Initial population.

1 files changed, 416 insertions, 0 deletions

diff --git a/src/hyper/pages/SREGSET.pht b/src/hyper/pages/SREGSET.pht
new file mode 100644
index 00000000..ea96c7b1
--- /dev/null
+++ b/src/hyper/pages/SREGSET.pht
@@ -0,0 +1,416 @@
+\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}
+