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\begin{patch}{PartialFractionXmpPagePatch1}
\begin{paste}{PartialFractionXmpPageFull1}{PartialFractionXmpPageEmpty1}
\pastebutton{PartialFractionXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{partialFraction(1,factorial 10)\bound{prev1 }}
\indentrel{3}\begin{verbatim}
159 23 12 1
(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}
(2)
1 1 1 1 1 1 2 1 2 2 2 1
� + �� + �� + �� + �� + �� - �� - �� - �� - � - �� + �
2 4 5 6 7 8 2 3 4 5 2 7
2 2 2 2 2 3 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}
159 23 12 1
(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) 12
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{nthFractionalTerm(f,3)\free{f }}
\indentrel{3}\begin{verbatim}
1
(5) ��
5
2
Type: PartialFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{PartialFractionXmpPageEmpty5}
\begin{paste}{PartialFractionXmpPageEmpty5}{PartialFractionXmpPagePatch5}
\pastebutton{PartialFractionXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{nthFractionalTerm(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 - 12x - ���
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)
1 1 1 17 3
��� � �� �� �
648 4 16 8 4
����� + ����� - �������� - ����� + ��������
x + 1 x + 2 2 x + 3 2
(x + 2) (x + 3)
+
1 607 403 13 1
� ��� ��� �� ��
2 324 432 36 12
- �������� + ����� + �������� + �������� + ��������
3 x + 4 2 3 4
(x + 3) (x + 4) (x + 4) (x + 4)
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}
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