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-rw-r--r--src/hyper/pages/LEXTRIPK.pht2553
1 files changed, 2553 insertions, 0 deletions
diff --git a/src/hyper/pages/LEXTRIPK.pht b/src/hyper/pages/LEXTRIPK.pht
new file mode 100644
index 00000000..18c3b7b9
--- /dev/null
+++ b/src/hyper/pages/LEXTRIPK.pht
@@ -0,0 +1,2553 @@
+\begin{patch}{LexTriangularPackageXmpPagePatch1}
+\begin{paste}{LexTriangularPackageXmpPageFull1}{LexTriangularPackageXmpPageEmpty1}
+\pastebutton{LexTriangularPackageXmpPageFull1}{\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}{LexTriangularPackageXmpPageEmpty1}
+\begin{paste}{LexTriangularPackageXmpPageEmpty1}{LexTriangularPackageXmpPagePatch1}
+\pastebutton{LexTriangularPackageXmpPageEmpty1}{\showpaste}
+\tab{5}\spadcommand{R := Integer\bound{R }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch2}
+\begin{paste}{LexTriangularPackageXmpPageFull2}{LexTriangularPackageXmpPageEmpty2}
+\pastebutton{LexTriangularPackageXmpPageFull2}{\hidepaste}
+\tab{5}\spadcommand{ls : List Symbol := [a,b,c,d,e,f]\bound{ls }}
+\indentrel{3}\begin{verbatim}
+ (2) [a,b,c,d,e,f]
+ Type: List Symbol
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty2}
+\begin{paste}{LexTriangularPackageXmpPageEmpty2}{LexTriangularPackageXmpPagePatch2}
+\pastebutton{LexTriangularPackageXmpPageEmpty2}{\showpaste}
+\tab{5}\spadcommand{ls : List Symbol := [a,b,c,d,e,f]\bound{ls }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch3}
+\begin{paste}{LexTriangularPackageXmpPageFull3}{LexTriangularPackageXmpPageEmpty3}
+\pastebutton{LexTriangularPackageXmpPageFull3}{\hidepaste}
+\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
+\indentrel{3}\begin{verbatim}
+ (3) OrderedVariableList [a,b,c,d,e,f]
+ Type: Domain
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty3}
+\begin{paste}{LexTriangularPackageXmpPageEmpty3}{LexTriangularPackageXmpPagePatch3}
+\pastebutton{LexTriangularPackageXmpPageEmpty3}{\showpaste}
+\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch4}
+\begin{paste}{LexTriangularPackageXmpPageFull4}{LexTriangularPackageXmpPageEmpty4}
+\pastebutton{LexTriangularPackageXmpPageFull4}{\hidepaste}
+\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
+\indentrel{3}\begin{verbatim}
+ (4)
+ NewSparseMultivariatePolynomial(Integer,OrderedVariable
+ List [a,b,c,d,e,f])
+ Type: Domain
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty4}
+\begin{paste}{LexTriangularPackageXmpPageEmpty4}{LexTriangularPackageXmpPagePatch4}
+\pastebutton{LexTriangularPackageXmpPageEmpty4}{\showpaste}
+\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch5}
+\begin{paste}{LexTriangularPackageXmpPageFull5}{LexTriangularPackageXmpPageEmpty5}
+\pastebutton{LexTriangularPackageXmpPageFull5}{\hidepaste}
+\tab{5}\spadcommand{p1: P := a*b*c*d*e*f - 1\free{P }\bound{p1 }}
+\indentrel{3}\begin{verbatim}
+ (5) f e d c b a - 1
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty5}
+\begin{paste}{LexTriangularPackageXmpPageEmpty5}{LexTriangularPackageXmpPagePatch5}
+\pastebutton{LexTriangularPackageXmpPageEmpty5}{\showpaste}
+\tab{5}\spadcommand{p1: P := a*b*c*d*e*f - 1\free{P }\bound{p1 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch6}
+\begin{paste}{LexTriangularPackageXmpPageFull6}{LexTriangularPackageXmpPageEmpty6}
+\pastebutton{LexTriangularPackageXmpPageFull6}{\hidepaste}
+\tab{5}\spadcommand{p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f\free{P }\bound{p2 }}
+\indentrel{3}\begin{verbatim}
+ (6)
+ ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty6}
+\begin{paste}{LexTriangularPackageXmpPageEmpty6}{LexTriangularPackageXmpPagePatch6}
+\pastebutton{LexTriangularPackageXmpPageEmpty6}{\showpaste}
+\tab{5}\spadcommand{p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f\free{P }\bound{p2 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch7}
+\begin{paste}{LexTriangularPackageXmpPageFull7}{LexTriangularPackageXmpPageEmpty7}
+\pastebutton{LexTriangularPackageXmpPageFull7}{\hidepaste}
+\tab{5}\spadcommand{p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f\free{P }\bound{p3 }}
+\indentrel{3}\begin{verbatim}
+ (7) (((d + f)c + f e)b + f e d)a + e d c b + f e d c
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty7}
+\begin{paste}{LexTriangularPackageXmpPageEmpty7}{LexTriangularPackageXmpPagePatch7}
+\pastebutton{LexTriangularPackageXmpPageEmpty7}{\showpaste}
+\tab{5}\spadcommand{p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f\free{P }\bound{p3 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch8}
+\begin{paste}{LexTriangularPackageXmpPageFull8}{LexTriangularPackageXmpPageEmpty8}
+\pastebutton{LexTriangularPackageXmpPageFull8}{\hidepaste}
+\tab{5}\spadcommand{p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f\free{P }\bound{p4 }}
+\indentrel{3}\begin{verbatim}
+ (8) ((c + f)b + f e)a + d c b + e d c + f e d
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty8}
+\begin{paste}{LexTriangularPackageXmpPageEmpty8}{LexTriangularPackageXmpPagePatch8}
+\pastebutton{LexTriangularPackageXmpPageEmpty8}{\showpaste}
+\tab{5}\spadcommand{p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f\free{P }\bound{p4 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch9}
+\begin{paste}{LexTriangularPackageXmpPageFull9}{LexTriangularPackageXmpPageEmpty9}
+\pastebutton{LexTriangularPackageXmpPageFull9}{\hidepaste}
+\tab{5}\spadcommand{p5: P := a*b + a*f + b*c + c*d + d*e + e*f\free{P }\bound{p5 }}
+\indentrel{3}\begin{verbatim}
+ (9) (b + f)a + c b + d c + e d + f e
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty9}
+\begin{paste}{LexTriangularPackageXmpPageEmpty9}{LexTriangularPackageXmpPagePatch9}
+\pastebutton{LexTriangularPackageXmpPageEmpty9}{\showpaste}
+\tab{5}\spadcommand{p5: P := a*b + a*f + b*c + c*d + d*e + e*f\free{P }\bound{p5 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch10}
+\begin{paste}{LexTriangularPackageXmpPageFull10}{LexTriangularPackageXmpPageEmpty10}
+\pastebutton{LexTriangularPackageXmpPageFull10}{\hidepaste}
+\tab{5}\spadcommand{p6: P := a + b + c + d + e + f\free{P }\bound{p6 }}
+\indentrel{3}\begin{verbatim}
+ (10) a + b + c + d + e + f
+Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty10}
+\begin{paste}{LexTriangularPackageXmpPageEmpty10}{LexTriangularPackageXmpPagePatch10}
+\pastebutton{LexTriangularPackageXmpPageEmpty10}{\showpaste}
+\tab{5}\spadcommand{p6: P := a + b + c + d + e + f\free{P }\bound{p6 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch11}
+\begin{paste}{LexTriangularPackageXmpPageFull11}{LexTriangularPackageXmpPageEmpty11}
+\pastebutton{LexTriangularPackageXmpPageFull11}{\hidepaste}
+\tab{5}\spadcommand{lp := [p1, p2, p3, p4, p5, p6]\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\bound{lp }}
+\indentrel{3}\begin{verbatim}
+ (11)
+ [f e d c b a - 1,
+ ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b,
+ (((d + f)c + f e)b + f e d)a + e d c b + f e d c,
+ ((c + f)b + f e)a + d c b + e d c + f e d,
+ (b + f)a + c b + d c + e d + f e,
+ a + b + c + d + e + f]
+Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty11}
+\begin{paste}{LexTriangularPackageXmpPageEmpty11}{LexTriangularPackageXmpPagePatch11}
+\pastebutton{LexTriangularPackageXmpPageEmpty11}{\showpaste}
+\tab{5}\spadcommand{lp := [p1, p2, p3, p4, p5, p6]\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\bound{lp }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch12}
+\begin{paste}{LexTriangularPackageXmpPageFull12}{LexTriangularPackageXmpPageEmpty12}
+\pastebutton{LexTriangularPackageXmpPageFull12}{\hidepaste}
+\tab{5}\spadcommand{lextripack := LEXTRIPK(R,ls)\free{R }\free{ls }\bound{lextripack }}
+\indentrel{3}\begin{verbatim}
+ (12) LexTriangularPackage(Integer,[a,b,c,d,e,f])
+ Type: Domain
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty12}
+\begin{paste}{LexTriangularPackageXmpPageEmpty12}{LexTriangularPackageXmpPagePatch12}
+\pastebutton{LexTriangularPackageXmpPageEmpty12}{\showpaste}
+\tab{5}\spadcommand{lextripack := LEXTRIPK(R,ls)\free{R }\free{ls }\bound{lextripack }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch13}
+\begin{paste}{LexTriangularPackageXmpPageFull13}{LexTriangularPackageXmpPageEmpty13}
+\pastebutton{LexTriangularPackageXmpPageFull13}{\hidepaste}
+\tab{5}\spadcommand{lg := groebner(lp)$lextripack\free{lp }\free{lextripack }\bound{lg }}
+\indentrel{3}\begin{verbatim}
+ (13)
+ [a + b + c + d + e + f,
+
+ 2
+ 3968379498283200b + 15873517993132800f b
+ +
+ 2
+ 3968379498283200d + 15873517993132800f d
+ +
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+ 3968379498283200f e - 15873517993132800f e
+ +
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+ +
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+ +
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+ +
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+ +
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+ +
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+ +
+ 13
+ - 365048404038768439269f
+ +
+ 7
+ - 292382820431504027669f - 2271898467631865497f
+ *
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+ +
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+ - 3988812642545399f + 10187423878429609997f
+ +
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+ +
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+ +
+ 14
+ - 1993494118301162145413f
+ +
+ 8 2
+ - 1596049742289689815053f - 11488171330159667449f
+ ,
+
+ (23810276989699200c - 23810276989699200f)b
+ +
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+ +
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+ +
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+ - 55557312975964800f e + 174608697924460800f e
+ +
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+ +
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+ +
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+ *
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+ +
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+ +
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+ +
+ 8 2
+ 18329944781867242497923f + 130258531002020420699f
+ ,
+
+ (7936758996566400d - 7936758996566400f)b
+ +
+ 3 5
+ - 7936758996566400f d - 7936758996566400f e
+ +
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+ +
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+ +
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+ +
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+ +
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+ +
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+ *
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+ +
+ 32
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+ +
+ 26
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+ +
+ 20
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+ +
+ 14
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+ +
+ 8 2
+ 2569858315395162617847f + 18326089487427735751f
+ ,
+
+ (11905138494849600e - 11905138494849600f)b
+ +
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+ +
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+ +
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+ +
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+ +
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+ +
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+ ,
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+ +
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+ +
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+ *
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+ +
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+ 197327352068200652911f + 1523373796389332143f
+ *
+ e
+ +
+ 44 38
+ 2679481081803026f - 6843392695421906608f
+ +
+ 32
+ - 1071020459642646913578f
+ +
+ 26 20
+ - 1339789169692041240060f - 852746750910750210f
+ +
+ 14
+ 1339105101971878401312f
+ +
+ 8 2
+ 1071900289758712984762f + 7555239072072727756f
+ ,
+
+ 6
+ (11905138494849600f - 11905138494849600)d
+ +
+ 2 5 3 4
+ - 7936758996566400f e + 31747035986265600f e
+ +
+ 4 3
+ - 31747035986265600f e
+ +
+ 11 5 2
+ (- 420648226818019200f - 404774708824886400f )e
+ +
+ 42 36
+ 15336187600889f - 39169739565161107f
+ +
+ 30
+ - 6127176127489690827f
+ +
+ 24
+ - 7217708742310509615f
+ +
+ 18 12
+ 538628483890722735f + 7506804353843507643f
+ +
+ 6
+ 5886160769782607203f + 63576108396535879
+ *
+ e
+ +
+ 43 37
+ 71737781777066f - 183218856207557938f
+ +
+ 31 25
+ - 28672874271132276078f - 35625223686939812010f
+ +
+ 19 13
+ 164831339634084390f + 35724160423073052642f
+ +
+ 7
+ 28627022578664910622f + 187459987029680506f
+ ,
+
+ 6 5
+ 1322793166094400e - 3968379498283200f e
+ +
+ 2 4 3 3
+ 3968379498283200f e - 5291172664377600f e
+ +
+ 10 4 2
+ (- 230166010900425600f - 226197631402142400f )e
+ +
+ 47
+ - 152375364610443885f
+ +
+ 41
+ 389166626064854890415f
+ +
+ 35
+ 60906097841360558987335f
+ +
+ 29
+ 76167367934608798697275f
+ +
+ 23
+ 27855066785995181125f
+ +
+ 17
+ - 76144952817052723145495f
+ +
+ 11
+ - 60933629892463517546975f
+ +
+ 5
+ - 411415071682002547795f
+ *
+ e
+ +
+ 42 36
+ - 209493533143822f + 535045979490560586f
+ +
+ 30 24
+ 83737947964973553146f + 104889507084213371570f
+ +
+ 18 12
+ 167117997269207870f - 104793725781390615514f
+ +
+ 6
+ - 83842685189903180394f - 569978796672974242
+ ,
+
+ 6 3
+ (25438330117200f + 25438330117200)e
+ +
+ 7 2
+ (76314990351600f + 76314990351600f)e
+ +
+ 44 38
+ - 1594966552735f + 4073543370415745f
+ +
+ 32 26
+ 637527159231148925f + 797521176113606525f
+ +
+ 20 14
+ 530440941097175f - 797160527306433145f
+ +
+ 8 2
+ - 638132320196044965f - 4510507167940725f
+ *
+ e
+ +
+ 45 39
+ - 6036376800443f + 15416903421476909f
+ +
+ 33 27
+ 2412807646192304449f + 3017679923028013705f
+ +
+ 21 15
+ 1422320037411955f - 3016560402417843941f
+ +
+ 9 3
+ - 2414249368183033161f - 16561862361763873f
+ ,
+
+ 12 2
+ (1387545279120f - 1387545279120)e
+ +
+ 43 37
+ 4321823003f - 11037922310209f
+ +
+ 31 25
+ - 1727510711947989f - 2165150991154425f
+ +
+ 19 13
+ - 5114342560755f + 2162682824948601f
+ +
+ 7
+ 1732620732685741f + 13506088516033f
+ *
+ e
+ +
+ 44 38
+ 24177661775f - 61749727185325f
+ +
+ 32 26
+ - 9664106795754225f - 12090487758628245f
+ +
+ 20 14
+ - 8787672733575f + 12083693383005045f
+ +
+ 8 2
+ 9672870290826025f + 68544102808525f
+ ,
+
+ 48 42 36 30 18
+ f - 2554f - 399710f - 499722f + 499722f
+ +
+ 12 6
+ 399710f + 2554f - 1
+ ]
+Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty13}
+\begin{paste}{LexTriangularPackageXmpPageEmpty13}{LexTriangularPackageXmpPagePatch13}
+\pastebutton{LexTriangularPackageXmpPageEmpty13}{\showpaste}
+\tab{5}\spadcommand{lg := groebner(lp)$lextripack\free{lp }\free{lextripack }\bound{lg }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch14}
+\begin{paste}{LexTriangularPackageXmpPageFull14}{LexTriangularPackageXmpPageEmpty14}
+\pastebutton{LexTriangularPackageXmpPageFull14}{\hidepaste}
+\tab{5}\spadcommand{lexTriangular(lg,false)$lextripack\free{lg }\free{lextripack }}
+\indentrel{3}\begin{verbatim}
+ (14)
+ [
+ 6
+ {f + 1,
+ 6 5 2 4 3 3 4 2 5
+ e - 3f e + 3f e - 4f e + 3f e - 3f e - 1,
+ 2 5 3 4 4 3 5 2
+ 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f,
+ 2 5 3 4 4 3 5 2
+ 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f,
+ 2 5 3 4 4 3 5 2
+ a - f e + 3f e - 3f e + 4f e + 3e - 3f}
+ ,
+
+ 6 2 2
+ {f - 1, e - f, d - f, c + 4f c + f ,
+ 2
+ (c - f)b - f c - 5f , a + b + c + 3f}
+ ,
+ 6 2 2
+ {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f},
+
+ 6 2 2
+ {f - 1, e - f, d + 4f d + f ,
+ 2
+ (d - f)c - f d - 5f , b - f, a + c + d + 3f}
+ ,
+
+ {
+ 36 30 24 18 12
+ f - 2554f - 399709f - 502276f - 399709f
+ +
+ 6
+ - 2554f + 1
+ ,
+
+ 12 2
+ (161718564f - 161718564)e
+ +
+ 31 25 19
+ - 504205f + 1287737951f + 201539391380f
+ +
+ 13 7
+ 253982817368f + 201940704665f + 1574134601f
+ *
+ e
+ +
+ 32 26 20
+ - 2818405f + 7198203911f + 1126548149060f
+ +
+ 14 8 2
+ 1416530563364f + 1127377589345f + 7988820725f
+ ,
+
+ 6
+ (693772639560f - 693772639560)d
+ +
+ 2 5 3 4
+ - 462515093040f e + 1850060372160f e
+ +
+ 4 3
+ - 1850060372160f e
+ +
+ 11 5 2
+ (- 24513299931120f - 23588269745040f )e
+ +
+ 30 24
+ - 890810428f + 2275181044754f
+ +
+ 18 12
+ 355937263869776f + 413736880104344f
+ +
+ 6
+ 342849304487996f + 3704966481878
+ *
+ e
+ +
+ 31 25
+ - 4163798003f + 10634395752169f
+ +
+ 19 13
+ 1664161760192806f + 2079424391370694f
+ +
+ 7
+ 1668153650635921f + 10924274392693f
+ ,
+
+ 6 31
+ (12614047992f - 12614047992)c - 7246825f
+ +
+ 25 19
+ 18508536599f + 2896249516034f
+ +
+ 13 7
+ 3581539649666f + 2796477571739f - 48094301893f
+ ,
+
+ 6
+ (693772639560f - 693772639560)b
+ +
+ 2 5 3 4
+ - 925030186080f e + 2312575465200f e
+ +
+ 4 3
+ - 2312575465200f e
+ +
+ 11 5 2
+ (- 40007555547960f - 35382404617560f )e
+ +
+ 30 24
+ - 3781280823f + 9657492291789f
+ +
+ 18 12
+ 1511158913397906f + 1837290892286154f
+ +
+ 6
+ 1487216006594361f + 8077238712093
+ *
+ e
+ +
+ 31 25
+ - 9736390478f + 24866827916734f
+ +
+ 19 13
+ 3891495681905296f + 4872556418871424f
+ +
+ 7
+ 3904047887269606f + 27890075838538f
+ ,
+ a + b + c + d + e + f}
+ ,
+
+ 6 2 2 2
+ {f - 1, e + 4f e + f , (e - f)d - f e - 5f ,
+ c - f, b - f, a + d + e + 3f}
+ ]
+ Type: List RegularChain(Integer,[a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty14}
+\begin{paste}{LexTriangularPackageXmpPageEmpty14}{LexTriangularPackageXmpPagePatch14}
+\pastebutton{LexTriangularPackageXmpPageEmpty14}{\showpaste}
+\tab{5}\spadcommand{lexTriangular(lg,false)$lextripack\free{lg }\free{lextripack }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch15}
+\begin{paste}{LexTriangularPackageXmpPageFull15}{LexTriangularPackageXmpPageEmpty15}
+\pastebutton{LexTriangularPackageXmpPageFull15}{\hidepaste}
+\tab{5}\spadcommand{lts := lexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }\bound{lts }}
+\indentrel{3}\begin{verbatim}
+ (15)
+ [
+ 6
+ {f + 1,
+ 6 5 2 4 3 3 4 2 5
+ e - 3f e + 3f e - 4f e + 3f e - 3f e - 1,
+ 2 5 3 4 4 3 5 2
+ 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f,
+ 2 5 3 4 4 3 5 2
+ 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f,
+ 2 5 3 4 4 3 5 2
+ a - f e + 3f e - 3f e + 4f e + 3e - 3f}
+ ,
+ 6 2 2
+ {f - 1,e - f,d - f,c + 4f c + f ,b + c + 4f,a - f},
+ 6 2 2
+ {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f},
+ 6 2 2
+ {f - 1,e - f,d + 4f d + f ,c + d + 4f,b - f,a - f},
+
+ {
+ 36 30 24 18 12
+ f - 2554f - 399709f - 502276f - 399709f
+ +
+ 6
+ - 2554f + 1
+ ,
+
+ 2
+ 1387545279120e
+ +
+ 31 25
+ 4321823003f - 11037922310209f
+ +
+ 19 13
+ - 1727506390124986f - 2176188913464634f
+ +
+ 7
+ - 1732620732685741f - 13506088516033f
+ *
+ e
+ +
+ 32 26
+ 24177661775f - 61749727185325f
+ +
+ 20 14
+ - 9664082618092450f - 12152237485813570f
+ +
+ 8 2
+ - 9672870290826025f - 68544102808525f
+ ,
+
+ 1387545279120d
+ +
+ 30 24
+ - 1128983050f + 2883434331830f
+ +
+ 18 12
+ 451234998755840f + 562426491685760f
+ +
+ 6
+ 447129055314890f - 165557857270
+ *
+ e
+ +
+ 31 25
+ - 1816935351f + 4640452214013f
+ +
+ 19 13
+ 726247129626942f + 912871801716798f
+ +
+ 7
+ 726583262666877f + 4909358645961f
+ ,
+
+ 31 25
+ 1387545279120c + 778171189f - 1987468196267f
+ +
+ 19 13
+ - 310993556954378f - 383262822316802f
+ +
+ 7
+ - 300335488637543f + 5289595037041f
+ ,
+
+ 1387545279120b
+ +
+ 30 24
+ 1128983050f - 2883434331830f
+ +
+ 18 12
+ - 451234998755840f - 562426491685760f
+ +
+ 6
+ - 447129055314890f + 165557857270
+ *
+ e
+ +
+ 31 25
+ - 3283058841f + 8384938292463f
+ +
+ 19 13
+ 1312252817452422f + 1646579934064638f
+ +
+ 7
+ 1306372958656407f + 4694680112151f
+ ,
+
+ 31
+ 1387545279120a + 1387545279120e + 4321823003f
+ +
+ 25 19
+ - 11037922310209f - 1727506390124986f
+ +
+ 13 7
+ - 2176188913464634f - 1732620732685741f
+ +
+ - 13506088516033f
+ }
+ ,
+ 6 2 2
+ {f - 1,e + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
+ Type: List RegularChain(Integer,[a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty15}
+\begin{paste}{LexTriangularPackageXmpPageEmpty15}{LexTriangularPackageXmpPagePatch15}
+\pastebutton{LexTriangularPackageXmpPageEmpty15}{\showpaste}
+\tab{5}\spadcommand{lts := lexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }\bound{lts }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch16}
+\begin{paste}{LexTriangularPackageXmpPageFull16}{LexTriangularPackageXmpPageEmpty16}
+\pastebutton{LexTriangularPackageXmpPageFull16}{\hidepaste}
+\tab{5}\spadcommand{[[init(p) for p in (ts :: List(P))] for ts in lts]\free{lts }}
+\indentrel{3}\begin{verbatim}
+ (16)
+ [[1,3,1,3,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1],
+ [1,1,1,1,1,1],
+
+ [1387545279120, 1387545279120, 1387545279120,
+ 1387545279120, 1387545279120, 1]
+ ,
+ [1,1,1,1,1,1]]
+Type: List List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty16}
+\begin{paste}{LexTriangularPackageXmpPageEmpty16}{LexTriangularPackageXmpPagePatch16}
+\pastebutton{LexTriangularPackageXmpPageEmpty16}{\showpaste}
+\tab{5}\spadcommand{[[init(p) for p in (ts :: List(P))] for ts in lts]\free{lts }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch17}
+\begin{paste}{LexTriangularPackageXmpPageFull17}{LexTriangularPackageXmpPageEmpty17}
+\pastebutton{LexTriangularPackageXmpPageFull17}{\hidepaste}
+\tab{5}\spadcommand{squareFreeLexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }}
+\indentrel{3}\begin{verbatim}
+ (17)
+ [
+ 6
+ {f + 1,
+ 6 5 2 4 3 3 4 2 5
+ e - 3f e + 3f e - 4f e + 3f e - 3f e - 1,
+ 2 5 3 4 4 3 5 2
+ 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f,
+ 2 5 3 4 4 3 5 2
+ 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f,
+ 2 5 3 4 4 3 5 2
+ a - f e + 3f e - 3f e + 4f e + 3e - 3f}
+ ,
+ 6 2 2
+ {f - 1,e - f,d - f,c + 4f c + f ,b + c + 4f,a - f},
+ 6 2 2
+ {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f},
+ 6 2 2
+ {f - 1,e - f,d + 4f d + f ,c + d + 4f,b - f,a - f},
+
+ {
+ 36 30 24 18 12
+ f - 2554f - 399709f - 502276f - 399709f
+ +
+ 6
+ - 2554f + 1
+ ,
+
+ 2
+ 1387545279120e
+ +
+ 31 25
+ 4321823003f - 11037922310209f
+ +
+ 19 13
+ - 1727506390124986f - 2176188913464634f
+ +
+ 7
+ - 1732620732685741f - 13506088516033f
+ *
+ e
+ +
+ 32 26
+ 24177661775f - 61749727185325f
+ +
+ 20 14
+ - 9664082618092450f - 12152237485813570f
+ +
+ 8 2
+ - 9672870290826025f - 68544102808525f
+ ,
+
+ 1387545279120d
+ +
+ 30 24
+ - 1128983050f + 2883434331830f
+ +
+ 18 12
+ 451234998755840f + 562426491685760f
+ +
+ 6
+ 447129055314890f - 165557857270
+ *
+ e
+ +
+ 31 25
+ - 1816935351f + 4640452214013f
+ +
+ 19 13
+ 726247129626942f + 912871801716798f
+ +
+ 7
+ 726583262666877f + 4909358645961f
+ ,
+
+ 31 25
+ 1387545279120c + 778171189f - 1987468196267f
+ +
+ 19 13
+ - 310993556954378f - 383262822316802f
+ +
+ 7
+ - 300335488637543f + 5289595037041f
+ ,
+
+ 1387545279120b
+ +
+ 30 24
+ 1128983050f - 2883434331830f
+ +
+ 18 12
+ - 451234998755840f - 562426491685760f
+ +
+ 6
+ - 447129055314890f + 165557857270
+ *
+ e
+ +
+ 31 25
+ - 3283058841f + 8384938292463f
+ +
+ 19 13
+ 1312252817452422f + 1646579934064638f
+ +
+ 7
+ 1306372958656407f + 4694680112151f
+ ,
+
+ 31
+ 1387545279120a + 1387545279120e + 4321823003f
+ +
+ 25 19
+ - 11037922310209f - 1727506390124986f
+ +
+ 13 7
+ - 2176188913464634f - 1732620732685741f
+ +
+ - 13506088516033f
+ }
+ ,
+ 6 2 2
+ {f - 1,e + 4f e + f ,d + e + 4f,c - f,b - f,a - f}]
+Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [a,b,c,d,e,f],OrderedVariableList [a,b,c,d,e,f],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]))
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty17}
+\begin{paste}{LexTriangularPackageXmpPageEmpty17}{LexTriangularPackageXmpPagePatch17}
+\pastebutton{LexTriangularPackageXmpPageEmpty17}{\showpaste}
+\tab{5}\spadcommand{squareFreeLexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch18}
+\begin{paste}{LexTriangularPackageXmpPageFull18}{LexTriangularPackageXmpPageEmpty18}
+\pastebutton{LexTriangularPackageXmpPageFull18}{\hidepaste}
+\tab{5}\spadcommand{reduce(+,[degree(ts) for ts in lts])\free{lts }}
+\indentrel{3}\begin{verbatim}
+ (18) 156
+ Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty18}
+\begin{paste}{LexTriangularPackageXmpPageEmpty18}{LexTriangularPackageXmpPagePatch18}
+\pastebutton{LexTriangularPackageXmpPageEmpty18}{\showpaste}
+\tab{5}\spadcommand{reduce(+,[degree(ts) for ts in lts])\free{lts }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch19}
+\begin{paste}{LexTriangularPackageXmpPageFull19}{LexTriangularPackageXmpPageEmpty19}
+\pastebutton{LexTriangularPackageXmpPageFull19}{\hidepaste}
+\tab{5}\spadcommand{ls2 : List Symbol := concat(ls,new()$Symbol)\free{ls }\bound{ls2 }}
+\indentrel{3}\begin{verbatim}
+ (19) [a,b,c,d,e,f,%A]
+ Type: List Symbol
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty19}
+\begin{paste}{LexTriangularPackageXmpPageEmpty19}{LexTriangularPackageXmpPagePatch19}
+\pastebutton{LexTriangularPackageXmpPageEmpty19}{\showpaste}
+\tab{5}\spadcommand{ls2 : List Symbol := concat(ls,new()$Symbol)\free{ls }\bound{ls2 }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch20}
+\begin{paste}{LexTriangularPackageXmpPageFull20}{LexTriangularPackageXmpPageEmpty20}
+\pastebutton{LexTriangularPackageXmpPageFull20}{\hidepaste}
+\tab{5}\spadcommand{zdpack := ZDSOLVE(R,ls,ls2)\free{R }\free{ls }\free{ls2 }\bound{zdpack }}
+\indentrel{3}\begin{verbatim}
+ (20)
+ ZeroDimensionalSolvePackage(Integer,[a,b,c,d,e,f],[a,b,
+ c,d,e,f,%A])
+ Type: Domain
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty20}
+\begin{paste}{LexTriangularPackageXmpPageEmpty20}{LexTriangularPackageXmpPagePatch20}
+\pastebutton{LexTriangularPackageXmpPageEmpty20}{\showpaste}
+\tab{5}\spadcommand{zdpack := ZDSOLVE(R,ls,ls2)\free{R }\free{ls }\free{ls2 }\bound{zdpack }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch21}
+\begin{paste}{LexTriangularPackageXmpPageFull21}{LexTriangularPackageXmpPageEmpty21}
+\pastebutton{LexTriangularPackageXmpPageFull21}{\hidepaste}
+\tab{5}\spadcommand{concat [univariateSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }}
+\indentrel{3}\begin{verbatim}
+ (21)
+ [
+ 4 2
+ [complexRoots= ? - 13? + 49,
+
+ coordinates =
+ 3 3
+ [7a + %A - 6%A, 21b + %A + %A,
+ 3 3
+ 21c - 2%A + 19%A, 7d - %A + 6%A,
+ 3 3
+ 21e - %A - %A, 21f + 2%A - 19%A]
+ ]
+ ,
+
+ 4 2
+ [complexRoots= ? + 11? + 49,
+
+ coordinates =
+ 3 3
+ [35a + 3%A + 19%A, 35b + %A + 18%A,
+ 3 3
+ 35c - 2%A - %A, 35d - 3%A - 19%A,
+ 3 3
+ 35e - %A - 18%A, 35f + 2%A + %A]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 3
+ ? - 12? + 58? - 120? + 207? - 360?
+ +
+ 2
+ 802? - 1332? + 1369
+ ,
+
+ coordinates =
+ [
+ 7 6 5
+ 43054532a + 33782%A - 546673%A + 3127348%A
+ +
+ 4 3 2
+ - 6927123%A + 4365212%A - 25086957%A
+ +
+ 39582814%A - 107313172
+ ,
+
+ 7 6 5
+ 43054532b - 33782%A + 546673%A - 3127348%A
+ +
+ 4 3 2
+ 6927123%A - 4365212%A + 25086957%A
+ +
+ - 39582814%A + 107313172
+ ,
+
+ 7 6 5
+ 21527266c - 22306%A + 263139%A - 1166076%A
+ +
+ 4 3 2
+ 1821805%A - 2892788%A + 10322663%A
+ +
+ - 9026596%A + 12950740
+ ,
+
+ 7 6 5
+ 43054532d + 22306%A - 263139%A + 1166076%A
+ +
+ 4 3 2
+ - 1821805%A + 2892788%A - 10322663%A
+ +
+ 30553862%A - 12950740
+ ,
+
+ 7 6 5
+ 43054532e - 22306%A + 263139%A - 1166076%A
+ +
+ 4 3 2
+ 1821805%A - 2892788%A + 10322663%A
+ +
+ - 30553862%A + 12950740
+ ,
+
+ 7 6 5
+ 21527266f + 22306%A - 263139%A + 1166076%A
+ +
+ 4 3 2
+ - 1821805%A + 2892788%A - 10322663%A
+ +
+ 9026596%A - 12950740
+ ]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 3
+ ? + 12? + 58? + 120? + 207? + 360?
+ +
+ 2
+ 802? + 1332? + 1369
+ ,
+
+ coordinates =
+ [
+ 7 6 5
+ 43054532a + 33782%A + 546673%A + 3127348%A
+ +
+ 4 3 2
+ 6927123%A + 4365212%A + 25086957%A
+ +
+ 39582814%A + 107313172
+ ,
+
+ 7 6 5
+ 43054532b - 33782%A - 546673%A - 3127348%A
+ +
+ 4 3 2
+ - 6927123%A - 4365212%A - 25086957%A
+ +
+ - 39582814%A - 107313172
+ ,
+
+ 7 6 5
+ 21527266c - 22306%A - 263139%A - 1166076%A
+ +
+ 4 3 2
+ - 1821805%A - 2892788%A - 10322663%A
+ +
+ - 9026596%A - 12950740
+ ,
+
+ 7 6 5
+ 43054532d + 22306%A + 263139%A + 1166076%A
+ +
+ 4 3 2
+ 1821805%A + 2892788%A + 10322663%A
+ +
+ 30553862%A + 12950740
+ ,
+
+ 7 6 5
+ 43054532e - 22306%A - 263139%A - 1166076%A
+ +
+ 4 3 2
+ - 1821805%A - 2892788%A - 10322663%A
+ +
+ - 30553862%A - 12950740
+ ,
+
+ 7 6 5
+ 21527266f + 22306%A + 263139%A + 1166076%A
+ +
+ 4 3 2
+ 1821805%A + 2892788%A + 10322663%A
+ +
+ 9026596%A + 12950740
+ ]
+ ]
+ ,
+
+ 4 2
+ [complexRoots= ? - ? + 1,
+
+ coordinates =
+ 3 3
+ [a - %A, b + %A - %A, c + %A , d + %A,
+ 3 3
+ e - %A + %A, f - %A ]
+ ]
+ ,
+
+ 8 6 4 2
+ [complexRoots= ? + 4? + 12? + 16? + 4,
+
+ coordinates =
+ 7 5 3
+ [4a - 2%A - 7%A - 20%A - 22%A,
+ 7 5 3
+ 4b + 2%A + 7%A + 20%A + 22%A,
+ 7 5 3
+ 4c + %A + 3%A + 10%A + 10%A,
+ 7 5 3
+ 4d + %A + 3%A + 10%A + 6%A,
+ 7 5 3
+ 4e - %A - 3%A - 10%A - 6%A,
+ 7 5 3
+ 4f - %A - 3%A - 10%A - 10%A]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? + 6? + 30? + 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A - 5%A - 30%A - 6,
+ 3 2
+ 6b + %A + 5%A + 24%A + 6,
+ 3 2
+ 30c - %A - 5%A - 6,
+ 3 2
+ 30d - %A - 5%A - 30%A - 6,
+ 3 2
+ 30e - %A - 5%A - 30%A - 6,
+ 3 2
+ 30f - %A - 5%A - 30%A - 6]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? - 6? + 30? - 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A + 5%A - 30%A + 6,
+ 3 2
+ 6b + %A - 5%A + 24%A - 6,
+ 3 2
+ 30c - %A + 5%A + 6,
+ 3 2
+ 30d - %A + 5%A - 30%A + 6,
+ 3 2
+ 30e - %A + 5%A - 30%A + 6,
+ 3 2
+ 30f - %A + 5%A - 30%A + 6]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? + 6? + 6,
+
+ coordinates =
+ [a + 1,b - %A - 5,c + %A + 1,d + 1,e + 1,f + 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 6? + 6,
+
+ coordinates =
+ [a - 1,b - %A + 5,c + %A - 1,d - 1,e - 1,f - 1]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? + 6? + 30? + 36? + 36,
+
+ coordinates =
+ 3 2
+ [6a + %A + 5%A + 24%A + 6,
+ 3 2
+ 30b - %A - 5%A - 6,
+ 3 2
+ 30c - %A - 5%A - 30%A - 6,
+ 3 2
+ 30d - %A - 5%A - 30%A - 6,
+ 3 2
+ 30e - %A - 5%A - 30%A - 6,
+ 3 2
+ 30f - %A - 5%A - 30%A - 6]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? - 6? + 30? - 36? + 36,
+
+ coordinates =
+ 3 2
+ [6a + %A - 5%A + 24%A - 6,
+ 3 2
+ 30b - %A + 5%A + 6,
+ 3 2
+ 30c - %A + 5%A - 30%A + 6,
+ 3 2
+ 30d - %A + 5%A - 30%A + 6,
+ 3 2
+ 30e - %A + 5%A - 30%A + 6,
+ 3 2
+ 30f - %A + 5%A - 30%A + 6]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? + 6? + 6,
+
+ coordinates =
+ [a - %A - 5,b + %A + 1,c + 1,d + 1,e + 1,f + 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 6? + 6,
+
+ coordinates =
+ [a - %A + 5,b + %A - 1,c - 1,d - 1,e - 1,f - 1]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? + 6? + 30? + 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A - 5%A - 30%A - 6,
+ 3 2
+ 30b - %A - 5%A - 30%A - 6,
+ 3 2
+ 6c + %A + 5%A + 24%A + 6,
+ 3 2
+ 30d - %A - 5%A - 6,
+ 3 2
+ 30e - %A - 5%A - 30%A - 6,
+ 3 2
+ 30f - %A - 5%A - 30%A - 6]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? - 6? + 30? - 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A + 5%A - 30%A + 6,
+ 3 2
+ 30b - %A + 5%A - 30%A + 6,
+ 3 2
+ 6c + %A - 5%A + 24%A - 6,
+ 3 2
+ 30d - %A + 5%A + 6,
+ 3 2
+ 30e - %A + 5%A - 30%A + 6,
+ 3 2
+ 30f - %A + 5%A - 30%A + 6]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? + 6? + 6,
+
+ coordinates =
+ [a + 1,b + 1,c - %A - 5,d + %A + 1,e + 1,f + 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 6? + 6,
+
+ coordinates =
+ [a - 1,b - 1,c - %A + 5,d + %A - 1,e - 1,f - 1]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 2
+ ? + 6? + 16? + 24? + 18? - 8? + 4
+ ,
+
+ coordinates =
+ [
+ 7 6 5 4 3
+ 2a + 2%A + 9%A + 18%A + 19%A + 4%A
+ +
+ 2
+ - 10%A - 2%A + 4
+ ,
+
+ 7 6 5 4 3
+ 2b + 2%A + 9%A + 18%A + 19%A + 4%A
+ +
+ 2
+ - 10%A - 4%A + 4
+ ,
+ 7 6 5 4 3
+ 2c - %A - 4%A - 8%A - 9%A - 4%A - 2%A - 4,
+ 7 6 5 4 3
+ 2d + %A + 4%A + 8%A + 9%A + 4%A + 2%A + 4,
+
+ 7 6 5 4 3
+ 2e - 2%A - 9%A - 18%A - 19%A - 4%A
+ +
+ 2
+ 10%A + 4%A - 4
+ ,
+
+ 7 6 5 4 3
+ 2f - 2%A - 9%A - 18%A - 19%A - 4%A
+ +
+ 2
+ 10%A + 2%A - 4
+ ]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 3
+ ? + 12? + 64? + 192? + 432? + 768?
+ +
+ 2
+ 1024? + 768? + 256
+ ,
+
+ coordinates =
+ [
+ 7 6 5 4
+ 1408a - 19%A - 200%A - 912%A - 2216%A
+ +
+ 3 2
+ - 4544%A - 6784%A - 6976%A - 1792
+ ,
+
+ 7 6 5 4
+ 1408b - 37%A - 408%A - 1952%A - 5024%A
+ +
+ 3 2
+ - 10368%A - 16768%A - 17920%A - 5120
+ ,
+
+ 7 6 5 4
+ 1408c + 37%A + 408%A + 1952%A + 5024%A
+ +
+ 3 2
+ 10368%A + 16768%A + 17920%A + 5120
+ ,
+
+ 7 6 5 4
+ 1408d + 19%A + 200%A + 912%A + 2216%A
+ +
+ 3 2
+ 4544%A + 6784%A + 6976%A + 1792
+ ,
+ 2e + %A, 2f - %A]
+ ]
+ ,
+
+ 8 6 4 2
+ [complexRoots= ? + 4? + 12? + 16? + 4,
+
+ coordinates =
+ 7 5 3
+ [4a - %A - 3%A - 10%A - 6%A,
+ 7 5 3
+ 4b - %A - 3%A - 10%A - 10%A,
+ 7 5 3
+ 4c - 2%A - 7%A - 20%A - 22%A,
+ 7 5 3
+ 4d + 2%A + 7%A + 20%A + 22%A,
+ 7 5 3
+ 4e + %A + 3%A + 10%A + 10%A,
+ 7 5 3
+ 4f + %A + 3%A + 10%A + 6%A]
+ ]
+ ,
+
+ 8 6 4 2
+ [complexRoots= ? + 16? - 96? + 256? + 256,
+
+ coordinates =
+ 7 5 3
+ [512a - %A - 12%A + 176%A - 448%A,
+ 7 5 3
+ 128b - %A - 16%A + 96%A - 256%A,
+ 7 5 3
+ 128c + %A + 16%A - 96%A + 256%A,
+ 7 5 3
+ 512d + %A + 12%A - 176%A + 448%A, 2e + %A,
+ 2f - %A]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 3
+ ? - 12? + 64? - 192? + 432? - 768?
+ +
+ 2
+ 1024? - 768? + 256
+ ,
+
+ coordinates =
+ [
+ 7 6 5 4
+ 1408a - 19%A + 200%A - 912%A + 2216%A
+ +
+ 3 2
+ - 4544%A + 6784%A - 6976%A + 1792
+ ,
+
+ 7 6 5 4
+ 1408b - 37%A + 408%A - 1952%A + 5024%A
+ +
+ 3 2
+ - 10368%A + 16768%A - 17920%A + 5120
+ ,
+
+ 7 6 5 4
+ 1408c + 37%A - 408%A + 1952%A - 5024%A
+ +
+ 3 2
+ 10368%A - 16768%A + 17920%A - 5120
+ ,
+
+ 7 6 5 4
+ 1408d + 19%A - 200%A + 912%A - 2216%A
+ +
+ 3 2
+ 4544%A - 6784%A + 6976%A - 1792
+ ,
+ 2e + %A, 2f - %A]
+ ]
+ ,
+
+ [
+ complexRoots =
+ 8 7 6 5 4 2
+ ? - 6? + 16? - 24? + 18? - 8? + 4
+ ,
+
+ coordinates =
+ [
+ 7 6 5 4 3
+ 2a + 2%A - 9%A + 18%A - 19%A + 4%A
+ +
+ 2
+ 10%A - 2%A - 4
+ ,
+
+ 7 6 5 4 3
+ 2b + 2%A - 9%A + 18%A - 19%A + 4%A
+ +
+ 2
+ 10%A - 4%A - 4
+ ,
+ 7 6 5 4 3
+ 2c - %A + 4%A - 8%A + 9%A - 4%A - 2%A + 4,
+ 7 6 5 4 3
+ 2d + %A - 4%A + 8%A - 9%A + 4%A + 2%A - 4,
+
+ 7 6 5 4 3
+ 2e - 2%A + 9%A - 18%A + 19%A - 4%A
+ +
+ 2
+ - 10%A + 4%A + 4
+ ,
+
+ 7 6 5 4 3
+ 2f - 2%A + 9%A - 18%A + 19%A - 4%A
+ +
+ 2
+ - 10%A + 2%A + 4
+ ]
+ ]
+ ,
+
+ 4 2
+ [complexRoots= ? + 12? + 144,
+
+ coordinates =
+ 2 2 2
+ [12a - %A - 12, 12b - %A - 12, 12c - %A - 12,
+ 2 2
+ 12d - %A - 12, 6e + %A + 3%A + 12,
+ 2
+ 6f + %A - 3%A + 12]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? + 6? + 30? + 36? + 36,
+
+ coordinates =
+ 3 2
+ [6a - %A - 5%A - 24%A - 6,
+ 3 2
+ 30b + %A + 5%A + 30%A + 6,
+ 3 2
+ 30c + %A + 5%A + 30%A + 6,
+ 3 2
+ 30d + %A + 5%A + 30%A + 6,
+ 3 2
+ 30e + %A + 5%A + 30%A + 6,
+ 3 2
+ 30f + %A + 5%A + 6]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? - 6? + 30? - 36? + 36,
+
+ coordinates =
+ 3 2
+ [6a - %A + 5%A - 24%A + 6,
+ 3 2
+ 30b + %A - 5%A + 30%A - 6,
+ 3 2
+ 30c + %A - 5%A + 30%A - 6,
+ 3 2
+ 30d + %A - 5%A + 30%A - 6,
+ 3 2
+ 30e + %A - 5%A + 30%A - 6,
+ 3 2
+ 30f + %A - 5%A - 6]
+ ]
+ ,
+
+ 4 2
+ [complexRoots= ? + 12? + 144,
+
+ coordinates =
+ 2 2 2
+ [12a + %A + 12, 12b + %A + 12, 12c + %A + 12,
+ 2 2
+ 12d + %A + 12, 6e - %A + 3%A - 12,
+ 2
+ 6f - %A - 3%A - 12]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 12,
+
+ coordinates =
+ [a - 1,b - 1,c - 1,d - 1,2e + %A + 4,2f - %A + 4]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? + 6? + 6,
+
+ coordinates =
+ [a + %A + 5,b - 1,c - 1,d - 1,e - 1,f - %A - 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 6? + 6,
+
+ coordinates =
+ [a + %A - 5,b + 1,c + 1,d + 1,e + 1,f - %A + 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 12,
+
+ coordinates =
+ [a + 1,b + 1,c + 1,d + 1,2e + %A - 4,2f - %A - 4]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? + 6? + 30? + 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A - 5%A - 30%A - 6,
+ 3 2
+ 30b - %A - 5%A - 30%A - 6,
+ 3 2
+ 30c - %A - 5%A - 30%A - 6,
+ 3 2
+ 6d + %A + 5%A + 24%A + 6,
+ 3 2
+ 30e - %A - 5%A - 6,
+ 3 2
+ 30f - %A - 5%A - 30%A - 6]
+ ]
+ ,
+
+ 4 3 2
+ [complexRoots= ? - 6? + 30? - 36? + 36,
+
+ coordinates =
+ 3 2
+ [30a - %A + 5%A - 30%A + 6,
+ 3 2
+ 30b - %A + 5%A - 30%A + 6,
+ 3 2
+ 30c - %A + 5%A - 30%A + 6,
+ 3 2
+ 6d + %A - 5%A + 24%A - 6,
+ 3 2
+ 30e - %A + 5%A + 6,
+ 3 2
+ 30f - %A + 5%A - 30%A + 6]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? + 6? + 6,
+
+ coordinates =
+ [a + 1,b + 1,c + 1,d - %A - 5,e + %A + 1,f + 1]
+ ]
+ ,
+
+ 2
+ [complexRoots= ? - 6? + 6,
+
+ coordinates =
+ [a - 1,b - 1,c - 1,d - %A + 5,e + %A - 1,f - 1]
+ ]
+ ]
+Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer)
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty21}
+\begin{paste}{LexTriangularPackageXmpPageEmpty21}{LexTriangularPackageXmpPagePatch21}
+\pastebutton{LexTriangularPackageXmpPageEmpty21}{\showpaste}
+\tab{5}\spadcommand{concat [univariateSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }}
+\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPagePatch22}
+\begin{paste}{LexTriangularPackageXmpPageFull22}{LexTriangularPackageXmpPageEmpty22}
+\pastebutton{LexTriangularPackageXmpPageFull22}{\hidepaste}
+\tab{5}\spadcommand{concat [realSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }}
+\indentrel{3}\begin{verbatim}
+ (22)
+ [[%R1,%R1,%R1,%R5,- %R5 - 4%R1,%R1],
+ [%R1,%R1,%R1,%R6,- %R6 - 4%R1,%R1],
+ [%R2,%R2,%R2,%R3,- %R3 - 4%R2,%R2],
+ [%R2,%R2,%R2,%R4,- %R4 - 4%R2,%R2],
+ [%R7,%R7,%R7,%R7,%R11,- %R11 - 4%R7],
+ [%R7,%R7,%R7,%R7,%R12,- %R12 - 4%R7],
+ [%R8,%R8,%R8,%R8,%R9,- %R9 - 4%R8],
+ [%R8,%R8,%R8,%R8,%R10,- %R10 - 4%R8],
+ [%R13,%R13,%R17,- %R17 - 4%R13,%R13,%R13],
+ [%R13,%R13,%R18,- %R18 - 4%R13,%R13,%R13],
+ [%R14,%R14,%R15,- %R15 - 4%R14,%R14,%R14],
+ [%R14,%R14,%R16,- %R16 - 4%R14,%R14,%R14],
+
+ [%R19, %R29,
+
+ 7865521 31 6696179241 25
+ 컴컴컴컴컴 %R19 - 컴컴컴컴컴 %R19
+ 6006689520 2002229840
+ +
+ 25769893181 19 1975912990729 13
+ - 컴컴컴컴컴� %R19 - 컴컴컴컴컴컴� %R19
+ 49235160 3003344760
+ +
+ 1048460696489 7 21252634831
+ - 컴컴컴컴컴컴� %R19 - 컴컴컴컴컴� %R19
+ 2002229840 6006689520
+ ,
+
+ 778171189 31 1987468196267 25
+ - 컴컴컴컴컴컴� %R19 + 컴컴컴컴컴컴� %R19
+ 1387545279120 1387545279120
+ +
+ 155496778477189 19 191631411158401 13
+ 컴컴컴컴컴컴컴� %R19 + 컴컴컴컴컴컴컴� %R19
+ 693772639560 693772639560
+ +
+ 300335488637543 7 755656433863
+ 컴컴컴컴컴컴컴� %R19 - 컴컴컴컴컴컴 %R19
+ 1387545279120 198220754160
+ ,
+
+ 1094352947 31 2794979430821 25
+ 컴컴컴컴컴컴 %R19 - 컴컴컴컴컴컴� %R19
+ 462515093040 462515093040
+ +
+ 218708802908737 19 91476663003591 13
+ - 컴컴컴컴컴컴컴� %R19 - 컴컴컴컴컴컴컴 %R19
+ 231257546520 77085848840
+ +
+ 145152550961823 7 1564893370717
+ - 컴컴컴컴컴컴컴� %R19 - 컴컴컴컴컴컴� %R19
+ 154171697680 462515093040
+ ,
+
+ 4321823003 31
+ - %R29 - 컴컴컴컴컴컴� %R19
+ 1387545279120
+ +
+ 180949546069 25 863753195062493 19
+ 컴컴컴컴컴컴 %R19 + 컴컴컴컴컴컴컴� %R19
+ 22746643920 693772639560
+ +
+ 1088094456732317 13 1732620732685741 7
+ 컴컴컴컴컴컴컴컴 %R19 + 컴컴컴컴컴컴컴컴 %R19
+ 693772639560 1387545279120
+ +
+ 13506088516033
+ 컴컴컴컴컴컴컴 %R19
+ 1387545279120
+ ]
+ ,
+
+ [%R19, %R30,
+
+ 7865521 31 6696179241 25
+ 컴컴컴컴컴 %R19 - 컴컴컴컴컴 %R19
+ 6006689520 2002229840
+ +
+ 25769893181 19 1975912990729 13
+ - 컴컴컴컴컴� %R19 - 컴컴컴컴컴컴� %R19
+ 49235160 3003344760
+ +
+ 1048460696489 7 21252634831
+ - 컴컴컴컴컴컴� %R19 - 컴컴컴컴컴� %R19
+ 2002229840 6006689520
+ ,
+
+ 778171189 31 1987468196267 25
+ - 컴컴컴컴컴컴� %R19 + 컴컴컴컴컴컴� %R19
+ 1387545279120 1387545279120
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+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{LexTriangularPackageXmpPageEmpty22}
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+\end{paste}\end{patch}
+
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