\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch1}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull1}{SquareFreeRegularTriangularSetXmpPageEmpty1}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\indentrel{3}\begin{verbatim}
   (1)  Integer
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty1}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty1}{SquareFreeRegularTriangularSetXmpPagePatch1}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch2}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull2}{SquareFreeRegularTriangularSetXmpPageEmpty2}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull2}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty2}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty2}{SquareFreeRegularTriangularSetXmpPagePatch2}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{ls : List Symbol := [x,y,z,t]\bound{ls }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch3}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull3}{SquareFreeRegularTriangularSetXmpPageEmpty3}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\indentrel{3}\begin{verbatim}
   (3)  OrderedVariableList([x,y,z,t])
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty3}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty3}{SquareFreeRegularTriangularSetXmpPagePatch3}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch4}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull4}{SquareFreeRegularTriangularSetXmpPageEmpty4}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\indentrel{3}\begin{verbatim}
   (4)  IndexedExponents(OrderedVariableList([x,y,z,t]))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty4}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty4}{SquareFreeRegularTriangularSetXmpPagePatch4}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch5}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull5}{SquareFreeRegularTriangularSetXmpPageEmpty5}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull5}{\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: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty5}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty5}{SquareFreeRegularTriangularSetXmpPagePatch5}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch6}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull6}{SquareFreeRegularTriangularSetXmpPageEmpty6}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull6}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty6}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty6}{SquareFreeRegularTriangularSetXmpPagePatch6}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch7}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull7}{SquareFreeRegularTriangularSetXmpPageEmpty7}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull7}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty7}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty7}{SquareFreeRegularTriangularSetXmpPagePatch7}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch8}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull8}{SquareFreeRegularTriangularSetXmpPageEmpty8}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull8}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty8}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty8}{SquareFreeRegularTriangularSetXmpPagePatch8}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch9}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull9}{SquareFreeRegularTriangularSetXmpPageEmpty9}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull9}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty9}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty9}{SquareFreeRegularTriangularSetXmpPagePatch9}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch10}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull10}{SquareFreeRegularTriangularSetXmpPageEmpty10}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{ST := SREGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{ST }}
\indentrel{3}\begin{verbatim}
   (10)
  SquareFreeRegularTriangularSet(Integer,IndexedExponents
  (OrderedVariableList([x,y,z,t])),OrderedVariableList([x
  ,y,z,t]),NewSparseMultivariatePolynomial(Integer,Ordere
  dVariableList([x,y,z,t])))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty10}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty10}{SquareFreeRegularTriangularSetXmpPagePatch10}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty10}{\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}{SquareFreeRegularTriangularSetXmpPagePatch11}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull11}{SquareFreeRegularTriangularSetXmpPageEmpty11}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull11}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty11}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty11}{SquareFreeRegularTriangularSetXmpPagePatch11}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{p1 := x ^ 31 - x ^ 6 - x - y\free{x }\free{y }\bound{p1 }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch12}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull12}{SquareFreeRegularTriangularSetXmpPageEmpty12}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull12}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty12}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty12}{SquareFreeRegularTriangularSetXmpPagePatch12}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{p2 := x ^ 8 - z\free{x }\free{z }\bound{p2 }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch13}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull13}{SquareFreeRegularTriangularSetXmpPageEmpty13}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull13}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty13}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty13}{SquareFreeRegularTriangularSetXmpPagePatch13}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{p3 := x ^ 10 - t\free{x }\free{t }\bound{p3 }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch14}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull14}{SquareFreeRegularTriangularSetXmpPageEmpty14}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull14}{\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}{SquareFreeRegularTriangularSetXmpPageEmpty14}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty14}{SquareFreeRegularTriangularSetXmpPagePatch14}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{lp := [p1, p2, p3]\free{p1 }\free{p2 }\free{p3 }\bound{lp }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch15}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull15}{SquareFreeRegularTriangularSetXmpPageEmpty15}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lp)$ST\free{lp }\free{ST }}
\indentrel{3}\begin{verbatim}
   (15)
   [
       5    4       2      3     8      5    3    2
     {z  - t , t z y  + 2 z y - t  + 2 t  + t  - t ,
        4                2
      (t  - t)x - t y - z }
     ]
Type: List(SquareFreeRegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty15}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty15}{SquareFreeRegularTriangularSetXmpPagePatch15}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp)$ST\free{lp }\free{ST }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch16}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull16}{SquareFreeRegularTriangularSetXmpPageEmpty16}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{zeroSetSplit(lp,false)$ST\free{lp }\free{ST }\bound{lts }}
\indentrel{3}\begin{verbatim}
   (16)
   [
       5    4       2      3     8      5    3    2
     {z  - t , t z y  + 2 z y - t  + 2 t  + t  - t ,
        4                2
      (t  - t)x - t y - z }
     ,
      3       5             2     2
    {t  - 1, z  - t, t y + z , z x  - t}, {t, z, y, x}]
Type: List(SquareFreeRegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty16}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty16}{SquareFreeRegularTriangularSetXmpPagePatch16}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp,false)$ST\free{lp }\free{ST }\bound{lts }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch17}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull17}{SquareFreeRegularTriangularSetXmpPageEmpty17}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{T := REGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }}
\indentrel{3}\begin{verbatim}
   (17)
  RegularTriangularSet(Integer,IndexedExponents(OrderedVa
  riableList([x,y,z,t])),OrderedVariableList([x,y,z,t]),N
  ewSparseMultivariatePolynomial(Integer,OrderedVariableL
  ist([x,y,z,t])))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty17}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty17}{SquareFreeRegularTriangularSetXmpPagePatch17}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty17}{\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}{SquareFreeRegularTriangularSetXmpPagePatch18}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull18}{SquareFreeRegularTriangularSetXmpPageEmpty18}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }}
\indentrel{3}\begin{verbatim}
   (18)
   [
       5    4       2      3     8      5    3    2
     {z  - t , t z y  + 2 z y - t  + 2 t  + t  - t ,
        4                2
      (t  - t)x - t y - z }
     ,
      3       5           2      3          2
    {t  - 1, z  - t, t z y  + 2 z y + 1, z x  - t},
    {t, z, y, x}]
Type: List(RegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty18}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty18}{SquareFreeRegularTriangularSetXmpPagePatch18}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch19}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull19}{SquareFreeRegularTriangularSetXmpPageEmpty19}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{ts := lts.2\free{lts }\bound{ts }}
\indentrel{3}\begin{verbatim}
           3       5           2      3          2
   (19)  {t  - 1, z  - t, t z y  + 2 z y + 1, z x  - t}
Type: RegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty19}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty19}{SquareFreeRegularTriangularSetXmpPagePatch19}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{ts := lts.2\free{lts }\bound{ts }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch20}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull20}{SquareFreeRegularTriangularSetXmpPageEmpty20}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{pol := select(ts,'y)$T\free{ts }\free{y }\free{T }\bound{pol }}
\indentrel{3}\begin{verbatim}
              2      3
   (20)  t z y  + 2 z y + 1
Type: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])),...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty20}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty20}{SquareFreeRegularTriangularSetXmpPagePatch20}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{pol := select(ts,'y)$T\free{ts }\free{y }\free{T }\bound{pol }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch21}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull21}{SquareFreeRegularTriangularSetXmpPageEmpty21}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{tower := collectUnder(ts,'y)$T\free{ts }\free{y }\free{T }\bound{tower }}
\indentrel{3}\begin{verbatim}
           3       5
   (21)  {t  - 1, z  - t}
Type: RegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty21}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty21}{SquareFreeRegularTriangularSetXmpPagePatch21}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{tower := collectUnder(ts,'y)$T\free{ts }\free{y }\free{T }\bound{tower }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch22}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull22}{SquareFreeRegularTriangularSetXmpPageEmpty22}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{pack := RegularTriangularSetGcdPackage(R,E,V,P,T)\free{R }\free{E }\free{V }\free{P }\free{T }\bound{pack }}
\indentrel{3}\begin{verbatim}
   (22)
  RegularTriangularSetGcdPackage(Integer,IndexedExponents
  (OrderedVariableList([x,y,z,t])),OrderedVariableList([x
  ,y,z,t]),NewSparseMultivariatePolynomial(Integer,Ordere
  dVariableList([x,y,z,t])),RegularTriangularSet(Integer,
  IndexedExponents(OrderedVariableList([x,y,z,t])),Ordere
  dVariableList([x,y,z,t]),NewSparseMultivariatePolynomia
  l(Integer,OrderedVariableList([x,y,z,t]))))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty22}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty22}{SquareFreeRegularTriangularSetXmpPagePatch22}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{pack := RegularTriangularSetGcdPackage(R,E,V,P,T)\free{R }\free{E }\free{V }\free{P }\free{T }\bound{pack }}
\end{paste}\end{patch}

\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch23}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull23}{SquareFreeRegularTriangularSetXmpPageEmpty23}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{toseSquareFreePart(pol,tower)$pack\free{pol }\free{tower }\free{pack }}
\indentrel{3}\begin{verbatim}
                        2            3       5
   (23)  [[val = t y + z , tower = {t  - 1, z  - t}]]
Type: List(Record(val: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])),tower: RegularTriangularSet(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}{SquareFreeRegularTriangularSetXmpPageEmpty23}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty23}{SquareFreeRegularTriangularSetXmpPagePatch23}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{toseSquareFreePart(pol,tower)$pack\free{pol }\free{tower }\free{pack }}
\end{paste}\end{patch}

