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|
\begin{patch}{LazardSetSolvingPackageXmpPagePatch1}
\begin{paste}{LazardSetSolvingPackageXmpPageFull1}{LazardSetSolvingPackageXmpPageEmpty1}
\pastebutton{LazardSetSolvingPackageXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\indentrel{3}\begin{verbatim}
(1) Integer
Type: Domain
\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: Domain
\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: Domain
\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: Domain
\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(Integer,O
rderedVariableList [b1,x,y,z,t,v,u,w]))
Type: Domain
\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],OrderedVariable
List [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial
(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]))
Type: Domain
\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 [b
1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Intege
r,OrderedVariableList [b1,x,y,z,t,v,u,w]),RegularTriang
ularSet(Integer,IndexedExponents OrderedVariableList [b
1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w]
,NewSparseMultivariatePolynomial(Integer,OrderedVariabl
eList [b1,x,y,z,t,v,u,w])),SquareFreeRegularTriangularS
et(Integer,IndexedExponents OrderedVariableList [b1,x,y
,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewS
parseMultivariatePolynomial(Integer,OrderedVariableList
[b1,x,y,z,t,v,u,w])))
Type: Domain
\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}
|
