\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}