\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull1}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull1}{\hidepaste}
\tab{5}\spadcommand{Dx: LODO(EXPR INT, f +-> D(f, x))\bound{Dxd }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}{\showpaste}
\tab{5}\spadcommand{Dx: LODO(EXPR INT, f +-> D(f, x))\bound{Dxd }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull2}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull2}{\hidepaste}
\tab{5}\spadcommand{Dx := D()\free{Dxd }\bound{Dx }}
\indentrel{3}\begin{verbatim}
   (2)  D
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap NIL)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}{\showpaste}
\tab{5}\spadcommand{Dx := D()\free{Dxd }\bound{Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull3}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull3}{\hidepaste}
\tab{5}\spadcommand{Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1\free{Dx }\bound{Dop }}
\indentrel{3}\begin{verbatim}
                       3
         3    G     - x  + H
   (3)  D  + �� D + ��������
              2         3
             x         x
Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap NIL)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}{\showpaste}
\tab{5}\spadcommand{Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1\free{Dx }\bound{Dop }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull4}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull4}{\hidepaste}
\tab{5}\spadcommand{n == 3\bound{n3 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}{\showpaste}
\tab{5}\spadcommand{n == 3\bound{n3 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull5}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull5}{\hidepaste}
\tab{5}\spadcommand{phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])\bound{phi }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}{\showpaste}
\tab{5}\spadcommand{phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])\bound{phi }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull6}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull6}{\hidepaste}
\tab{5}\spadcommand{phi1 == Dop(phi) / exp x\bound{phi1 }\free{Dop phi }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}{\showpaste}
\tab{5}\spadcommand{phi1 == Dop(phi) / exp x\bound{phi1 }\free{Dop phi }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull7}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull7}{\hidepaste}
\tab{5}\spadcommand{phi2 == phi1 *x**(n+3)\bound{phi2 }\free{phi1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}{\showpaste}
\tab{5}\spadcommand{phi2 == phi1 *x**(n+3)\bound{phi2 }\free{phi1 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull8}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull8}{\hidepaste}
\tab{5}\spadcommand{phi3 == retract(phi2)@(POLY INT)\bound{phi3 }\free{phi2 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}{\showpaste}
\tab{5}\spadcommand{phi3 == retract(phi2)@(POLY INT)\bound{phi3 }\free{phi2 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull9}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull9}{\hidepaste}
\tab{5}\spadcommand{pans == phi3 ::UP(x,POLY INT)\free{phi3 }\bound{pans }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}{\showpaste}
\tab{5}\spadcommand{pans == phi3 ::UP(x,POLY INT)\free{phi3 }\bound{pans }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull10}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull10}{\hidepaste}
\tab{5}\spadcommand{pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]\bound{pans1 }\free{pans }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}{\showpaste}
\tab{5}\spadcommand{pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]\bound{pans1 }\free{pans }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull11}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull11}{\hidepaste}
\tab{5}\spadcommand{leq == solve(pans1,[subscript(s,[i]) for i in 1..n])\bound{leq }\free{pans1 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}{\showpaste}
\tab{5}\spadcommand{leq == solve(pans1,[subscript(s,[i]) for i in 1..n])\bound{leq }\free{pans1 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch12}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull12}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull12}{\hidepaste}
\tab{5}\spadcommand{leq\free{n3 leq }}
\indentrel{3}\begin{verbatim}
   (12)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ���, s = ������������������,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = ��������������������������������������]
       3                    162
     ]
   Type: List List Equation Fraction Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch12}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}{\showpaste}
\tab{5}\spadcommand{leq\free{n3 leq }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch13}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull13}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull13}{\hidepaste}
\tab{5}\spadcommand{n==4\bound{n4 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch13}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}{\showpaste}
\tab{5}\spadcommand{n==4\bound{n4 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch14}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull14}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull14}{\hidepaste}
\tab{5}\spadcommand{leq\free{n4 leq }}
\indentrel{3}\begin{verbatim}
   (14)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ���, s = ������������������,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = ��������������������������������������,
       3                    162

       s  =
        4
                  2         2                          4
             27s H  + (18s G  + 378s G + 1296s )H + s G
                0         0         0         0      0
           + 
                  3         2
             36s G  + 396s G  + 1296s G
                0         0          0
        /
           1944
       ]
     ]
   Type: List List Equation Fraction Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch14}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}{\showpaste}
\tab{5}\spadcommand{leq\free{n4 leq }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch15}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull15}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull15}{\hidepaste}
\tab{5}\spadcommand{n==7\bound{n7 }}
\indentrel{3}\begin{verbatim}
                                             Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch15}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}{\showpaste}
\tab{5}\spadcommand{n==7\bound{n7 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch16}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull16}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull16}{\hidepaste}
\tab{5}\spadcommand{leq\free{n7 leq }}
\indentrel{3}\begin{verbatim}
   (16)
   [
                             2
          s G      3s H + s G  + 6s G
           0         0     0       0
     [s = ���, s = ������������������,
       1   3    2          18
                              3        2
          (9s G + 54s )H + s G  + 18s G  + 72s G
             0       0      0        0        0
      s = ��������������������������������������,
       3                    162

       s  =
        4
                  2         2                          4
             27s H  + (18s G  + 378s G + 1296s )H + s G
                0         0         0         0      0
           + 
                  3         2
             36s G  + 396s G  + 1296s G
                0         0          0
        /
           1944
       ,

       s  =
        5
                               2
             (135s G + 2268s )H
                  0         0
           + 
                   3          2
             (30s G  + 1350s G  + 16416s G + 38880s )H
                 0          0           0          0
           + 
              5        4          3          2
           s G  + 60s G  + 1188s G  + 9504s G  + 25920s G
            0        0          0          0           0
        /
           29160
       ,

       s  =
        6
                   3          2                        2
             405s H  + (405s G  + 18468s G + 174960s )H
                 0          0           0           0
           + 
                      4          3           2
                 45s G  + 3510s G  + 88776s G  + 777600s G
                    0          0           0            0
               + 
                 1166400s
                         0
            *
               H
           + 
                6        5          4           3
             s G  + 90s G  + 2628s G  + 27864s G
              0        0          0           0
           + 
                     2
             90720s G
                   0
        /
           524880
       ,

       s  =
        7
                                 3
             (2835s G + 91854s )H
                   0          0
           + 
                       3           2
                 945s G  + 81648s G  + 2082996s G
                     0           0             0
               + 
                 14171760s
                          0
            *
                2
               H
           + 
                      5          4            3
                 63s G  + 7560s G  + 317520s G
                    0          0            0
               + 
                           2
                 5554008s G  + 34058880s G
                         0              0
            *
               H
           + 
                7         6          5           4
             s G  + 126s G  + 4788s G  + 25272s G
              0         0          0           0
           + 
                         3              2
             - 1744416s G  - 26827200s G  - 97977600s G
                       0              0              0
        /
           11022480
       ]
     ]
   Type: List List Equation Fraction Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch16}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}{\showpaste}
\tab{5}\spadcommand{leq\free{n7 leq }}
\end{paste}\end{patch}