{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 
0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "restart:f:=x/y^2*exp
(1-x/y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(f,y=0..x):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(int(f,y)=u2,y);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\",&F&!\"\"-%#lnG6#%#u2
GF&F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" }{MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "M:=Int(Int(f*exp(t*x+u*y
),y=0..x),x=0..1):  evalf(int(int(f*x,y=x..1),x=0..1));evalf(int(int(f
*y,y=x..1),x=0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*G=G=#!\"*
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*949f$!\"*" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 53 "m:=(i,j)->evalf(subs(\{t=0,u=0\},diff(ln(M),
t$i,u$j))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "mu(0,0):=0:m
u(1,0):=0:mu(0,1):=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "au
x:=subs(\{t=0,u=0\},diff(exp(add(add(mu(i,j)*t^i*u^j/i!/j!,i=0..3),j=0
..2)),t$3,u$2)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "aux:=su
bs(exp(0)=1,aux):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "for i \+
from 0 to 3 do for j from 0 to 2 do aux:=subs(mu(i,j)=mu(i,j)/n^(i+j-1
),aux) end do end do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "au
x:=subs(mu=m,aux);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG,**&-%\"m
G6$\"\"$\"\"#\"\"\"%\"nG!\"%F,*(-F(6$F*\"\"!F,F-!\"$-F(6$F2F+F,F,**\"
\"'F,-F(6$F+F,F,F-F3-F(6$F,F,F,F,**F*F,-F(6$F+F2F,F-F3-F(6$F,F+F,F," }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(aux);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&*&$\"(q=+%!#5\"\"\"%\"nG!\"%!\"\"*&$\"+\\zY+5!
#7F(F)!\"$F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "M:=Int(Int(f*exp(t*x
+t*y),y=0..x),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "m
:=i->evalf(subs(t=0,diff(ln(M),t$i))):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "for i to 4 do k[i]:=evalf(m(i)) end do;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%\"kG6#\"\"\"$\"+7ot\")z!#5" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%\"kG6#\"\"#$\"+a*yOG#!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"kG6#\"\"$$\")A-@>!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"kG6#\"\"%$!)>b!)\\!\"*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 64 "for i to 3 do g[i]:=evalf(subs(x=k[1],diff(sin(x),x
$i))) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"gG6#\"\"\"$\"+wm
:!)p!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"gG6#\"\"#$!+n[#3;(!#5
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"gG6#\"\"$$!+wm:!)p!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "evalf(sin(k[1])+g[2]*k[2]/2/
n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+n[#3;(!#5\"\"\"*&$\"+?D^w
\")!#6F'%\"nG!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "eva
lf(g[1]^2*k[2]/n+(g[1]*g[2]*k[3]+g[1]*g[3]*k[2]^2+g[2]^2*k[2]^2/2)/n^2
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&$\"+qum76!#5\"\"\"%\"nG!\"\"
F(*&$\"+Cd1k@!#6F(F)!\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
44 "evalf(g[1]^2/n^2*(g[1]*k[3]+3*g[2]*k[2]^2));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&$\"+!y?`![!#6\"\"\"%\"nG!\"#!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 95 "evalf((g[1]^4*k[4]+12*g[1]^3*g[2]*k[3]*k[
2]+4*g[1]^3*g[3]*k[2]^3+12*g[1]^2*g[2]^2*k[2]^3)/n^3);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&$\")^fnC!#6\"\"\"%\"nG!\"$!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 109 "restart:assume(a>0):f:=(1+x/a)^(-1-a):  aux
0:=diff(ln(f),a):  aux:=simplify(series(subs(a=a+a1*e,aux0),e,2));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG+)%\"eG*(,.*&-%#lnG6#%#a|irG\"
\"\")F-\"\"#F.F.*(F*F.F-F.%\"xGF.F.*&-F+6#,&F-F.F2F.F.F/F.!\"\"*(F4F.F
-F.F2F.F7F2F.*&F-F.F2F.F.F.F-F7F6F7\"\"!*,F2F.%#a1GF.F-!\"#,(F9F.*&F0F
.F-F.F7F2F7F.F6F=F.-%\"OG6#F.F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 36 "int(coeff(aux,e,0)*f,x=0..infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "aux
2:=factor(int(coeff(aux,e,1)*f,x=0..infinity))/a1;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%aux2G,$**\"\"#\"\"\"%#a|irG!\"#,&F(F(F)F(!\"\",&F)
F(F'F(F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a1:=factor(co
eff(aux,e,0)/aux2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a1G,$*&#\"\"
\"\"\"#F(*,,.*&-%#lnG6#%#a|irGF()F0F)F(!\"\"*(F-F(F0F(%\"xGF(F2*&-F.6#
,&F0F(F4F(F(F1F(F(*(F6F(F0F(F4F(F(F4F2*&F0F(F4F(F2F(F0F(,&F(F(F0F(F(,&
F0F(F)F(F(F8F2F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "facto
r(int(a1^2*f,x=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**
\"\"#!\"\",&\"\"\"F(%#a|irGF(F(F)F%,&F)F(F%F(F(F(" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 106 "with(stats): u:=random[uniform](10): X:=[ 0
.35, 0.45, 3.93, 0.041, 0.097, 24.32, 4.35, 0.83, 1.81, 11.60]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "RIS:=add(eval(aux0,x=X[i]),i
=1..10):plot(RIS,a=.1..10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "fsolve(RIS,a=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Ctu]y!#5" 
}}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "restart: ifactor(2213314919066161);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*$)-%!G6#\"#>\"#7\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "with(numtheory):" }}{PARA 7 "" 1 "" {TEXT -1 69 "Wa
rning, the protected name order has been redefined and unprotected\n" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "seq(order(i,19),i=1..18);
   # must be  2,3,10,13,14,15   mod 19" }}{PARA 11 "" 1 "" {XPPMATH 
20 "64\"\"\"\"#=F$\"\"*F%F%\"\"$\"\"'F%F$F&F'F$F$F$F%F%\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "aux:=msolve(i^18=1,19^2);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG64<#/%\"iG\"\"\"<#/F(\"$X#<#/F
(\"$F\"<#/F(\"$i#<#/F(\"#G<#/F(\"$#H<#/F(\"$$H<#/F(\"#a<#/F(\"$*H<#/F(
\"#i<#/F(\"$2$<#/F(\"#o<#/F(\"#p<#/F(\"$L$<#/F(\"#**<#/F(\"$M#<#/F(\"$
;\"<#/F(\"$g$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "seq(rhs(au
x[i,1])mod 19,i=1..18);  # but not 116, 307, 333, 127, 299, 262 respec
tively" }}{PARA 11 "" 1 "" {XPPMATH 20 "64\"\"\"\"#<\"#8\"#:\"\"*\"\"(
\"\")\"#;\"#9\"\"&\"\"$\"#6\"#7\"#5\"\"%\"\"'\"\"#\"#=" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "18*19^11;   #length" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"1Uz;gY#o4#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "2*3*18*19^10;   #number" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"03D%e:b@m" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "888888
88 mod 19;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "88888888 mod 19^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"$>#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}}{MARK "31 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }