\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 + 컴 D + 컴컴컴컴 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 = 컴�, s = 컴컴컴컴컴컴컴컴컴, 1 3 2 18 3 2 (9s G + 54s )H + s G + 18s G + 72s G 0 0 0 0 0 s = 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴] 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 = 컴�, s = 컴컴컴컴컴컴컴컴컴, 1 3 2 18 3 2 (9s G + 54s )H + s G + 18s G + 72s G 0 0 0 0 0 s = 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴, 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 = 컴�, s = 컴컴컴컴컴컴컴컴컴, 1 3 2 18 3 2 (9s G + 54s )H + s G + 18s G + 72s G 0 0 0 0 0 s = 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴, 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}