 4 w)t - 8 w  - 12 w
     + 
             2
       - 14 w  - 3 w - 1
     ,

           2           3       2               4       3
       12 v z x + (12 w  + 12 w  + 8 w)t - 12 w  - 18 w
     + 
             2
       - 14 w  - w - 1
     ,

              3       2               4       3       2
       (- 24 w  - 24 w  - 8 w)t + 24 w  + 36 w  + 26 w
     + 
       7 w + 1
     ]
Type: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w])))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty23}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty23}{LazardSetSolvingPackageXmpPagePatch23}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{lp := [p0, p1, p2, p3, p4, p5, p6, p7]\free{p0 }\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\free{p7 }\bound{lp }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch24}
\begin{paste}{LazardSetSolvingPackageXmpPageFull24}{LazardSetSolvingPackageXmpPageEmpty24}
\pastebutton{LazardSetSolvingPackageXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }}
\indentrel{3}\begin{verbatim}
   (24)
   [{w + 1, u, v, t + 1, b1 + y + z + 2},
    {w + 1, v, t + 1, z, b1 + y + 2},
    {w + 1, t + 1, z, y, b1 + 2},
    {w + 1, v - u, t + 1, y + z, x, b1 + 2},
    {w + 1, u, t + 1, y, x, b1 + z + 2},

           5        4       3      2
     {144 w  + 216 w  + 96 w  + 6 w  - 11 w - 1,

              2                   5        4       3
         (12 w  + 9 w + 1)u - 72 w  - 108 w  - 42 w
       + 
              2
         - 9 w  - 3 w
       ,
           2                   4       3       2
      (12 w  + 9 w + 1)v + 36 w  + 54 w  + 18 w ,

              3       2               4       3       2
         (24 w  + 24 w  + 8 w)t - 24 w  - 36 w  - 26 w
       + 
         - 7 w - 1
       ,

                       2                   2
         (12 u v - 12 u )z + (12 w v + 12 w  + 4)t
       + 
                          4       3      2
         (3 w - 5)v + 36 w  + 42 w  + 6 w  - 16 w
       ,
                                 2
      2 v y + 2 u z + 2 w t - 2 w  - w - 1,
                      2                  3      2
      6 v z x + (- 6 w  - 3 w - 1)t + 6 w  + 6 w  + 4 w,
      b1 + y + z - t - w}
     ]
Type: List(RegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty24}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty24}{LazardSetSolvingPackageXmpPagePatch24}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch25}
\begin{paste}{LazardSetSolvingPackageXmpPageFull25}{LazardSetSolvingPackageXmpPageEmpty25}
\pastebutton{LazardSetSolvingPackageXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{[coHeight(ts) for ts in lts]\free{lts }}
\indentrel{3}\begin{verbatim}
   (25)  [3, 3, 3, 2, 2, 0]
                         Type: List(NonNegativeInteger)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty25}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty25}{LazardSetSolvingPackageXmpPagePatch25}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{[coHeight(ts) for ts in lts]\free{lts }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch26}
\begin{paste}{LazardSetSolvingPackageXmpPageFull26}{LazardSetSolvingPackageXmpPageEmpty26}
\pastebutton{LazardSetSolvingPackageXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{ST := SREGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{ST }}
\indentrel{3}\begin{verbatim}
   (26)
   SquareFreeRegularTriangularSet
      Integer
  ,
      IndexedExponents
         OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      NewSparseMultivariatePolynomial
         Integer
     ,
         OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty26}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty26}{LazardSetSolvingPackageXmpPagePatch26}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{ST := SREGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{ST }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch27}
\begin{paste}{LazardSetSolvingPackageXmpPageFull27}{LazardSetSolvingPackageXmpPageEmpty27}
\pastebutton{LazardSetSolvingPackageXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{pack := LAZM3PK(R,E,V,P,T,ST)\free{R }\free{E }\free{V }\free{P }\free{T }\free{ST }\bound{pack }}
\indentrel{3}\begin{verbatim}
   (27)
   LazardSetSolvingPackage
      Integer
  ,
      IndexedExponents
         OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      NewSparseMultivariatePolynomial
         Integer
     ,
         OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      RegularTriangularSet
         Integer
     ,
         IndexedExponents
            OrderedVariableList([b1, x, y, z, t, v, u, w])
     ,
         OrderedVariableList([b1, x, y, z, t, v, u, w])
     ,
         NewSparseMultivariatePolynomial
            Integer
        ,
            OrderedVariableList([b1, x, y, z, t, v, u, w])
  ,
      SquareFreeRegularTriangularSet
         Integer
     ,
         IndexedExponents
            OrderedVariableList([b1, x, y, z, t, v, u, w])
     ,
         OrderedVariableList([b1, x, y, z, t, v, u, w])
     ,
         NewSparseMultivariatePolynomial
            Integer
        ,
            OrderedVariableList([b1, x, y, z, t, v, u, w])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty27}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty27}{LazardSetSolvingPackageXmpPagePatch27}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{pack := LAZM3PK(R,E,V,P,T,ST)\free{R }\free{E }\free{V }\free{P }\free{T }\free{ST }\bound{pack }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch28}
\begin{paste}{LazardSetSolvingPackageXmpPageFull28}{LazardSetSolvingPackageXmpPageEmpty28}
\pastebutton{LazardSetSolvingPackageXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lp,false)$pack\free{lp }\free{pack }}
\indentrel{3}\begin{verbatim}
   (28)
   [{w + 1, t + 1, z, y, b1 + 2},
    {w + 1, v, t + 1, z, b1 + y + 2},
    {w + 1, u, v, t + 1, b1 + y + z + 2},
    {w + 1, v - u, t + 1, y + z, x, b1 + 2},
    {w + 1, u, t + 1, y, x, b1 + z + 2},

           5        4       3      2
     {144 w  + 216 w  + 96 w  + 6 w  - 11 w - 1,
              4       3       2
      u - 24 w  - 36 w  - 14 w  + w + 1,
                4       3       2
      3 v - 48 w  - 60 w  - 10 w  + 8 w + 2,
              4       3       2
      t - 24 w  - 36 w  - 14 w  - w + 1,
                    4         3         2
      486 z - 2772 w  - 4662 w  - 2055 w  + 30 w + 127,

                         4          3         2
         2916 y - 22752 w  - 30312 w  - 8220 w  + 2064 w
       + 
         1561
       ,
                    4         3        2
      356 x - 3696 w  - 4536 w  - 968 w  + 822 w + 371,

                          4          3          2
         2916 b1 - 30600 w  - 46692 w  - 20274 w  - 8076 w
       + 
         593
       }
     ]
Type: List(SquareFreeRegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty28}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty28}{LazardSetSolvingPackageXmpPagePatch28}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp,false)$pack\free{lp }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch29}
\begin{paste}{LazardSetSolvingPackageXmpPageFull29}{LazardSetSolvingPackageXmpPageEmpty29}
\pastebutton{LazardSetSolvingPackageXmpPageFull29}{\hidepaste}
\tab{5}\spadcommand{f0 := (w - v) ^ 2 + (u - t) ^ 2 - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f0 }}
\indentrel{3}\begin{verbatim}
          2            2            2    2
   (29)  t  - 2 u t + v  - 2 w v + u  + w  - 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty29}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty29}{LazardSetSolvingPackageXmpPagePatch29}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty29}{\showpaste}
\tab{5}\spadcommand{f0 := (w - v) ^ 2 + (u - t) ^ 2 - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f0 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch30}
\begin{paste}{LazardSetSolvingPackageXmpPageFull30}{LazardSetSolvingPackageXmpPageEmpty30}
\pastebutton{LazardSetSolvingPackageXmpPageFull30}{\hidepaste}
\tab{5}\spadcommand{f1 := t ^ 2 - v ^ 3\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f1 }}
\indentrel{3}\begin{verbatim}
          2    3
   (30)  t  - v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty30}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty30}{LazardSetSolvingPackageXmpPagePatch30}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty30}{\showpaste}
\tab{5}\spadcommand{f1 := t ^ 2 - v ^ 3\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f1 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch31}
\begin{paste}{LazardSetSolvingPackageXmpPageFull31}{LazardSetSolvingPackageXmpPageEmpty31}
\pastebutton{LazardSetSolvingPackageXmpPageFull31}{\hidepaste}
\tab{5}\spadcommand{f2 := 2 * t * (w - v) + 3 * v ^ 2 * (u - t)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f2 }}
\indentrel{3}\begin{verbatim}
               2                      2
   (31)  (- 3 v  - 2 v + 2 w)t + 3 u v
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty31}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty31}{LazardSetSolvingPackageXmpPagePatch31}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty31}{\showpaste}
\tab{5}\spadcommand{f2 := 2 * t * (w - v) + 3 * v ^ 2 * (u - t)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f2 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch32}
\begin{paste}{LazardSetSolvingPackageXmpPageFull32}{LazardSetSolvingPackageXmpPageEmpty32}
\pastebutton{LazardSetSolvingPackageXmpPageFull32}{\hidepaste}
\tab{5}\spadcommand{f3 := (3 * z * v ^ 2 - 1) * (2 * z * t - 1)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f3 }}
\indentrel{3}\begin{verbatim}
            2   2               2
   (32)  6 v t z  + (- 2 t - 3 v )z + 1
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty32}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty32}{LazardSetSolvingPackageXmpPagePatch32}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty32}{\showpaste}
\tab{5}\spadcommand{f3 := (3 * z * v ^ 2 - 1) * (2 * z * t - 1)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f3 }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch33}
\begin{paste}{LazardSetSolvingPackageXmpPageFull33}{LazardSetSolvingPackageXmpPageEmpty33}
\pastebutton{LazardSetSolvingPackageXmpPageFull33}{\hidepaste}
\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }}
\indentrel{3}\begin{verbatim}
   (33)
     2            2            2    2       2    3
   [t  - 2 u t + v  - 2 w v + u  + w  - 1, t  - v ,
          2                      2
    (- 3 v  - 2 v + 2 w)t + 3 u v ,
       2   2               2
    6 v t z  + (- 2 t - 3 v )z + 1]
Type: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w])))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty33}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty33}{LazardSetSolvingPackageXmpPagePatch33}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty33}{\showpaste}
\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch34}
\begin{paste}{LazardSetSolvingPackageXmpPageFull34}{LazardSetSolvingPackageXmpPageEmpty34}
\pastebutton{LazardSetSolvingPackageXmpPageFull34}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lf,true)$T\free{lf }\free{T }}
\indentrel{3}\begin{verbatim}
   (34)
   [
     {
              6            3        2                  4
         729 u  + (- 1458 w  + 729 w  - 4158 w - 1685)u
       + 
                  6         5         4         3        2
             729 w  - 1458 w  - 2619 w  - 4892 w  - 297 w
           + 
             5814 w + 427
        *
            2
           u
       + 
              8        7         6         5         4
         729 w  + 216 w  - 2900 w  - 2376 w  + 3870 w
       + 
               3         2
         4072 w  - 1188 w  - 1656 w + 529
       ,

                   4
             2187 u
           + 
                      3        2                   2
             (- 4374 w  - 972 w  - 12474 w - 2868)u
           + 
                   6         5          4         3
             2187 w  - 1944 w  - 10125 w  - 4800 w
           + 
                   2
             2501 w  + 4968 w - 1587
        *
           v
       + 
                3        2  2        6         5         4
         (1944 w  - 108 w )u  + 972 w  + 3024 w  - 1080 w
       + 
              3         2
         496 w  + 1116 w
       ,
          2                      2
      (3 v  + 2 v - 2 w)t - 3 u v ,
                           2  2             2
      ((4 v - 4 w)t - 6 u v )z  + (2 t + 3 v )z - 1}
     ]
Type: List(RegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty34}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty34}{LazardSetSolvingPackageXmpPagePatch34}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty34}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lf,true)$T\free{lf }\free{T }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch35}
\begin{paste}{LazardSetSolvingPackageXmpPageFull35}{LazardSetSolvingPackageXmpPageEmpty35}
\pastebutton{LazardSetSolvingPackageXmpPageFull35}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lf,false)$T\free{lf }\free{T }}
\indentrel{3}\begin{verbatim}
   (35)
   [
     {
              6            3        2                  4
         729 u  + (- 1458 w  + 729 w  - 4158 w - 1685)u
       + 
                  6         5         4         3        2
             729 w  - 1458 w  - 2619 w  - 4892 w  - 297 w
           + 
             5814 w + 427
        *
            2
           u
       + 
              8        7         6         5         4
         729 w  + 216 w  - 2900 w  - 2376 w  + 3870 w
       + 
               3         2
         4072 w  - 1188 w  - 1656 w + 529
       ,

                   4
             2187 u
           + 
                      3        2                   2
             (- 4374 w  - 972 w  - 12474 w - 2868)u
           + 
                   6         5          4         3
             2187 w  - 1944 w  - 10125 w  - 4800 w
           + 
                   2
             2501 w  + 4968 w - 1587
        *
           v
       + 
                3        2  2        6         5         4
         (1944 w  - 108 w )u  + 972 w  + 3024 w  - 1080 w
       + 
              3         2
         496 w  + 1116 w
       ,
          2                      2
      (3 v  + 2 v - 2 w)t - 3 u v ,
                           2  2             2
      ((4 v - 4 w)t - 6 u v )z  + (2 t + 3 v )z - 1}
     ,

          4      3       2
     {27 w  + 4 w  - 54 w  - 36 w + 23, u,
                       2
      (12 w + 2)v - 9 w  - 2 w + 9,
         2            2
      6 t  - 2 v - 3 w  + 2 w + 3, 2 t z - 1}
     ,

     {
                6          5          4           3
         59049 w  + 91854 w  - 45198 w  + 145152 w
       + 
                2
         63549 w  + 60922 w + 21420
       ,

                             5                   4
             31484448266904 w  - 18316865522574 w
           + 
                             3                  2
             23676995746098 w  + 6657857188965 w
           + 
             8904703998546 w + 3890631403260
        *
            2
           u
       + 
                         5                   4
         94262810316408 w  - 82887296576616 w
       + 
                         3                   2
         89801831438784 w  + 28141734167208 w
       + 
         38070359425432 w + 16003865949120
       ,

               2              2
         (243 w  + 36 w + 85)v
       + 
                2        3       2                      3
         (- 81 u  - 162 w  + 36 w  + 154 w + 72)v - 72 w
       + 
            2
         4 w
       ,
          2                      2
      (3 v  + 2 v - 2 w)t - 3 u v ,
                           2  2             2
      ((4 v - 4 w)t - 6 u v )z  + (2 t + 3 v )z - 1}
     ,

          4      3       2
     {27 w  + 4 w  - 54 w  - 36 w + 23, u,
                       2
      (12 w + 2)v - 9 w  - 2 w + 9,
         2            2               2
      6 t  - 2 v - 3 w  + 2 w + 3, 3 v z - 1}
     ]
Type: List(RegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty35}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty35}{LazardSetSolvingPackageXmpPagePatch35}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty35}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lf,false)$T\free{lf }\free{T }}
\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPagePatch36}
\begin{paste}{LazardSetSolvingPackageXmpPageFull36}{LazardSetSolvingPackageXmpPageEmpty36}
\pastebutton{LazardSetSolvingPackageXmpPageFull36}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lf,false)$pack\free{lf }\free{pack }}
\indentrel{3}\begin{verbatim}
   (36)
   [
     {
              6            3        2                  4
         729 u  + (- 1458 w  + 729 w  - 4158 w - 1685)u
       + 
                  6         5         4         3        2
             729 w  - 1458 w  - 2619 w  - 4892 w  - 297 w
           + 
             5814 w + 427
        *
            2
           u
       + 
              8        7         6         5         4
         729 w  + 216 w  - 2900 w  - 2376 w  + 3870 w
       + 
               3         2
         4072 w  - 1188 w  - 1656 w + 529
       ,

                   4
             2187 u
           + 
                      3        2                   2
             (- 4374 w  - 972 w  - 12474 w - 2868)u
           + 
                   6         5          4         3
             2187 w  - 1944 w  - 10125 w  - 4800 w
           + 
                   2
             2501 w  + 4968 w - 1587
        *
           v
       + 
                3        2  2        6         5         4
         (1944 w  - 108 w )u  + 972 w  + 3024 w  - 1080 w
       + 
              3         2
         496 w  + 1116 w
       ,
          2                      2
      (3 v  + 2 v - 2 w)t - 3 u v ,
                           2  2             2
      ((4 v - 4 w)t - 6 u v )z  + (2 t + 3 v )z - 1}
     ,

          2                   2
     {81 w  + 18 w + 28, 729 u  - 1890 w - 533,
          2
      81 v  + (- 162 w + 27)v - 72 w - 112,
      11881 t + (972 w + 2997)u v + (- 11448 w - 11536)u,

                          2
         641237934604288 z
       + 
                 (78614584763904 w + 26785578742272)u
               + 
                 236143618655616 w + 70221988585728
            *
               v
           + 
             (358520253138432 w + 101922133759488)u
           + 
             142598803536000 w + 54166419595008
        *
           z
       + 
         (32655103844499 w - 44224572465882)u v
       + 
         (43213900115457 w - 32432039102070)u
       }
     ,

          4      3       2
     {27 w  + 4 w  - 54 w  - 36 w + 23, u,
                   3      2
      218 v - 162 w  + 3 w  + 160 w + 153,
           2       3       2
      109 t  - 27 w  - 54 w  + 63 w + 80,
                        3       2
      1744 z + (- 1458 w  + 27 w  + 1440 w + 505)t}
     ,

          4      3       2
     {27 w  + 4 w  - 54 w  - 36 w + 23, u,
                   3      2
      218 v - 162 w  + 3 w  + 160 w + 153,
           2       3       2
      109 t  - 27 w  - 54 w  + 63 w + 80,
                    3      2
      1308 z + 162 w  - 3 w  - 814 w - 153}
     ,

           4        3         2
     {729 w  + 972 w  - 1026 w  + 1684 w + 765,
          2       2
      81 u  + 72 w  + 16 w - 72,
                   3        2
      702 v - 162 w  - 225 w  + 40 w - 99,
                      3        2
      11336 t + (324 w  - 603 w  - 1718 w - 1557)u,

                    2
         595003968 z
       + 
                              3              2
                 - 963325386 w  - 898607682 w
               + 
                 1516286466 w - 3239166186
            *
               u
           + 
                           3               2
             - 1579048992 w  - 1796454288 w
           + 
             2428328160 w - 4368495024
        *
           z
       + 
                         3               2
             9713133306 w  + 9678670317 w  - 16726834476 w
           + 
             28144233593
        *
           u
       }
     ]
Type: List(SquareFreeRegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([b1,x,y,z,t,v,u,w]))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{LazardSetSolvingPackageXmpPageEmpty36}
\begin{paste}{LazardSetSolvingPackageXmpPageEmpty36}{LazardSetSolvingPackageXmpPagePatch36}
\pastebutton{LazardSetSolvingPackageXmpPageEmpty36}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lf,false)$pack\free{lf }\free{pack }}
\end{paste}\end{patch}

