{VERSION 6 0 "Windows 10" "6.0" }
{USTYLETAB {PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0
 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "War
ning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0
 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Outp
ut" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 
}1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "
" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 
0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 
255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Head
ing 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1
 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 
0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "T
imes" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }
{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2
 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" 
-1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 
0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1
 "Courier" 1 10 64 128 64 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2
 2 -1 1 }{PSTYLE "Ordered List 1" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE 
"Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2
 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 2" 
-1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 
1 0 0 3 3 2 36 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE
 "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2
 0 2 2 -1 1 }{PSTYLE "Normal262" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 
24 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE 
"Ordered List 4" -1 204 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 
2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Normal261" -1 
205 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0
 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 206 1 {CSTYLE "" 
-1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 
2 2 -1 1 }{PSTYLE "Annotation Title" -1 207 1 {CSTYLE "" -1 -1 "Times"
 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }
{PSTYLE "Normal260" -1 208 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1
 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "HyperlinkErro
r" -1 209 1 {CSTYLE "" -1 -1 "Courier New" 1 12 255 0 255 1 2 2 1 2 2 
1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "HyperlinkWarning" -1
 210 1 {CSTYLE "" -1 -1 "Courier New" 1 12 0 0 255 1 2 2 1 2 2 1 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3
 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time
s" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 
2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal259" -1 
211 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0
 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal257" -1 212 1 {CSTYLE "" -1 -1
 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 
1 }{PSTYLE "Normal256" -1 213 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item"
 -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 
1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "C
ourier" 1 10 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 
-1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 
1 1 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal" -1
 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 
0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author258" -1 214 1 {CSTYLE "" -1 -1 
"Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1
 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2
 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{CSTYLE "Help Variable" 
-1 25 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underl
ined Bold" -1 41 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "Co
pyright" -1 34 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Mapl
e Comment" -1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "
Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "At
omic Variable" -1 200 "Times" 1 12 175 0 175 1 1 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2
 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 
0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 255 0 0 1 2 2 2 2 1 2 0
 0 0 1 }{CSTYLE "Code" -1 201 "Courier New" 1 12 255 0 0 1 2 2 2 2 2 2
 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2
 2 0 0 0 1 }{CSTYLE "2D Math Small" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2
 2 0 0 0 1 }{CSTYLE "2D Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1
 2 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 
2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 2
 2 2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2
 2 2 2 0 0 0 1 }{CSTYLE "2D Inert Output" -1 202 "Times" 1 12 144 144 
144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 1 12 
255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Header and Footer" -1 203 "Ti
mes" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small20
4" -1 204 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed
" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math I
talic Small206" -1 205 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 
}{CSTYLE "2D Math Italic Small205" -1 206 "Times" 1 1 0 0 0 1 1 2 2 2 
2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2
 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1
 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 207 "Times" 1 1 0 0 
0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 16 "Times" 1 12
 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Courier" 1 
12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Annotation Text" -1 208 "Time
s" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "
Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 209 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "Tim
es" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic"
 -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Caption Refe
rence" -1 210 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Defau
lt" -1 38 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Ital
ic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Mapl
e Input Placeholder" -1 211 "Courier New" 1 12 200 0 200 1 2 1 2 2 1 2
 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0
 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0
 0 0 1 }{CSTYLE "Equation Label" -1 212 "Times" 1 12 0 0 0 1 2 1 2 2 2
 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 
2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 
2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 
0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 
0 0 1 }{CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 
0 0 0 1 }{CSTYLE "Caption Text" -1 213 "Times" 1 12 0 0 0 1 2 1 2 2 2 
2 0 0 0 1 }{PSTYLE "" -1 215 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 255 1
 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 216 
1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0
 0 2 0 2 0 2 2 -1 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 209 149 "In this Maple file, we \+
compute the Casimir coefficients of the Lax matrix L associated to the
 Painlev\351 3 equation in relation with the spectral curve" }{TEXT 
209 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }
{MPLTEXT 1 0 34 "P1:=x-> P021/x^2+P011/x+Pinfty01;\n" }{MPLTEXT 1 0 
52 "P2:=x-> P042/x^4+P032/x^3+P022/x^2+P012/x+Pinfty02;\n" }{MPLTEXT 
1 0 45 "SpectralCurve:=unapply( y^2-P1(x)*y+P2(x),y);" }}{PARA 11 "" 1
 "" {XPPMATH 20 ">I#P1G6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,(*&
I%P021GF$\"\"\")F'\"\"#!\"\"F.*&I%P011GF$F.F'F1F.I)Pinfty01GF$F.F$F$F$
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6\"f*6#I\"xGF$F$6$I)operatorGF
$I&arrowGF$F$,,*&I%P042GF$\"\"\")F'\"\"%!\"\"F.*&I%P032GF$F.)F'\"\"$F1
F.*&I%P022GF$F.)F'\"\"#F1F.*&I%P012GF$F.F'F1F.I)Pinfty02GF$F.F$F$F$" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I.SpectralCurveG6\"f*6#I\"yGF$F$6$I)op
eratorGF$I&arrowGF$F$,0*$)F'\"\"#\"\"\"F/*&,(*&I%P021GF$F/)I\"xGF$F.!
\"\"F/*&I%P011GF$F/F5F6F/I)Pinfty01GF$F/F/F'F/F6*&I%P042GF$F/)F5\"\"%F
6F/*&I%P032GF$F/)F5\"\"$F6F/*&I%P022GF$F/F4F6F/*&I%P012GF$F/F5F6F/I)Pi
nfty02GF$F/F$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Diagin
ftySheet1" }{MPLTEXT 1 0 36 ":=-tinfty11-tinfty10/x+Unknown/x^2;\n" }
{MPLTEXT 1 0 15 "DiaginftySheet2" }{MPLTEXT 1 0 37 ":=-tinfty21-tinfty
20/x+Unknown2/x^2;\n" }{MPLTEXT 1 0 11 "Diag0Sheet1" }{MPLTEXT 1 0 28 
":=t011/x^2+t010/x+Unknown3;\n" }{MPLTEXT 1 0 11 "Diag0Sheet2" }
{MPLTEXT 1 0 28 ":=t021/x^2+t020/x+Unknown4; " }{MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I0DiaginftySheet1G6\",(I)tinfty11GF$!\"
\"*&I)tinfty10GF$\"\"\"I\"xGF$F'F'*&I(UnknownGF$F*)F+\"\"#F'F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I0DiaginftySheet2G6\",(I)tinfty21GF$!\"
\"*&I)tinfty20GF$\"\"\"I\"xGF$F'F'*&I)Unknown2GF$F*)F+\"\"#F'F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,Diag0Sheet1G6\",(*&I%t011GF$\"\"\")I
\"xGF$\"\"#!\"\"F(*&I%t010GF$F(F*F,F(I)Unknown3GF$F(" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I,Diag0Sheet2G6\",(*&I%t021GF$\"\"\")I\"xGF$\"\"#!\"
\"F(*&I%t020GF$F(F*F,F(I)Unknown4GF$F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 214 67 "Expression of P_1 in terms of the diagonal expansion in \+
both sheets" }{TEXT 214 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "series(" }{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 1 "+" }
{MPLTEXT 1 0 15 "DiaginftySheet2" }{MPLTEXT 1 0 20 "-P1(x),x=infinity)
;\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 11 "Diag0Sheet1" }
{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 11 "Diag0Sheet2" }{MPLTEXT 1 0 14 "-P
1(x),x=0,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,I)Pinfty01G6\"!\"\"I)t
infty11GF$F%I)tinfty21GF$F%*&,(I%P011GF$F%I)tinfty10GF$F%I)tinfty20GF$
F%\"\"\"I\"xGF$F%F-*&,(I%P021GF$F%I(UnknownGF$F-I)Unknown2GF$F-F-)F.\"
\"#F%F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "+)I\"xG6\",(I%t011GF$\"\"\"I%
t021GF$F'I%P021GF$!\"\"!\"#,(I%t010GF$F'I%t020GF$F'I%P011GF$F*F*,(I)Un
known3GF$F'I)Unknown4GF$F'I)Pinfty01GF$F*\"\"!" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 17 "P021:=t011+t021;\n" }{MPLTEXT 1 0 17 "P011:=t01
0+t020;\n" }{MPLTEXT 1 0 32 "Pinfty01:=-(tinfty11+tinfty21);\n" }
{MPLTEXT 1 0 9 "Coherence" }{MPLTEXT 1 0 19 "Equation1:=residue(" }
{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 
15 "DiaginftySheet2" }{MPLTEXT 1 0 19 "-P1(x),x=infinity);" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I%P021G6\",&I%t011GF$\"\"\"I%t021GF$F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I%P011G6\",&I%t010GF$\"\"\"I%t020GF$F'"
 }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty01G6\",&I)tinfty11GF$!\"\"I)
tinfty21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3CoherenceEquation1G6
\",*I)tinfty10GF$\"\"\"I)tinfty20GF$F'I%t010GF$F'I%t020GF$F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 214 12 "Study at x=0" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "factor(series(" }{MPLTEXT 1 0 14 "SpectralCu
rve(" }{MPLTEXT 1 0 11 "Diag0Sheet1" }{MPLTEXT 1 0 9 "),x=0)):\n" }
{MPLTEXT 1 0 14 "factor(series(" }{MPLTEXT 1 0 14 "SpectralCurve(" }
{MPLTEXT 1 0 11 "Diag0Sheet2" }{MPLTEXT 1 0 9 "),x=0)):\n" }{MPLTEXT 
1 0 18 "EQ01:=residue(x^3*" }{MPLTEXT 1 0 14 "SpectralCurve(" }
{MPLTEXT 1 0 11 "Diag0Sheet1" }{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 
0 18 "EQ02:=residue(x^3*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 
1 0 11 "Diag0Sheet2" }{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 0 18 "EQ0
3:=residue(x^2*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "D
iag0Sheet1" }{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 0 18 "EQ04:=residu
e(x^2*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "Diag0Sheet
2" }{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 0 16 "EQ05:=residue(x*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "Diag0Sheet1" }
{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 0 16 "EQ06:=residue(x*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "Diag0Sheet2" }
{MPLTEXT 1 0 8 "),x=0);\n" }{MPLTEXT 1 0 18 "EQ07:=residue(x^0*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "Diag0Sheet1" }
{MPLTEXT 1 0 8 "),x=0):\n" }{MPLTEXT 1 0 18 "EQ08:=residue(x^0*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 11 "Diag0Sheet2" }
{MPLTEXT 1 0 8 "),x=0):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ01G6\",&*&I%t011GF$\"\"\"I%t021GF$
F(!\"\"I%P042GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ02G6\",&*&I%t
011GF$\"\"\"I%t021GF$F(!\"\"I%P042GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I%EQ03G6\",(*&I%t010GF$\"\"\"I%t021GF$F(!\"\"*&I%t011GF$F(I%t020G
F$F(F*I%P032GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ04G6\",(*&I%t0
10GF$\"\"\"I%t021GF$F(!\"\"*&I%t011GF$F(I%t020GF$F(F*I%P032GF$F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ05G6\",.*&I%t010GF$\"\"\"I%t020GF$F
(!\"\"*&I%t011GF$F(I)Unknown3GF$F(F(*&F,F(I)tinfty11GF$F(F(*&F,F(I)tin
fty21GF$F(F(*&I%t021GF$F(F-F(F*I%P022GF$F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%EQ06G6\",.*&I%t010GF$\"\"\"I%t020GF$F(!\"\"*&I%t011GF$
F(I)Unknown4GF$F(F**&I%t021GF$F(F-F(F(*&F/F(I)tinfty11GF$F(F(*&F/F(I)t
infty21GF$F(F(I%P022GF$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "P042:=solve(EQ01,P042);\n" }{MPLTEXT 1 0 24 "P032:=solve(EQ03,P032
);\n" }{MPLTEXT 1 0 16 "simplify(EQ01);\n" }{MPLTEXT 1 0 16 "simplify(
EQ02);\n" }{MPLTEXT 1 0 16 "simplify(EQ03);\n" }{MPLTEXT 1 0 16 "simpl
ify(EQ04);\n" }{MPLTEXT 1 0 16 "simplify(EQ05);\n" }{MPLTEXT 1 0 16 "s
implify(EQ06);\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I%P042G6\"*&I%t011GF$\"\"\"I%t021GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I%P032G6\",&*&I%t010GF$\"\"\"I%t021GF$F(F(*&I%t011GF$F(I%t020GF$F
(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&,(I)Un
known3G6\"\"\"\"I)tinfty11GF&F'I)tinfty21GF&F'F'I%t011GF&F'F'*&I%t010G
F&F'I%t020GF&F'!\"\"*&F%F'I%t021GF&F'F.I%P022GF&F'" }}{PARA 11 "" 1 ""
 {XPPMATH 20 ",**&,(I)Unknown4G6\"\"\"\"I)tinfty11GF&F'I)tinfty21GF&F'
F'I%t021GF&F'F'*&I%t010GF&F'I%t020GF&F'!\"\"*&F%F'I%t011GF&F'F.I%P022G
F&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 214 17 "Study at infinity" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 14 "Sp
ectralCurve(" }{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 17 "),x
=infinity,3):\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 14 "SpectralC
urve(" }{MPLTEXT 1 0 15 "DiaginftySheet2" }{MPLTEXT 1 0 17 "),x=infini
ty,3):\n" }{MPLTEXT 1 0 25 "EQinfty1:=residue(x^(-2)*" }{MPLTEXT 1 0 
14 "SpectralCurve(" }{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 
15 "),x=infinity);\n" }{MPLTEXT 1 0 25 "EQinfty2:=residue(x^(-2)*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 15 "DiaginftySheet2" }
{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 0 25 "EQinfty3:=residue
(x^(-1)*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 15 "Diaginft
ySheet1" }{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 0 25 "EQinfty
4:=residue(x^(-1)*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 
15 "DiaginftySheet2" }{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 
0 24 "EQinfty5:=residue(x^(0)*" }{MPLTEXT 1 0 14 "SpectralCurve(" }
{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 15 "),x=infinity);\n" 
}{MPLTEXT 1 0 24 "EQinfty6:=residue(x^(0)*" }{MPLTEXT 1 0 14 "Spectral
Curve(" }{MPLTEXT 1 0 15 "DiaginftySheet2" }{MPLTEXT 1 0 15 "),x=infin
ity);\n" }{MPLTEXT 1 0 24 "EQinfty7:=residue(x^(1)*" }{MPLTEXT 1 0 14 
"SpectralCurve(" }{MPLTEXT 1 0 15 "DiaginftySheet1" }{MPLTEXT 1 0 15 "
),x=infinity);\n" }{MPLTEXT 1 0 24 "EQinfty8:=residue(x^(1)*" }
{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 15 "DiaginftySheet2" }
{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 0 24 "EQinfty9:=residue
(x^(2)*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 15 "Diaginfty
Sheet1" }{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 0 25 "EQinfty1
0:=residue(x^(2)*" }{MPLTEXT 1 0 14 "SpectralCurve(" }{MPLTEXT 1 0 15 
"DiaginftySheet2" }{MPLTEXT 1 0 15 "),x=infinity);\n" }{MPLTEXT 1 0 1 
"\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty1G6\"\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I)EQinfty2G6\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)EQinfty3G6\",(*$)I)tinfty11GF$\"\"#\"\"\"!\"\"*&,&F(F+
I)tinfty21GF$F+F*F(F*F+I)Pinfty02GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I)EQinfty4G6\",(*$)I)tinfty21GF$\"\"#\"\"\"!\"\"*&,&I)tinfty11GF$F+
F(F+F*F(F*F+I)Pinfty02GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinft
y5G6\",**(\"\"#\"\"\"I)tinfty11GF$F(I)tinfty10GF$F(!\"\"*&,&F)F+I)tinf
ty21GF$F+F(F*F(F+*&,&I%t010GF$F(I%t020GF$F(F(F)F(F+I%P012GF$F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty6G6\",**(\"\"#\"\"\"I)tinfty21
GF$F(I)tinfty20GF$F(!\"\"*&,&I)tinfty11GF$F+F)F+F(F*F(F+*&,&I%t010GF$F
(I%t020GF$F(F(F)F(F+I%P012GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQ
infty7G6\",.*(\"\"#\"\"\"I)tinfty11GF$F(I(UnknownGF$F(F(*$)I)tinfty10G
F$F'F(!\"\"*&,&F)F.I)tinfty21GF$F.F(F*F(F(*&,&I%t010GF$F(I%t020GF$F(F(
F-F(F.*&,&I%t011GF$F(I%t021GF$F(F(F)F(F.I%P022GF$F." }}{PARA 11 "" 1 "
" {XPPMATH 20 ">I)EQinfty8G6\",.*(\"\"#\"\"\"I)tinfty21GF$F(I)Unknown2
GF$F(F(*$)I)tinfty20GF$F'F(!\"\"*&,&I)tinfty11GF$F.F)F.F(F*F(F(*&,&I%t
010GF$F(I%t020GF$F(F(F-F(F.*&,&I%t011GF$F(I%t021GF$F(F(F)F(F.I%P022GF$
F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty9G6\",,*(\"\"#\"\"\"I)ti
nfty10GF$F(I(UnknownGF$F(F(*&,&I%t010GF$F(I%t020GF$F(F(F*F(F(*&,&I%t01
1GF$F(I%t021GF$F(F(F)F(!\"\"*&F-F(F2F(F3*&F1F(F.F(F3" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I*EQinfty10G6\",,*(\"\"#\"\"\"I)tinfty20GF$F(I)Unknow
n2GF$F(F(*&,&I%t010GF$F(I%t020GF$F(F(F*F(F(*&,&I%t011GF$F(I%t021GF$F(F
(F)F(!\"\"*&F-F(F2F(F3*&F1F(F.F(F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "Pinfty02:=solve(EQinfty3,Pinfty02);\n" }{MPLTEXT 1 0 
20 "simplify(EQinfty3);\n" }{MPLTEXT 1 0 20 "simplify(EQinfty4);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty02G6\"*&I)tinfty11GF$\"\"\"I)ti
nfty21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 ""
 {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "P012
:=factor(solve(EQinfty5+EQinfty6,P012)):\n" }{MPLTEXT 1 0 91 "P012bis:
=-1/2*(t010+t020)*(tinfty11+tinfty21)-1/2*(tinfty10-tinfty20)*(tinfty1
1-tinfty21):\n" }{MPLTEXT 1 0 88 "P012:=-1/2*(t010+t020)*(tinfty11+tin
fty21)-1/2*(tinfty10-tinfty20)*(tinfty11-tinfty21);\n" }{MPLTEXT 1 0 
24 "simplify(P012-P012bis);\n" }{MPLTEXT 1 0 38 "factor(EQinfty5-(tinf
ty21-tinfty11)/2*" }{MPLTEXT 1 0 9 "Coherence" }{MPLTEXT 1 0 12 "Equat
ion1);\n" }{MPLTEXT 1 0 38 "factor(EQinfty6+(tinfty21-tinfty11)/2*" }
{MPLTEXT 1 0 9 "Coherence" }{MPLTEXT 1 0 11 "Equation1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I%P012G6\",&*(#\"\"\"\"\"#F(,&I%t010GF$F(I%t020GF
$F(F(,&I)tinfty11GF$F(I)tinfty21GF$F(F(!\"\"*(F'F(,&I)tinfty10GF$F(I)t
infty20GF$F0F(,&F.F(F/F0F(F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }
}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 215 "" 1 "" {XPPMATH 20 
"\"\"!" }}}{EXCHG {PARA 216 "" 0 "" {TEXT 209 23 "Summary of coefficie
nts" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "P042:=P042;\n" }
{MPLTEXT 1 0 12 "P032:=P032;\n" }{MPLTEXT 1 0 12 "P022:=P022;\n" }
{MPLTEXT 1 0 12 "P012:=P012;\n" }{MPLTEXT 1 0 12 "P011:=P011;\n" }
{MPLTEXT 1 0 12 "P021:=P021;\n" }{MPLTEXT 1 0 20 "Pinfty01:=Pinfty01;
\n" }{MPLTEXT 1 0 20 "Pinfty02:=Pinfty02;\n" }{MPLTEXT 1 0 9 "Coherenc
e" }{MPLTEXT 1 0 40 "Equation1:=tinfty10+tinfty20+t010+t020;\n" }
{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P042G6\"*&I%t01
1GF$\"\"\"I%t021GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P032G6\",&*&
I%t010GF$\"\"\"I%t021GF$F(F(*&I%t011GF$F(I%t020GF$F(F(" }}{PARA 11 "" 
1 "" {XPPMATH 20 ">I%P022G6\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P0
12G6\",&*(#\"\"\"\"\"#F(,&I%t010GF$F(I%t020GF$F(F(,&I)tinfty11GF$F(I)t
infty21GF$F(F(!\"\"*(F'F(,&I)tinfty10GF$F(I)tinfty20GF$F0F(,&F.F(F/F0F
(F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P011G6\",&I%t010GF$\"\"\"I%t02
0GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P021G6\",&I%t011GF$\"\"\"I%
t021GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty01G6\",&I)tinfty11
GF$!\"\"I)tinfty21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty02G6
\"*&I)tinfty11GF$\"\"\"I)tinfty21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I3CoherenceEquation1G6\",*I)tinfty10GF$\"\"\"I)tinfty20GF$F'I%t010G
F$F'I%t020GF$F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 209 32 "We have one u
nknown coefficient " }{TEXT 209 5 "P022." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2
 33 1 1 }