\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}