{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 "Maple Output1
2" -1 209 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 "HyperlinkError" -1 210 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" -1 211 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 "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 "List It
em" -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" -1 212 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" -1 213 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 "Norm
al256" -1 214 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 "Courier" 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 "T
itle" -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" -1 215 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 "Autho
r" -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 Underlined Bold" -1 41
 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "
Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21
 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" -1 31 "Ti
mes" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Atomic Variable" 
-1 200 "Times" 1 12 175 0 175 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Dictiona
ry 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 "Times" 1 10 
0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small204" -1 204 
"Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "C
ourier" 1 10 0 0 0 1 2 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 Sm
all205" -1 205 "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 U
nderlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D
 Math Italic Small" -1 206 "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" -1 207 "Times" 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" -1 208 "Times" 1 12 0 0 0 1 2 2 2 2
 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "Times" 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 Reference" -1 209 "Times" 1 
12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 38 "Times" 1 12 0
 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1
 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 
210 "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 Emphas
ized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Equatio
n Label" -1 211 "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 "Prom
pt" -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 "Hyperlin
k" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Captio
n Text" -1 212 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1
 213 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 208 201 "In this Maple file, we \+
compute the coefficients of the polynomials P_1 and P_2 in terms of th
e irregular times for the second element of the Painlev\351 1 hierarch
y. We check with the theoretical results." }{TEXT 208 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 11 "rinfty
:=4:\n" }{MPLTEXT 1 0 10 "rinfty-2;\n" }{MPLTEXT 1 0 12 "2*rinfty-3;\n
" }{MPLTEXT 1 0 27 "P1:=x-> Pinfty01+Pinfty11*x" }{MPLTEXT 1 0 13 "+Pi
nfty21*x^2" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 54 "P2:=x-> Pinfty02+P
infty12*x+Pinfty22*x^2+Pinfty32*x^3+" }{MPLTEXT 1 0 13 "Pinfty42*x^4+"
 }{MPLTEXT 1 0 12 "Pinfty52*x^5" }{MPLTEXT 1 0 1 ";" }}{PARA 11 "" 1 "
" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF
$F$,(I)Pinfty01GF$\"\"\"*&I)Pinfty11GF$F-9$F-F-*&I)Pinfty21GF$F-F0\"\"
#F-F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6\"f*6#I\"xGF$F$6$I)o
peratorGF$I&arrowGF$F$,.I)Pinfty02GF$\"\"\"*&I)Pinfty12GF$F-9$F-F-*&I)
Pinfty22GF$F-F0\"\"#F-*&I)Pinfty32GF$F-F0\"\"$F-*&I)Pinfty42GF$F-F0\"
\"%F-*&I)Pinfty52GF$F-F0\"\"&F-F$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "ClassicalSpectralCurve:=unapply( y^2-P1(x)*y+P2(x),y)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I7ClassicalSpectralCurveG6\"f*6#I
\"yGF$F$6$I)operatorGF$I&arrowGF$F$,2*$9$\"\"#\"\"\"*&,(*&I\"xGF$F.I)P
infty21GF$F/F/*&F3F/I)Pinfty11GF$F/F/I)Pinfty01GF$F/F/F-F/!\"\"*&I)Pin
fty52GF$F/F3\"\"&F/*&I)Pinfty42GF$F/F3\"\"%F/*&I)Pinfty32GF$F/F3\"\"$F
/*&I)Pinfty22GF$F/F3F.F/*&I)Pinfty12GF$F/F3F/F/I)Pinfty02GF$F/F$F$F$" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "2*rinfty-1;\n" }{MPLTEXT 
1 0 8 "Yinfty:=" }{MPLTEXT 1 0 21 "-1/2*tinfty17*x^(5/2)" }{MPLTEXT 1 
0 19 "-1/2*tinfty16*x^(2)" }{MPLTEXT 1 0 21 "-1/2*tinfty15*x^(3/2)" }
{MPLTEXT 1 0 15 "-1/2*tinfty14*x" }{MPLTEXT 1 0 21 "-1/2*tinfty13*x^(1
/2)" }{MPLTEXT 1 0 13 "-1/2*tinfty12" }{MPLTEXT 1 0 59 "-1/2*tinfty11*
x^(-1/2)-1/2*tinfty10*x^(-1)+ Unknown/x^(3/2)" }{MPLTEXT 1 0 2 ";\n" }
{MPLTEXT 1 0 11 "Yinftybis:=" }{MPLTEXT 1 0 40 "-1/2*tinfty27*x^(5/2)-
1/2*tinfty26*x^(2)" }{MPLTEXT 1 0 21 "-1/2*tinfty25*x^(3/2)" }{MPLTEXT
 1 0 109 "-1/2*tinfty24*x-1/2*tinfty23*x^(1/2)-1/2*tinfty22-1/2*tinfty
21*x^(-1/2)-1/2*tinfty20*x^(-1)+ Unknownn/x^(3/2)" }{MPLTEXT 1 0 1 ";"
 }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"(" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I'YinftyG6\",4*&I)tinfty17GF$\"\"\"I\"xGF$#\"
\"&\"\"##!\"\"F,*&I)tinfty16GF$F(F)F,F-*&I)tinfty15GF$F(F)#\"\"$F,F-*&
I)tinfty14GF$F(F)F(F-*&I)tinfty13GF$F(F)#F(F,F-I)tinfty12GF$F-*&I)tinf
ty11GF$F(F)F-F-*&I)tinfty10GF$F(F)F.F-*&I(UnknownGF$F(F)#!\"$F,F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I*YinftybisG6\",4*&I)tinfty27GF$\"\"\"I
\"xGF$#\"\"&\"\"##!\"\"F,*&I)tinfty26GF$F(F)F,F-*&I)tinfty25GF$F(F)#\"
\"$F,F-*&I)tinfty24GF$F(F)F(F-*&I)tinfty23GF$F(F)#F(F,F-I)tinfty22GF$F
-*&I)tinfty21GF$F(F)F-F-*&I)tinfty20GF$F(F)F.F-*&I)UnknownnGF$F(F)#!\"
$F,F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 214 40 "Expression of P1 in ter
ms of both sheets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "series
(Yinfty+Yinftybis-P1(x),x=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
,8*&,&I)tinfty17G6\"#!\"\"\"\"#I)tinfty27GF&F'\"\"\"*$I\"xGF&F(#!\"&F)
F+*&,(I)tinfty16GF&F'I)tinfty26GF&F'I)Pinfty21GF&F(F+F-F)F+*&,&I)tinft
y15GF&F'I)tinfty25GF&F'F+F,#!\"$F)F+*&,(I)tinfty14GF&F'I)tinfty24GF&F'
I)Pinfty11GF&F(F+F-F+F+*&,&I)tinfty13GF&F'I)tinfty23GF&F'F+F,F'F+I)tin
fty12GF&F'I)tinfty22GF&F'I)Pinfty01GF&F(*&,&I)tinfty11GF&F'I)tinfty21G
F&F'F+F,#F+F)F+*&,&I)tinfty10GF&F'I)tinfty20GF&F'F+F-F(F+*&,&I(Unknown
GF&F+I)UnknownnGF&F+F+F,#\"\"$F)F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
208 130 "We check that the odd irregular times must be opposite and th
at coefficients of P_1 are reconstructed by only even irregular times"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "tinfty27:=-tinfty17:" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "tinfty25:=-tinfty15:\n" }
{MPLTEXT 1 0 21 "tinfty23:=-tinfty13:\n" }{MPLTEXT 1 0 21 "tinfty21:=-
tinfty11:\n" }{MPLTEXT 1 0 21 "tinfty20:=-tinfty10:\n" }{MPLTEXT 1 0 
33 "Pinfty21:=-(tinfty16+tinfty26)/2;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 34 "Pinfty11:=-(tinfty14+tinfty24)/2;\n" }{MPLTEXT 1 0 34 "Pinfty0
1:=-(tinfty12+tinfty22)/2;\n" }{MPLTEXT 1 0 20 "Unknownn:=-Unknown:\n"
 }{MPLTEXT 1 0 20 "Unknownn2:=Unknown2:" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 42 "series(Yinfty+Yinftybis-P1(x),x=infinity);" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty21G6\",&I)tinfty16GF$#!\"\"\"\"#I)tin
fty26GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty11G6\",&I)tinfty1
4GF$#!\"\"\"\"#I)tinfty24GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pin
fty01G6\",&I)tinfty12GF$#!\"\"\"\"#I)tinfty22GF$F'" }}{PARA 11 "" 1 ""
 {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "seri
es(simplify(ClassicalSpectralCurve(Yinfty)),x=infinity);" }{MPLTEXT 1 
0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ",L*&,&*$I)tinfty17G6\"\"\"##\"
\"\"\"\"%I)Pinfty52GF'F*F*I\"xGF'\"\"&F**(F&F*,&I)tinfty16GF'F*I)tinft
y26GF'!\"\"F**$F-F3#!\"*F(F)*&,(*&I)tinfty15GF'F*F&F*#F*F(*&F1F*F2F*#F
3F+I)Pinfty42GF'F*F*F-F+F**&,&*&F0F*F:F*F)*&F&F*,&I)tinfty14GF'F*I)tin
fty24GF'F3F*F)F*F4#!\"(F(F**&,,*&I)tinfty13GF'F*F&F*F;*&FDF*F2F*F=*$F:
F(F)*&F1F*FEF*F=I)Pinfty32GF'F*F*F-\"\"$F**&,(*&F0F*FKF*F)*&FCF*F:F*F)
*&F&F*,&I)tinfty12GF'F*I)tinfty22GF'F3F*F)F*F4#!\"&F(F**&,.*&I)tinfty1
1GF'F*F&F*F;*&FWF*F2F*F=*&FKF*F:F*F;*&FDF*FEF*F=*&F1F*FXF*F=I)Pinfty22
GF'F*F*F-F(F**&,**&I)tinfty10GF'F*F&F*F;*&F0F*FhnF*F)*&FCF*FKF*F)*&F:F
*FVF*F)F*F4#!\"$F(F**&,0*&F0F*FaoF*F)*&F:F*FhnF*F;*&FWF*FEF*F=*$FKF(F)
*&FDF*FXF*F=*&F&F*I(UnknownGF'F*F3I)Pinfty12GF'F*F*F-F*F**&,**&FaoF*F:
F*F;*&FCF*FhnF*F)*&FVF*FKF*F)*&F_pF*F0F*#F3F(F*F4FgpF**&FCF*FaoF*F)*&F
KF*FhnF*F;*&FWF*FXF*F=*&F:F*F_pF*F3I)Pinfty02GF'F**&,(*&FaoF*FKF*F;*&F
VF*FhnF*F)*&F_pF*FCF*FgpF*F4F;F**&,(*&FVF*FaoF*F)*$FhnF(F)*&FKF*F_pF*F
3F*F-F3F**&,&*&FaoF*FhnF*F;*&F_pF*FVF*FgpF*F4#FPF(F**&,&*&F_pF*FhnF*F3
*$FaoF(F)F*F-!\"#F**(F_pF*FaoF*F4#F.F(F3*&F_pF(F-FfoF*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 208 153 "We check here that even irregular times
 are equal and that there cannot be monodromies otherwise we would get
 half-power coefficients that should be null" }}}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 19 "tinfty26:=tinfty16:" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 20 "tinfty24:=tinfty14:\n" }{MPLTEXT 1 0 20 "tinfty22:=ti
nfty12:\n" }{MPLTEXT 1 0 13 "tinfty10:=0:\n" }{MPLTEXT 1 0 60 "series(
simplify(ClassicalSpectralCurve(Yinfty)),x=infinity);" }}{PARA 11 "" 1
 "" {XPPMATH 20 ",:*&,&*$I)tinfty17G6\"\"\"##\"\"\"\"\"%I)Pinfty52GF'F
*F*I\"xGF'\"\"&F**&,(*&I)tinfty15GF'F*F&F*#F*F(*$I)tinfty16GF'F(#!\"\"
F+I)Pinfty42GF'F*F*F-F+F**&,**&I)tinfty13GF'F*F&F*F3*&I)tinfty14GF'F*F
5F*#F7F(*$F2F(F)I)Pinfty32GF'F*F*F-\"\"$F**&,,*&I)tinfty11GF'F*F&F*F3*
&I)tinfty12GF'F*F5F*F?*&F<F*F2F*F3*$F>F(F6I)Pinfty22GF'F*F*F-F(F**&,,*
&F&F*I(UnknownGF'F*F7*&F2F*FFF*F3*&FHF*F>F*F?*$F<F(F)I)Pinfty12GF'F*F*
F-F*F**&F2F*FOF*F7*&F<F*FFF*F3*$FHF(F6I)Pinfty02GF'F**&,&*&F<F*FOF*F7*
$FFF(F)F*F-F7F**(FOF*FFF*F-!\"#F7*&FOF(F-!\"$F*" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 214 36 "Study of the asymptotics at infinity" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "series(ClassicalSpectralCurve(Yinft
y),x=infinity,8):\n" }{MPLTEXT 1 0 56 "series(ClassicalSpectralCurve(Y
inftybis),x=infinity,8):\n" }{MPLTEXT 1 0 79 "EQinfty0:=residue(simpli
fy(x^(-6)*ClassicalSpectralCurve(Yinfty)),x=infinity);\n" }{MPLTEXT 1 
0 82 "EQinfty00:=residue(simplify(x^(-6)*ClassicalSpectralCurve(Yinfty
bis)),x=infinity);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "EQinfty1:=r
esidue(" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 52 "x^(-5)*Classica
lSpectralCurve(Yinfty)),x=infinity);\n" }{MPLTEXT 1 0 82 "EQinfty2:=re
sidue(simplify(x^(-5)*ClassicalSpectralCurve(Yinftybis)),x=infinity);
\n" }{MPLTEXT 1 0 18 "EQinfty3:=residue(" }{MPLTEXT 1 0 9 "simplify(" 
}{MPLTEXT 1 0 52 "x^(-4)*ClassicalSpectralCurve(Yinfty)),x=infinity);
\n" }{MPLTEXT 1 0 18 "EQinfty4:=residue(" }{MPLTEXT 1 0 9 "simplify(" 
}{MPLTEXT 1 0 55 "x^(-4)*ClassicalSpectralCurve(Yinftybis)),x=infinity
);\n" }{MPLTEXT 1 0 18 "EQinfty5:=residue(" }{MPLTEXT 1 0 9 "simplify(
" }{MPLTEXT 1 0 52 "x^(-3)*ClassicalSpectralCurve(Yinfty)),x=infinity)
;\n" }{MPLTEXT 1 0 18 "EQinfty6:=residue(" }{MPLTEXT 1 0 9 "simplify("
 }{MPLTEXT 1 0 55 "x^(-3)*ClassicalSpectralCurve(Yinftybis)),x=infinit
y);\n" }{MPLTEXT 1 0 18 "EQinfty7:=residue(" }{MPLTEXT 1 0 9 "simplify
(" }{MPLTEXT 1 0 52 "x^(-2)*ClassicalSpectralCurve(Yinfty)),x=infinity
);\n" }{MPLTEXT 1 0 18 "EQinfty8:=residue(" }{MPLTEXT 1 0 9 "simplify(
" }{MPLTEXT 1 0 55 "x^(-2)*ClassicalSpectralCurve(Yinftybis)),x=infini
ty);\n" }{MPLTEXT 1 0 18 "EQinfty9:=residue(" }{MPLTEXT 1 0 9 "simplif
y(" }{MPLTEXT 1 0 52 "x^(-1)*ClassicalSpectralCurve(Yinfty)),x=infinit
y);\n" }{MPLTEXT 1 0 19 "EQinfty10:=residue(" }{MPLTEXT 1 0 9 "simplif
y(" }{MPLTEXT 1 0 55 "x^(-1)*ClassicalSpectralCurve(Yinftybis)),x=infi
nity);\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQin
fty0G6\",&*$I)tinfty17GF$\"\"##!\"\"\"\"%I)Pinfty52GF$F*" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I*EQinfty00G6\",&*$I)tinfty17GF$\"\"##!\"\"\"\"%I
)Pinfty52GF$F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty1G6\",(*&I)t
infty15GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*$I)tinfty16GF$F,#F(\"\"%I)P
infty42GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty2G6\",(*&I)tin
fty15GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*$I)tinfty16GF$F,#F(\"\"%I)Pin
fty42GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty3G6\",**&I)tinft
y13GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty14GF$F(I)tinfty16GF$F(
#F(F,*$I)tinfty15GF$F,#F+\"\"%I)Pinfty32GF$F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)EQinfty4G6\",**&I)tinfty13GF$\"\"\"I)tinfty17GF$F(#!\"
\"\"\"#*&I)tinfty14GF$F(I)tinfty16GF$F(#F(F,*$I)tinfty15GF$F,#F+\"\"%I
)Pinfty32GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty5G6\",,*&I)t
infty11GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty12GF$F(I)tinfty16G
F$F(#F(F,*&I)tinfty13GF$F(I)tinfty15GF$F(F**$I)tinfty14GF$F,#F(\"\"%I)
Pinfty22GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty6G6\",,*&I)ti
nfty11GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty12GF$F(I)tinfty16GF
$F(#F(F,*&I)tinfty13GF$F(I)tinfty15GF$F(F**$I)tinfty14GF$F,#F(\"\"%I)P
infty22GF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty7G6\",,*&I)tin
fty17GF$\"\"\"I(UnknownGF$F(F(*&I)tinfty15GF$F(I)tinfty11GF$F(#!\"\"\"
\"#*&I)tinfty12GF$F(I)tinfty14GF$F(#F(F/*$I)tinfty13GF$F/#F.\"\"%I)Pin
fty12GF$F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty8G6\",,*&I)tinft
y17GF$\"\"\"I(UnknownGF$F(F(*&I)tinfty15GF$F(I)tinfty11GF$F(#!\"\"\"\"
#*&I)tinfty12GF$F(I)tinfty14GF$F(#F(F/*$I)tinfty13GF$F/#F.\"\"%I)Pinft
y12GF$F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty9G6\",**&I)tinfty1
5GF$\"\"\"I(UnknownGF$F(F(*&I)tinfty13GF$F(I)tinfty11GF$F(#!\"\"\"\"#*
$I)tinfty12GF$F/#F(\"\"%I)Pinfty02GF$F." }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I*EQinfty10G6\",**&I)tinfty15GF$\"\"\"I(UnknownGF$F(F(*&I)tinfty1
3GF$F(I)tinfty11GF$F(#!\"\"\"\"#*$I)tinfty12GF$F/#F(\"\"%I)Pinfty02GF$
F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 48 "We compute the value of so
me coefficients of P_2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "P
infty52:=factor(solve(EQinfty0,Pinfty52));" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 43 "Pinfty42:=factor(solve(EQinfty1,Pinfty42));" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 44 "Pinfty32:=factor(solve(EQinfty3,
Pinfty32));\n" }{MPLTEXT 1 0 43 "Pinfty22:=factor(solve(EQinfty5,Pinft
y22));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "simplify(EQinfty00);\n"
 }{MPLTEXT 1 0 19 "simplify(EQinfty2);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT
 1 0 19 "simplify(EQinfty4);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "s
implify(EQinfty6);\n" }{MPLTEXT 1 0 19 "simplify(EQinfty8);" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty52G6\",$*$I)tinfty17GF$\"\"##!\"\"\"
\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty42G6\",&*&I)tinfty15GF$
\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*$I)tinfty16GF$F,#F(\"\"%" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I)Pinfty32G6\",(*&I)tinfty13GF$\"\"\"I)tinfty17G
F$F(#!\"\"\"\"#*&I)tinfty14GF$F(I)tinfty16GF$F(#F(F,*$I)tinfty15GF$F,#
F+\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty22G6\",**&I)tinfty11
GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty12GF$F(I)tinfty16GF$F(#F(
F,*&I)tinfty13GF$F(I)tinfty15GF$F(F**$I)tinfty14GF$F,#F(\"\"%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&I)tinfty17G6\"
\"\"\"I(UnknownGF%F&F&*&I)tinfty15GF%F&I)tinfty11GF%F&#!\"\"\"\"#*&I)t
infty12GF%F&I)tinfty14GF%F&#F&F-*$I)tinfty13GF%F-#F,\"\"%I)Pinfty12GF%
F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 213 23 "Summary of coefficients" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Pinfty01:=Pinfty01;\n" }
{MPLTEXT 1 0 20 "Pinfty11:=Pinfty11;\n" }{MPLTEXT 1 0 19 "Pinfty21:=Pi
nfty21;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "P
infty02:=Pinfty02;\n" }{MPLTEXT 1 0 20 "Pinfty12:=Pinfty12;\n" }
{MPLTEXT 1 0 20 "Pinfty22:=Pinfty22;\n" }{MPLTEXT 1 0 20 "Pinfty32:=Pi
nfty32;\n" }{MPLTEXT 1 0 20 "Pinfty42:=Pinfty42;\n" }{MPLTEXT 1 0 19 "
Pinfty52:=Pinfty52;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty01G6\",$I)tinfty12GF$!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty11G6\",$I)tinfty14GF$!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty21G6\",$I)tinfty16GF$!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I)Pinfty02G6\"F#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)Pinfty12G6\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pin
fty22G6\",**&I)tinfty11GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty12
GF$F(I)tinfty16GF$F(#F(F,*&I)tinfty13GF$F(I)tinfty15GF$F(F**$I)tinfty1
4GF$F,#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty32G6\",(*&I)t
infty13GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty14GF$F(I)tinfty16G
F$F(#F(F,*$I)tinfty15GF$F,#F+\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
)Pinfty42G6\",&*&I)tinfty15GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*$I)tinf
ty16GF$F,#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty52G6\",$*$
I)tinfty17GF$\"\"##!\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 214 53 
"We have 2 unknown coefficients: Pinfty02 and Pinfty12" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 208 48 "We check the formula for the coefficient
s of P_2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "Pinfty22theo:=
 1/4*sum((-1)^i*tinfty[i]*tinfty[2*(rinfty-2)-i+4],i=2*(rinfty-2)-2*ri
nfty+5..2*rinfty-1);\n" }{MPLTEXT 1 0 15 "Pinfty32theo:= " }{MPLTEXT 
1 0 52 "1/4*sum((-1)^i*tinfty[i]*tinfty[2*(rinfty-1)-i+4],i=" }
{MPLTEXT 1 0 23 "2*(rinfty-1)-2*rinfty+5" }{MPLTEXT 1 0 15 "..2*rinfty
-1);\n" }{MPLTEXT 1 0 15 "Pinfty42theo:= " }{MPLTEXT 1 0 86 "1/4*sum((
-1)^i*tinfty[i]*tinfty[2*(rinfty)-i+4],i=2*(rinfty)-2*rinfty+5..2*rinf
ty-1);\n" }{MPLTEXT 1 0 15 "Pinfty52theo:= " }{MPLTEXT 1 0 89 "1/4*sum
((-1)^i*tinfty[i]*tinfty[2*(rinfty+1)-i+4],i=2*(rinfty+1)-2*rinfty+5..
2*rinfty-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-Pinfty22theoG6\",**&&
I'tinftyGF$6#\"\"\"F*&F(6#\"\"(F*#!\"\"\"\"#*&&F(6#F0F*&F(6#\"\"'F*#F*
F0*&&F(6#\"\"$F*&F(6#\"\"&F*F.*$&F(6#\"\"%F0#F*FB" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I-Pinfty32theoG6\",(*&&I'tinftyGF$6#\"\"$\"\"\"&F(6#\"\"
(F+#!\"\"\"\"#*&&F(6#\"\"%F+&F(6#\"\"'F+#F+F1*$&F(6#\"\"&F1#F0F5" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I-Pinfty42theoG6\",&*&&I'tinftyGF$6#\"
\"&\"\"\"&F(6#\"\"(F+#!\"\"\"\"#*$&F(6#\"\"'F1#F+\"\"%" }}{PARA 11 "" 
1 "" {XPPMATH 20 ">I-Pinfty52theoG6\",$*$&I'tinftyGF$6#\"\"(\"\"##!\"
\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{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 }