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|
\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}
|
