{VERSION 3 0 "APPLE_PPC_MAC" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 258 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "Gen
eva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "Geneva" 1 10 
0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "Geneva" 1 10 0 0 0 1 0 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 263 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 264 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 265 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "Gen
eva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "Geneva" 1 10 
0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "Geneva" 1 10 0 0 0 1 0 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 270 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 271 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 272 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "Gen
eva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "Geneva" 1 10 
0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "Geneva" 1 10 0 0 0 1 0 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 277 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 278 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 279 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "Gen
eva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "Geneva" 1 10 
0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "Geneva" 1 10 0 0 0 1 0 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 284 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 285 "Geneva" 1 10 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "No
rmal" -1 0 1 {CSTYLE "" -1 -1 "Geneva" 1 10 0 0 0 1 2 2 2 0 0 0 0 0 0 
}0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo
nt 0" -1 256 1 {CSTYLE "" -1 -1 "Monaco" 1 9 0 0 255 1 2 2 2 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 
{CSTYLE "" -1 -1 "Monaco" 1 9 255 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 96 "#The procedure \"tsc\" \+
defined below computes the Taylor series coefficients at x0 to degree \+
d of " }}{PARA 256 "" 0 "" {TEXT 273 96 "#a k dimensional vector field
 f, each entry of which is a symbolic expression in nx variables.  " }
}{PARA 256 "" 0 "" {TEXT 274 90 "#The symbolic expressions must be fun
ctions of the variables x=[ x[1],x[2],...,x[nx]] and " }}{PARA 256 "" 
0 "" {TEXT 275 90 "#Maple must be able to differentiate them.  The coe
fficients which are returned in a k by " }}{PARA 256 "" 0 "" {TEXT 
276 86 "#binomial(nx+d,d) matrix ordered by increasing degree and then
 lexographically within " }}{PARA 256 "" 0 "" {TEXT 277 88 "#degree fo
llowing the format of the Nonlinear Systems Toolbox (c). The degree d \+
must be " }}{PARA 256 "" 0 "" {TEXT 278 91 "#between 0 and 6  We start
 by defining the vector field f and the parameters k,nx,d,x0 and " }}
{PARA 256 "" 0 "" {TEXT 279 87 "#then we call \"tsc\".  The output mat
rix fx from \"tsc\" is passed to the maple procedure " }}{PARA 256 "" 
0 "" {TEXT 280 93 "#\"fortran\" which returns the fortran statements t
hat define the matrix.  These can be pasted " }}{PARA 256 "" 0 "" 
{TEXT 281 96 "#into a MATLAB script file and after making the appropri
ate changes of notation, e.g. replacing " }}{PARA 256 "" 0 "" {TEXT 
282 89 "#** by ^, it can be executed to put fx in the MATLAB workspace
.  To speed execution, add " }}{PARA 256 "" 0 "" {TEXT 283 140 "#semic
olons after each fortran statement. \n#  Suppose the vector field is a
 function of two or more vector variables, e.g., f=f(x,u), where " }}
{PARA 256 "" 0 "" {TEXT 284 93 "#x is dimension n and u is dimension m
.  First use MAPLE's subs command to replace u[1] with " }}{PARA 256 "
" 0 "" {TEXT 285 463 "#x[n+1], ..., u[m] by x[n+m] in f as follows.\n#
\n#for i from 1 by 1 to k\n#\011for j from 1 by 1 to m\n#\011\011f[i]=
subs(u[j]=x[n+j],f[i]):\n#\011od:\n#od:\n#\n#Then call \"tsc\" with nx
=n+m. After loading fx into the MATLAB workspace, the following\n#MATL
AB code will convert fx from lexographic form in the single vector [x;
u] to block #lexographic form in the two vectors x and u.\n#\n#nf=[k n
+m];\n#df=[0 d];\n#ng=[n+m 0;n m]';\n#dg=[1 1];\n#g=eye(n+m);\n#fx=cmp
(fx,nf,df,g,ng,dg,df);\n\n\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 213 "re
start:\nk:=3:\nnx:=3:\nd:=6:\nf:=array(1..k):\nfx:=array(1..k,1..binom
ial(nx+d,d)):\n\nx0:=array(1..nx):\nx:=array(1..nx):\nx0[1]:=1:\nx0[2]
:=-1:\nx0[3]:=1:\n\n\nf[1]:=x[1]*x[2]^4:\nf[2]:=x[1]*x[2]*x[3]*x[3]^3:
\nf[3]:=1+x[3]^6:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 257 1 "\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 181 "tsc:=proc(f,k,nx,d,x0)\nlocal ff,i,j,j1,j2,j3,j4,j5,
j6,l2,l3,l4,l5,l6,r,r2,r3,r4,r5,r6;\nff:=array(1..k,1..binomial(nx+d,d
));\nfor i from 1 by 1 to k do\n ff[i,1]:=f[i]:\n if d>0 then\n  " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "for j1 from 1 by 1 to nx do\011
\011\n   ff[i,j1+1]:=diff(f[i],x[j1]):\n   l2:=binomial(nx+2,2)-binomi
al(nx-j1+2,2)+1:\n   " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "if d>1 the
n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "\n    for j2 from j1 by 1 to \+
nx do\n \011 if j1=j2 then r2:=2: else r2:=1:fi:\n\011 ff[i,l2]:=diff(
ff[i,j1+1],x[j2])/r2:\n\011" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if \+
d>2 then\n     " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 94 "l3:=binomial(nx+3,3)-binomial(nx-j1+3,3):\n
\011  l3:=l3+binomial(nx-j1+2,2)-binomial(nx-j2+2,2)+1:" }}{PARA 256 "
" 0 "" {TEXT 258 7 "\n\n\011    " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"for j3 from j2 by 1 to nx do\n\011  " }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 40 " if j2=j3 then r3:=r2+1: else r3:=1: fi:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "\n\011   ff[i,l3]:=diff(ff[i,l2]," }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "x[j3]" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1083 ")/r3:
\n\011   if d>3 then\n\011    l4:=binomial(nx+4,4)-binomial(nx-j1+4,4)
:\n\011    l4:=l4+binomial(nx-j1+3,3)-binomial(nx-j2+3,3):\n\011    l4
:=l4+binomial(nx-j2+2,2)-binomial(nx-j3+2,2)+1:\n\011\011for j4 from j
3 by 1 to nx do\n\011\011if j3=j4 then r4:=r3+1: else r4:=1 fi:\n\011 \+
    ff[i,l4]:=diff(ff[i,l3],x[j4])/r4:\n\011\011 if d>4 then\n\011\011
  l5:=binomial(nx+5,5)-binomial(nx-j1+5,5):\n\011      l5:=l5+binomial
(nx-j1+4,4)-binomial(nx-j2+4,4):\n          l5:=l5+binomial(nx-j2+3,3)
-binomial(nx-j3+3,3):\n\011\011  l5:=l5+binomial(nx-j3+2,2)-binomial(n
x-j4+2,2)+1:\n\011\011  for j5 from j4 by 1 to nx do\n\011       if j4
=j5 then r5:=r4+1: else r5:=1 fi:\n\011\011   ff[i,l5]:=diff(ff[i,l4],
x[j5])/r5:\n\011\011   if d>5 then\n\011\011\011l6:=binomial(nx+6,6)-b
inomial(nx-j1+6,6):\n\011        l6:=l6+binomial(nx-j1+5,5)-binomial(n
x-j2+5,5):\n            l6:=l6+binomial(nx-j2+4,4)-binomial(nx-j3+4,4)
:\n\011\011    l6:=l6+binomial(nx-j3+3,3)-binomial(nx-j4+3,3):\n\011
\011    l6:=l6+binomial(nx-j4+2,2)-binomial(nx-j5+2,2)+1:\n\011\011   \+
 for j6 from j5 by 1 to nx do\n\011         if j5=j6 then r6:=r5+1: el
se r6:=1 fi:\n\011\011     ff[i,l6]:=diff(ff[i,l5],x[j6])/r6:\n\011
\011\n\011\011     l6:=l6+1:\n\011\011    od: " }}{PARA 256 "" 0 "" 
{TEXT 259 3 "#j6" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "\n\011       fi
: " }}{PARA 256 "" 0 "" {TEXT 260 4 "#d>5" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "\n\011\011   l5:=l5+1:\n\011\011  od: " }}{PARA 256 "
" 0 "" {TEXT 261 3 "#j5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "\n\011  \+
   fi: " }}{PARA 256 "" 0 "" {TEXT 262 4 "#d>4" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "\n\011\011 l4:=l4+1:\n        od: " }}{PARA 256 "" 0 
"" {TEXT 263 3 "#j4" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "\n\011   fi:
  " }}{PARA 256 "" 0 "" {TEXT 264 4 "#d>3" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "\n       l3:=l3+1:\n\011  od: " }}{PARA 256 "" 0 "" 
{TEXT 265 3 "#j3" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "\n\011 fi:  " }}
{PARA 256 "" 0 "" {TEXT 266 5 "#d>2\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 "     l2:=l2+1:\n    od: " }}{PARA 256 "" 0 "" {TEXT 267 3 "#j2" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "\n   fi: " }}{PARA 256 "" 0 "" 
{TEXT 268 4 "#d>1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "\n  od:  " }}
{PARA 256 "" 0 "" {TEXT 269 3 "#j1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "\n fi: " }}{PARA 256 "" 0 "" {TEXT 270 4 "#d>0" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "\nod: " }}{PARA 256 "" 0 "" {TEXT 271 3 "#i\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "for i from 1 by 1 to k do\n for r \+
from 1 by 1 to nx do\n  for j from 1 by 1 to binomial(nx+d,d) do\n   f
f[i,j]:=subs(x[r]=eval(x0[r]),ff[i,j]);\n   ff[i,j]:=simplify(ff[i,j])
;\n  od:\011\n od:\nod:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "\n\neval
(ff)\nend: " }}}{EXCHG {PARA 256 "" 0 "" {TEXT 272 4 "#tsc" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fx:=tsc(f,k,nx,d
,x0):\nfortran(fx);" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(1,1) = 1
" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(1,2) = 1" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,3) = -4" }}{PARA 6 "" 1 "" {TEXT -1 17 "      \+
fx(1,4) = 0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(1,5) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,6) = -4" }}{PARA 6 "" 1 "" 
{TEXT -1 17 "      fx(1,7) = 0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      f
x(1,8) = 6" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(1,9) = 0" }}{PARA 
6 "" 1 "" {TEXT -1 18 "      fx(1,10) = 0" }}{PARA 6 "" 1 "" {TEXT -1 
18 "      fx(1,11) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,12) \+
= 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,13) = 0" }}{PARA 6 "" 
1 "" {TEXT -1 18 "      fx(1,14) = 6" }}{PARA 6 "" 1 "" {TEXT -1 18 " \+
     fx(1,15) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,16) = 0" 
}}{PARA 6 "" 1 "" {TEXT -1 19 "      fx(1,17) = -4" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,18) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,19) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,20) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,21) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,22) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,23) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,24) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,25) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,26) = 0" }}{PARA 6 "" 1 "" {TEXT -1 19 "      \+
fx(1,27) = -4" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,28) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,29) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,30) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,31) = 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,32) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,33) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,34) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,35) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,36) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,37) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,38) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,39) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,40) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,41) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,42) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,43) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,44) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,45) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,46) = 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,47) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,48) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,49) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,50) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,51) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,52) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,53) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,54) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,55) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,56) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,57) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,58) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,59) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,60) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,61) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,62) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,63) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,64) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,65) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,66) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,67) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,68) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,69) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,70) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,71) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,72) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,73) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,74) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,75) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,76) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,77) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,78) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,79) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,80) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,81) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(1,82) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(1,83) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(1,84) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,1) = -1" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,2) = -1" }}{PARA 6 "" 1 "" {TEXT -1 17 "      \+
fx(2,3) = 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,4) = -4" }}
{PARA 6 "" 1 "" {TEXT -1 17 "      fx(2,5) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 17 "      fx(2,6) = 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      f
x(2,7) = -4" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(2,8) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 17 "      fx(2,9) = 4" }}{PARA 6 "" 1 "" 
{TEXT -1 19 "      fx(2,10) = -6" }}{PARA 6 "" 1 "" {TEXT -1 18 "     \+
 fx(2,11) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,12) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,13) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,14) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,15) = 4" }}{PARA 6 "" 1 "" {TEXT -1 19 "      fx(2,16) = -6" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,17) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,18) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,19) = 6" }}{PARA 6 "" 1 "" {TEXT -1 19 "      fx(2,20) = -4" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,21) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,22) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,23) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,24) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,25) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,26) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,27) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,28) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,29) = 6" }}{PARA 6 "" 1 "" 
{TEXT -1 19 "      fx(2,30) = -4" }}{PARA 6 "" 1 "" {TEXT -1 18 "     \+
 fx(2,31) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,32) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,33) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,34) = 4" }}{PARA 6 "" 1 "" {TEXT -1 19 "      \+
fx(2,35) = -1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,36) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,37) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,38) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,39) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,40) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,41) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,42) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,43) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,44) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,45) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,46) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,47) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,48) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,49) = 4" }}{PARA 6 "" 1 "" 
{TEXT -1 19 "      fx(2,50) = -1" }}{PARA 6 "" 1 "" {TEXT -1 18 "     \+
 fx(2,51) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,52) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,53) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,54) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,55) = 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,56) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,57) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,58) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,59) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,60) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,61) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,62) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,63) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,64) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,65) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,66) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,67) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,68) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,69) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,70) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,71) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,72) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,73) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,74) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,75) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,76) = 1" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,77) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,78) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,79) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,80) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,81) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(2,82) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(2,83) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(2,84) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 17 "      fx(3,1) = 2" }}{PARA 6 "" 1 "" 
{TEXT -1 17 "      fx(3,2) = 0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      f
x(3,3) = 0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(3,4) = 6" }}{PARA 
6 "" 1 "" {TEXT -1 17 "      fx(3,5) = 0" }}{PARA 6 "" 1 "" {TEXT -1 
17 "      fx(3,6) = 0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(3,7) = \+
0" }}{PARA 6 "" 1 "" {TEXT -1 17 "      fx(3,8) = 0" }}{PARA 6 "" 1 "
" {TEXT -1 17 "      fx(3,9) = 0" }}{PARA 6 "" 1 "" {TEXT -1 19 "     \+
 fx(3,10) = 15" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,11) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,12) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,13) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,14) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,15) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,16) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,17) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,18) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,19) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 19 "      fx(3,20) = 20" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,21) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,22) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,23) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,24) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,25) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,26) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,27) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,28) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,29) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,30) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,31) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,32) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,33) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,34) = 0" }}{PARA 6 "" 1 "" {TEXT -1 19 "      fx(3,35) = 15" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,36) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,37) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,38) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,39) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,40) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,41) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,42) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,43) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,44) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,45) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,46) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,47) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,48) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,49) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,50) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,51) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,52) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,53) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,54) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,55) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,56) = 6" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,57) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,58) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,59) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,60) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,61) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,62) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,63) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,64) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,65) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,66) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,67) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,68) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,69) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,70) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,71) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,72) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,73) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,74) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,75) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,76) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,77) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,78) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,79) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,80) = 0" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      fx(3,81) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
fx(3,82) = 0" }}{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,83) = 0" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      fx(3,84) = 1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 6 0" 16 }{VIEWOPTS 1 1 0 1 1 
1803 }
