\begin{patch}{PartialFractionXmpPagePatch1}
\begin{paste}{PartialFractionXmpPageFull1}{PartialFractionXmpPageEmpty1}
\pastebutton{PartialFractionXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{partialFraction(1,factorial 10)\bound{prev1 }}
\indentrel{3}\begin{verbatim}
          97   58   13   6
   (1)  - -- + -- + -- - -
           8    4    2   7
          2    3    5
                         Type: PartialFraction(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty1}
\begin{paste}{PartialFractionXmpPageEmpty1}{PartialFractionXmpPagePatch1}
\pastebutton{PartialFractionXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{partialFraction(1,factorial 10)\bound{prev1 }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch2}
\begin{paste}{PartialFractionXmpPageFull2}{PartialFractionXmpPageEmpty2}
\pastebutton{PartialFractionXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{f := padicFraction(\%)\free{prev1 }\bound{f }}
\indentrel{3}\begin{verbatim}
           1    1    1   2    1    1   2    3   6
   (2)  - -- - -- - -- + - + -- + -- + - + -- - -
           2    3    8   3    3    4   5    2   7
          2    2    2        3    3        5
                         Type: PartialFraction(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty2}
\begin{paste}{PartialFractionXmpPageEmpty2}{PartialFractionXmpPagePatch2}
\pastebutton{PartialFractionXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{f := padicFraction(\%)\free{prev1 }\bound{f }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch3}
\begin{paste}{PartialFractionXmpPageFull3}{PartialFractionXmpPageEmpty3}
\pastebutton{PartialFractionXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{compactFraction(f)\free{f }}
\indentrel{3}\begin{verbatim}
          97   58   13   6
   (3)  - -- + -- + -- - -
           8    4    2   7
          2    3    5
                         Type: PartialFraction(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty3}
\begin{paste}{PartialFractionXmpPageEmpty3}{PartialFractionXmpPagePatch3}
\pastebutton{PartialFractionXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{compactFraction(f)\free{f }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch4}
\begin{paste}{PartialFractionXmpPageFull4}{PartialFractionXmpPageEmpty4}
\pastebutton{PartialFractionXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{numberOfFractionalTerms(f)\free{f }}
\indentrel{3}\begin{verbatim}
   (4)  9
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty4}
\begin{paste}{PartialFractionXmpPageEmpty4}{PartialFractionXmpPagePatch4}
\pastebutton{PartialFractionXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{numberOfFractionalTerms(f)\free{f }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch5}
\begin{paste}{PartialFractionXmpPageFull5}{PartialFractionXmpPageEmpty5}
\pastebutton{PartialFractionXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{fractionalTerms(f).3\free{f }}
\indentrel{3}\begin{verbatim}
   (5)  [num = - 1, d_fact = 2, d_exp = 8]
Type: Record(num: Integer,d_fact: Integer,d_exp: NonNegativeInteger)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty5}
\begin{paste}{PartialFractionXmpPageEmpty5}{PartialFractionXmpPagePatch5}
\pastebutton{PartialFractionXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{fractionalTerms(f).3\free{f }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch6}
\begin{paste}{PartialFractionXmpPageFull6}{PartialFractionXmpPageEmpty6}
\pastebutton{PartialFractionXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{partialFraction(1,- 13 + 14 * \%i)\bound{prev2 }}
\indentrel{3}\begin{verbatim}
              1          4
   (6)  - -------- + --------
          1 + 2 %i   3 + 8 %i
                Type: PartialFraction(Complex(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty6}
\begin{paste}{PartialFractionXmpPageEmpty6}{PartialFractionXmpPagePatch6}
\pastebutton{PartialFractionXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{partialFraction(1,- 13 + 14 * \%i)\bound{prev2 }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch7}
\begin{paste}{PartialFractionXmpPageFull7}{PartialFractionXmpPageEmpty7}
\pastebutton{PartialFractionXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{prev2 }}
\indentrel{3}\begin{verbatim}
              %i
   (7)  - ----------
          14 + 13 %i
                       Type: Fraction(Complex(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty7}
\begin{paste}{PartialFractionXmpPageEmpty7}{PartialFractionXmpPagePatch7}
\pastebutton{PartialFractionXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{prev2 }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch8}
\begin{paste}{PartialFractionXmpPageFull8}{PartialFractionXmpPageEmpty8}
\pastebutton{PartialFractionXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])\bound{u }}
\indentrel{3}\begin{verbatim}
                      2       3       4
   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
Type: Factored(UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty8}
\begin{paste}{PartialFractionXmpPageEmpty8}{PartialFractionXmpPagePatch8}
\pastebutton{PartialFractionXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])\bound{u }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch9}
\begin{paste}{PartialFractionXmpPageFull9}{PartialFractionXmpPageEmpty9}
\pastebutton{PartialFractionXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{partialFraction(1,u)\free{u }\bound{prev3 }}
\indentrel{3}\begin{verbatim}
   (9)
       1     1      7     17  2          139
      ---    - x + --   - -- x  - 12 x - ---
      648    4     16      8              8
     ----- + -------- + --------------------
     x + 1          2                3
             (x + 2)          (x + 3)
   + 
     607  3   10115  2   391     44179
     --- x  + ----- x  + --- x + -----
     324       432        4       324
     ---------------------------------
                         4
                  (x + 4)
Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty9}
\begin{paste}{PartialFractionXmpPageEmpty9}{PartialFractionXmpPagePatch9}
\pastebutton{PartialFractionXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{partialFraction(1,u)\free{u }\bound{prev3 }}
\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPagePatch10}
\begin{paste}{PartialFractionXmpPageFull10}{PartialFractionXmpPageEmpty10}
\pastebutton{PartialFractionXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{padicFraction \%\free{prev3 }}
\indentrel{3}\begin{verbatim}
   (10)
      607       403        13          1        17
      ---       ---        --         --        --
      324       432        36         12         8
     ----- + -------- + -------- + -------- - -----
     x + 4          2          3          4   x + 3
             (x + 4)    (x + 4)    (x + 4)
   + 
         3          1        1         1        1
         -          -        -        --       ---
         4          2        4        16       648
     -------- - -------- + ----- - -------- + -----
            2          3   x + 2          2   x + 1
     (x + 3)    (x + 3)            (x + 2)
Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{PartialFractionXmpPageEmpty10}
\begin{paste}{PartialFractionXmpPageEmpty10}{PartialFractionXmpPagePatch10}
\pastebutton{PartialFractionXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{padicFraction \%\free{prev3 }}
\end{paste}\end{patch}

