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|
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch1}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull1}{WuWenTsunTriangularSetXmpPageEmpty1}
\pastebutton{WuWenTsunTriangularSetXmpPageFull1}{\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}{WuWenTsunTriangularSetXmpPageEmpty1}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty1}{WuWenTsunTriangularSetXmpPagePatch1}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch2}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull2}{WuWenTsunTriangularSetXmpPageEmpty2}
\pastebutton{WuWenTsunTriangularSetXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{ls : List Symbol := [x,y,z,t]\bound{ls }}
\indentrel{3}\begin{verbatim}
(2) [x,y,z,t]
Type: List Symbol
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty2}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty2}{WuWenTsunTriangularSetXmpPagePatch2}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{ls : List Symbol := [x,y,z,t]\bound{ls }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch3}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull3}{WuWenTsunTriangularSetXmpPageEmpty3}
\pastebutton{WuWenTsunTriangularSetXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\indentrel{3}\begin{verbatim}
(3) OrderedVariableList [x,y,z,t]
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty3}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty3}{WuWenTsunTriangularSetXmpPagePatch3}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch4}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull4}{WuWenTsunTriangularSetXmpPageEmpty4}
\pastebutton{WuWenTsunTriangularSetXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\indentrel{3}\begin{verbatim}
(4) IndexedExponents OrderedVariableList [x,y,z,t]
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty4}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty4}{WuWenTsunTriangularSetXmpPagePatch4}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch5}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull5}{WuWenTsunTriangularSetXmpPageEmpty5}
\pastebutton{WuWenTsunTriangularSetXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
\indentrel{3}\begin{verbatim}
(5)
NewSparseMultivariatePolynomial(Integer,OrderedVariable
List [x,y,z,t])
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty5}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty5}{WuWenTsunTriangularSetXmpPagePatch5}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch6}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull6}{WuWenTsunTriangularSetXmpPageEmpty6}
\pastebutton{WuWenTsunTriangularSetXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }}
\indentrel{3}\begin{verbatim}
(6) x
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty6}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty6}{WuWenTsunTriangularSetXmpPagePatch6}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch7}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull7}{WuWenTsunTriangularSetXmpPageEmpty7}
\pastebutton{WuWenTsunTriangularSetXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }}
\indentrel{3}\begin{verbatim}
(7) y
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty7}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty7}{WuWenTsunTriangularSetXmpPagePatch7}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch8}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull8}{WuWenTsunTriangularSetXmpPageEmpty8}
\pastebutton{WuWenTsunTriangularSetXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }}
\indentrel{3}\begin{verbatim}
(8) z
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty8}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty8}{WuWenTsunTriangularSetXmpPagePatch8}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch9}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull9}{WuWenTsunTriangularSetXmpPageEmpty9}
\pastebutton{WuWenTsunTriangularSetXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }}
\indentrel{3}\begin{verbatim}
(9) t
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty9}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty9}{WuWenTsunTriangularSetXmpPagePatch9}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch10}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull10}{WuWenTsunTriangularSetXmpPageEmpty10}
\pastebutton{WuWenTsunTriangularSetXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{T := WUTSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }}
\indentrel{3}\begin{verbatim}
(10)
WuWenTsunTriangularSet(Integer,IndexedExponents Ordered
VariableList [x,y,z,t],OrderedVariableList [x,y,z,t],Ne
wSparseMultivariatePolynomial(Integer,OrderedVariableLi
st [x,y,z,t]))
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty10}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty10}{WuWenTsunTriangularSetXmpPagePatch10}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{T := WUTSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch11}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull11}{WuWenTsunTriangularSetXmpPageEmpty11}
\pastebutton{WuWenTsunTriangularSetXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{p1 := x ** 31 - x ** 6 - x - y\free{x }\free{y }\bound{p1 }}
\indentrel{3}\begin{verbatim}
31 6
(11) x - x - x - y
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty11}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty11}{WuWenTsunTriangularSetXmpPagePatch11}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{p1 := x ** 31 - x ** 6 - x - y\free{x }\free{y }\bound{p1 }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch12}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull12}{WuWenTsunTriangularSetXmpPageEmpty12}
\pastebutton{WuWenTsunTriangularSetXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{p2 := x ** 8 - z\free{x }\free{z }\bound{p2 }}
\indentrel{3}\begin{verbatim}
8
(12) x - z
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty12}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty12}{WuWenTsunTriangularSetXmpPagePatch12}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{p2 := x ** 8 - z\free{x }\free{z }\bound{p2 }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch13}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull13}{WuWenTsunTriangularSetXmpPageEmpty13}
\pastebutton{WuWenTsunTriangularSetXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{p3 := x ** 10 - t\free{x }\free{t }\bound{p3 }}
\indentrel{3}\begin{verbatim}
10
(13) x - t
Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty13}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty13}{WuWenTsunTriangularSetXmpPagePatch13}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{p3 := x ** 10 - t\free{x }\free{t }\bound{p3 }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch14}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull14}{WuWenTsunTriangularSetXmpPageEmpty14}
\pastebutton{WuWenTsunTriangularSetXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{lp := [p1, p2, p3]\free{p1 }\free{p2 }\free{p3 }\bound{lp }}
\indentrel{3}\begin{verbatim}
31 6 8 10
(14) [x - x - x - y,x - z,x - t]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty14}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty14}{WuWenTsunTriangularSetXmpPagePatch14}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{lp := [p1, p2, p3]\free{p1 }\free{p2 }\free{p3 }\bound{lp }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch15}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull15}{WuWenTsunTriangularSetXmpPageEmpty15}
\pastebutton{WuWenTsunTriangularSetXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{characteristicSet(lp)$T\free{lp }\free{T }}
\indentrel{3}\begin{verbatim}
(15)
5 4 4 2 2 3 4 7 4 6 6
{z - t , t z y + 2t z y + (- t + 2t - t)z + t z,
3 3 3 3
(t - 1)z x - z y - t }
Type: Union(WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t])),...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty15}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty15}{WuWenTsunTriangularSetXmpPagePatch15}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{characteristicSet(lp)$T\free{lp }\free{T }}
\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPagePatch16}
\begin{paste}{WuWenTsunTriangularSetXmpPageFull16}{WuWenTsunTriangularSetXmpPageEmpty16}
\pastebutton{WuWenTsunTriangularSetXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lp)$T\free{lp }\free{T }}
\indentrel{3}\begin{verbatim}
(16)
3 5 4 3 3 2
[{t,z,y,x}, {t - 1,z - t ,z y + t ,z x - t},
5 4
{z - t ,
4 2 2 3 4 7 4 6 6
t z y + 2t z y + (- t + 2t - t)z + t z,
3 3 3 3
(t - 1)z x - z y - t }
]
Type: List WuWenTsunTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{WuWenTsunTriangularSetXmpPageEmpty16}
\begin{paste}{WuWenTsunTriangularSetXmpPageEmpty16}{WuWenTsunTriangularSetXmpPagePatch16}
\pastebutton{WuWenTsunTriangularSetXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp)$T\free{lp }\free{T }}
\end{paste}\end{patch}
|
