\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,OrderedVariable
  List([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(OrderedVa
  riableList([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1
  ,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Intege
  r,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)  2v y + 2u z + 2w t - 2w  - 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}
           2      2         2           3     2
   (17)  3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w
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}
                       2                3     2
   (18)  6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w
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
   4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - 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      2
     8u v z x + (8w  + 4w  + 4w)t - 8w  - 12w  - 14w  - 3w
   + 
     - 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      2
     12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w
   + 
     - 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
   (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 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)
                                               2
   [b1 + y + z - t - w, 2v y + 2u z + 2w t - 2w  - w - 1,
      2      2         2           3     2
    3v y + 3u z + (- 3w  - 1)t + 3w  + 3w  + 4w,
                  2                3     2
    6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w,
      3      3       3            4     3      2
    4v y + 4u z + (4w  + 4w)t - 4w  - 6w  - 10w  - w - 1,

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

          2          3      2             4      3      2
       12v z x + (12w  + 12w  + 8w)t - 12w  - 18w  - 14w
     + 
       - w - 1
     ,
          3      2             4      3      2
    (- 24w  - 24w  - 8w)t + 24w  + 36w  + 26w  + 7w + 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
     {144w  + 216w  + 96w  + 6w  - 11w - 1,
          2                 5       4      3     2
      (12w  + 9w + 1)u - 72w  - 108w  - 42w  - 9w  - 3w,
          2                 4      3      2
      (12w  + 9w + 1)v + 36w  + 54w  + 18w ,
          3      2             4      3      2
      (24w  + 24w  + 8w)t - 24w  - 36w  - 26w  - 7w - 1,

                     2                 2
         (12u v - 12u )z + (12w v + 12w  + 4)t + (3w - 5)v
       + 
            4      3     2
         36w  + 42w  + 6w  - 16w
       ,
                             2
      2v y + 2u z + 2w t - 2w  - w - 1,
                    2                3     2
      6v z x + (- 6w  - 3w - 1)t + 6w  + 6w  + 4w,
      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])),OrderedVariab
  leList([b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynom
  ial(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(Ordere
  dVariableList([b1,x,y,z,t,v,u,w])),OrderedVariableList(
  [b1,x,y,z,t,v,u,w]),NewSparseMultivariatePolynomial(Int
  eger,OrderedVariableList([b1,x,y,z,t,v,u,w])),RegularTr
  iangularSet(Integer,IndexedExponents(OrderedVariableLis
  t([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,
  v,u,w]),NewSparseMultivariatePolynomial(Integer,Ordered
  VariableList([b1,x,y,z,t,v,u,w]))),SquareFreeRegularTri
  angularSet(Integer,IndexedExponents(OrderedVariableList
  ([b1,x,y,z,t,v,u,w])),OrderedVariableList([b1,x,y,z,t,v
  ,u,w]),NewSparseMultivariatePolynomial(Integer,OrderedV
  ariableList([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
     {144w  + 216w  + 96w  + 6w  - 11w - 1,
             4      3      2
      u - 24w  - 36w  - 14w  + w + 1,
              4      3      2
      3v - 48w  - 60w  - 10w  + 8w + 2,
             4      3      2
      t - 24w  - 36w  - 14w  - w + 1,
                  4        3        2
      486z - 2772w  - 4662w  - 2055w  + 30w + 127,
                    4         3        2
      2916y - 22752w  - 30312w  - 8220w  + 2064w + 1561,
                  4        3       2
      356x - 3696w  - 4536w  - 968w  + 822w + 371,
                     4         3         2
      2916b1 - 30600w  - 46692w  - 20274w  - 8076w + 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  - 2u t + v  - 2w 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)  (- 3v  - 2v + 2w)t + 3u 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)  6v t z  + (- 2t - 3v )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  - 2u t + v  - 2w v + u  + w  - 1, t  - v ,
         2                   2
    (- 3v  - 2v + 2w)t + 3u v ,
      2   2             2
    6v t z  + (- 2t - 3v )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
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
                 6        5        4        3       2
             729w  - 1458w  - 2619w  - 4892w  - 297w
           + 
             5814w + 427
        *
            2
           u
       + 
             8       7        6        5        4        3
         729w  + 216w  - 2900w  - 2376w  + 3870w  + 4072w
       + 
                2
         - 1188w  - 1656w + 529
       ,

                  4           3       2                  2
             2187u  + (- 4374w  - 972w  - 12474w - 2868)u
           + 
                  6        5         4        3        2
             2187w  - 1944w  - 10125w  - 4800w  + 2501w
           + 
             4968w - 1587
        *
           v
       + 
               3       2  2       6        5        4
         (1944w  - 108w )u  + 972w  + 3024w  - 1080w
       + 
             3        2
         496w  + 1116w
       ,
         2                   2
      (3v  + 2v - 2w)t - 3u v ,
                        2  2           2
      ((4v - 4w)t - 6u v )z  + (2t + 3v )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
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
                 6        5        4        3       2
             729w  - 1458w  - 2619w  - 4892w  - 297w
           + 
             5814w + 427
        *
            2
           u
       + 
             8       7        6        5        4        3
         729w  + 216w  - 2900w  - 2376w  + 3870w  + 4072w
       + 
                2
         - 1188w  - 1656w + 529
       ,

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

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

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

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

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

         4     3      2
     {27w  + 4w  - 54w  - 36w + 23, u,
                     2             2          2
      (12w + 2)v - 9w  - 2w + 9, 6t  - 2v - 3w  + 2w + 3,
        2
      3v 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
         729u  + (- 1458w  + 729w  - 4158w - 1685)u
       + 
                 6        5        4        3       2
             729w  - 1458w  - 2619w  - 4892w  - 297w
           + 
             5814w + 427
        *
            2
           u
       + 
             8       7        6        5        4        3
         729w  + 216w  - 2900w  - 2376w  + 3870w  + 4072w
       + 
                2
         - 1188w  - 1656w + 529
       ,

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

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

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

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

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

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

                   2
         595003968z
       + 
                             3             2
                 - 963325386w  - 898607682w  + 1516286466w
               + 
                 - 3239166186
            *
               u
           + 
                          3              2
             - 1579048992w  - 1796454288w  + 2428328160w
           + 
             - 4368495024
        *
           z
       + 
                        3              2
             9713133306w  + 9678670317w  - 16726834476w
           + 
             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}

