\begin{patch}{TableXmpPagePatch1}
\begin{paste}{TableXmpPageFull1}{TableXmpPageEmpty1}
\pastebutton{TableXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{t: Table(Polynomial Integer, String) := table()\bound{t }}
\indentrel{3}\begin{verbatim}
   (1)  table()
                Type: Table(Polynomial(Integer),String)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty1}
\begin{paste}{TableXmpPageEmpty1}{TableXmpPagePatch1}
\pastebutton{TableXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{t: Table(Polynomial Integer, String) := table()\bound{t }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch2}
\begin{paste}{TableXmpPageFull2}{TableXmpPageEmpty2}
\pastebutton{TableXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{setelt!(t, x^2 - 1, "Easy to factor")\bound{p1 }\free{t }}
\indentrel{3}\begin{verbatim}
   (2)  "Easy to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty2}
\begin{paste}{TableXmpPageEmpty2}{TableXmpPagePatch2}
\pastebutton{TableXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{setelt!(t, x^2 - 1, "Easy to factor")\bound{p1 }\free{t }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch3}
\begin{paste}{TableXmpPageFull3}{TableXmpPageEmpty3}
\pastebutton{TableXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{t(x^3 + 1) := "Harder to factor"\bound{p2 }\free{p1 }}
\indentrel{3}\begin{verbatim}
   (3)  "Harder to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty3}
\begin{paste}{TableXmpPageEmpty3}{TableXmpPagePatch3}
\pastebutton{TableXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{t(x^3 + 1) := "Harder to factor"\bound{p2 }\free{p1 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch4}
\begin{paste}{TableXmpPageFull4}{TableXmpPageEmpty4}
\pastebutton{TableXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{t(x) := "The easiest to factor"\bound{p3 }\free{p2 }}
\indentrel{3}\begin{verbatim}
   (4)  "The easiest to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty4}
\begin{paste}{TableXmpPageEmpty4}{TableXmpPagePatch4}
\pastebutton{TableXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{t(x) := "The easiest to factor"\bound{p3 }\free{p2 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch5}
\begin{paste}{TableXmpPageFull5}{TableXmpPageEmpty5}
\pastebutton{TableXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{elt(t, x)\free{p3 }}
\indentrel{3}\begin{verbatim}
   (5)  "The easiest to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty5}
\begin{paste}{TableXmpPageEmpty5}{TableXmpPagePatch5}
\pastebutton{TableXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{elt(t, x)\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch6}
\begin{paste}{TableXmpPageFull6}{TableXmpPageEmpty6}
\pastebutton{TableXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{t.x\free{p3 }}
\indentrel{3}\begin{verbatim}
   (6)  "The easiest to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty6}
\begin{paste}{TableXmpPageEmpty6}{TableXmpPagePatch6}
\pastebutton{TableXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{t.x\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch7}
\begin{paste}{TableXmpPageFull7}{TableXmpPageEmpty7}
\pastebutton{TableXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{t x\free{p3 }}
\indentrel{3}\begin{verbatim}
   (7)  "The easiest to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty7}
\begin{paste}{TableXmpPageEmpty7}{TableXmpPagePatch7}
\pastebutton{TableXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{t x\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch8}
\begin{paste}{TableXmpPageFull8}{TableXmpPageEmpty8}
\pastebutton{TableXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{t.(x^2 - 1)\free{p3 }}
\indentrel{3}\begin{verbatim}
   (8)  "Easy to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty8}
\begin{paste}{TableXmpPageEmpty8}{TableXmpPagePatch8}
\pastebutton{TableXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{t.(x^2 - 1)\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch9}
\begin{paste}{TableXmpPageFull9}{TableXmpPageEmpty9}
\pastebutton{TableXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{t (x^3 + 1)\free{p3 }}
\indentrel{3}\begin{verbatim}
   (9)  "Harder to factor"
                                           Type: String
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty9}
\begin{paste}{TableXmpPageEmpty9}{TableXmpPagePatch9}
\pastebutton{TableXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{t (x^3 + 1)\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch10}
\begin{paste}{TableXmpPageFull10}{TableXmpPageEmpty10}
\pastebutton{TableXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{keys t\free{p3 }}
\indentrel{3}\begin{verbatim}
              3       2
   (10)  [x, x  + 1, x  - 1]
                        Type: List(Polynomial(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty10}
\begin{paste}{TableXmpPageEmpty10}{TableXmpPagePatch10}
\pastebutton{TableXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{keys t\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch11}
\begin{paste}{TableXmpPageFull11}{TableXmpPageEmpty11}
\pastebutton{TableXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{search(x, t)\free{p3 }}
\indentrel{3}\begin{verbatim}
   (11)  "The easiest to factor"
                                Type: Union(String,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty11}
\begin{paste}{TableXmpPageEmpty11}{TableXmpPagePatch11}
\pastebutton{TableXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{search(x, t)\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch12}
\begin{paste}{TableXmpPageFull12}{TableXmpPageEmpty12}
\pastebutton{TableXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{search(x^2, t)\free{p3 }}
\indentrel{3}\begin{verbatim}
   (12)  "failed"
                              Type: Union("failed",...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty12}
\begin{paste}{TableXmpPageEmpty12}{TableXmpPagePatch12}
\pastebutton{TableXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{search(x^2, t)\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch13}
\begin{paste}{TableXmpPageFull13}{TableXmpPageEmpty13}
\pastebutton{TableXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{search(x^2, t) case "failed"\free{p3 }}
\indentrel{3}\begin{verbatim}
   (13)  true
                                          Type: Boolean
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty13}
\begin{paste}{TableXmpPageEmpty13}{TableXmpPagePatch13}
\pastebutton{TableXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{search(x^2, t) case "failed"\free{p3 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch14}
\begin{paste}{TableXmpPageFull14}{TableXmpPageEmpty14}
\pastebutton{TableXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{remove!(x^2-1, t)\free{p3 }\bound{p4 }}
\indentrel{3}\begin{verbatim}
   (14)  "Easy to factor"
                                Type: Union(String,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty14}
\begin{paste}{TableXmpPageEmpty14}{TableXmpPagePatch14}
\pastebutton{TableXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{remove!(x^2-1, t)\free{p3 }\bound{p4 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch15}
\begin{paste}{TableXmpPageFull15}{TableXmpPageEmpty15}
\pastebutton{TableXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{remove!(x-1, t)\free{p4 }\bound{p5 }}
\indentrel{3}\begin{verbatim}
   (15)  "failed"
                              Type: Union("failed",...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty15}
\begin{paste}{TableXmpPageEmpty15}{TableXmpPagePatch15}
\pastebutton{TableXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{remove!(x-1, t)\free{p4 }\bound{p5 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch16}
\begin{paste}{TableXmpPageFull16}{TableXmpPageEmpty16}
\pastebutton{TableXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{\#t\free{p5 }}
\indentrel{3}\begin{verbatim}
   (16)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty16}
\begin{paste}{TableXmpPageEmpty16}{TableXmpPagePatch16}
\pastebutton{TableXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{\#t\free{p5 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch17}
\begin{paste}{TableXmpPageFull17}{TableXmpPageEmpty17}
\pastebutton{TableXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{members t\free{p5 }}
\indentrel{3}\begin{verbatim}
   (17)  ["The easiest to factor", "Harder to factor"]
                                     Type: List(String)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty17}
\begin{paste}{TableXmpPageEmpty17}{TableXmpPagePatch17}
\pastebutton{TableXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{members t\free{p5 }}
\end{paste}\end{patch}

\begin{patch}{TableXmpPagePatch18}
\begin{paste}{TableXmpPageFull18}{TableXmpPageEmpty18}
\pastebutton{TableXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{count(s: String +-> prefix?("Hard", s), t)\free{p5 }}
\indentrel{3}\begin{verbatim}
   (18)  1
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{TableXmpPageEmpty18}
\begin{paste}{TableXmpPageEmpty18}{TableXmpPagePatch18}
\pastebutton{TableXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{count(s: String +-> prefix?("Hard", s), t)\free{p5 }}
\end{paste}\end{patch}

