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|
\begin{patch}{SquareFreeRegularTriangularSetXmpPagePatch1}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageFull1}{SquareFreeRegularTriangularSetXmpPageEmpty1}
\pastebutton{SquareFreeRegularTriangularSetXmpPageFull1}{\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}{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: Domain
\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: Domain
\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: Domain
\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,OrderedVa
riableList [x,y,z,t]))
Type: Domain
\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)$ST\free{lp }\free{ST }}
\indentrel{3}\begin{verbatim}
(15)
[
5 4 2 3 8 5 3 2
{z - t , t z y + 2z y - t + 2t + t - t ,
4 2
(t - t)x - t y - z }
]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty15}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty15}{SquareFreeRegularTriangularSetXmpPagePatch15}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp)$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)$ST\free{lp }\free{ST }\bound{lts }}
\indentrel{3}\begin{verbatim}
(16)
[
5 4 2 3 8 5 3 2
{z - t , t z y + 2z y - t + 2t + t - t ,
4 2
(t - t)x - t y - z }
,
3 5 2 2
{t - 1,z - t,t y + z ,z x - t}, {t,z,y,x}]
Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty16}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty16}{SquareFreeRegularTriangularSetXmpPagePatch16}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{zeroSetSplit(lp,false)$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],NewS
parseMultivariatePolynomial(Integer,OrderedVariableList
[x,y,z,t]))
Type: Domain
\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)$T\free{lp }\free{T }\bound{lts }}
\indentrel{3}\begin{verbatim}
(18)
[
5 4 2 3 8 5 3 2
{z - t , t z y + 2z y - t + 2t + t - t ,
4 2
(t - t)x - t y - z }
,
3 5 2 3 2
{t - 1,z - t,t z y + 2z y + 1,z x - t},
{t,z,y,x}]
Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [x,y,z,t],OrderedVariableList [x,y,z,t],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty18}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty18}{SquareFreeRegularTriangularSetXmpPagePatch18}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$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 + 2z 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)$T\free{ts }\free{y }\free{T }\bound{pol }}
\indentrel{3}\begin{verbatim}
2 3
(20) t z y + 2z y + 1
Type: Union(NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z,t]),...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{SquareFreeRegularTriangularSetXmpPageEmpty20}
\begin{paste}{SquareFreeRegularTriangularSetXmpPageEmpty20}{SquareFreeRegularTriangularSetXmpPagePatch20}
\pastebutton{SquareFreeRegularTriangularSetXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{pol := select(ts,'y)$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,OrderedVa
riableList [x,y,z,t]),RegularTriangularSet(Integer,Inde
xedExponents OrderedVariableList [x,y,z,t],OrderedVaria
bleList [x,y,z,t],NewSparseMultivariatePolynomial(Integ
er,OrderedVariableList [x,y,z,t])))
Type: Domain
\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}
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