\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}