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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 128 0 0 1 0 1 0 0 
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart: " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "show_bool:=false: " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "__ici:= `c:/@lips3/map/ch_05/`; # r
ead ``.(__ici).`manip.m`: " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&__ici
G%5c:/@lips3/map/ch_05/G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 
"with(plots): with(plottools): readlib(eliminate): with(student,equate
); with(linalg): with(pldx):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%'eq
uateG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%_opldx~~;~~author~:~<douille
t@cnam.fr>~~;~~last~modif~:~Sam~19/06/1999G" }}}{EXCHG {PARA 0 "" 0 "
" {MPLTEXT 0 21 94 "mmax:=5; read ``.(__ici).th_.mmax._mach: ma.mmax:=
 evalf(matrix(ma),5); mb.mmax:= evalf(mb,5);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 271 "mc4 := matrix([[0, .74082, 0, 0], [1., .23374, \+
.81873, 0], [0, .24582e-1, .17221, .90484], [0, .86178e-3, .90559e-2, \+
.95163e-1]]);\nmd4 := matrix([[0, .74082, 0, 0, 0], [1., 0, .89293, 0,
 0], [0, .25918, 0, .96093, 0], [0, 0, .10707, 0, 1.0000], [0, 0, 0, .
39067e-1, 0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$mc4GL&7&\"\"!$\"
&#3u!\"&F'F'7&$\"\"\"F'$\"&uL#F*$\"&t=)F*F'7&F'$\"&#eC!\"'$\"&@s\"F*$
\"&%[!*F*7&F'$\"&yh)!\")$\"&f0*!\"($\"&j^*F5%'matrixG" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$md4GL'7'\"\"!$\"&#3u!\"&F'F'F'7'$\"\"\"F'F'$\"&
$H*)F*F'F'7'F'$\"&=f#F*F'$\"&$4'*F*F'7'F'F'$\"&22\"F*F'$\"&++\"!\"%7'F
'F'F'$\"&n!R!\"'F'%'matrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
382 "mc5 := matrix([[0, .67032, 0, 0, 0], [1., .28199, .74082, 0, 0], \+
[0, .44486e-1, .23374, .81873, 0], [0, .31191e-2, .24582e-1, .17221, .
90484], [0, .82010e-4, .86178e-3, .90559e-2, .95163e-1]]);\nmd5 := mat
rix([[0, .67032, 0, 0, 0, 0], [1., 0, .83664, 0, 0, 0], [0, .32968, 0,
 .91590, 0, 0], [0, 0, .16336, 0, .96552, 0], [0, 0, 0, .84095e-1, 0, \+
1.0000], [0, 0, 0, 0, .34485e-1, 0]]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$mc5GL'7'\"\"!$\"&Kq'!\"&F'F'F'7'$\"\"\"F'$\"&*>GF*$\"&#3uF*F'
F'7'F'$\"&'[W!\"'$\"&uL#F*$\"&t=)F*F'7'F'$\"&\">J!\"($\"&#eCF5$\"&@s\"
F*$\"&%[!*F*7'F'$\"&5?)!\"*$\"&yh)!\")$\"&f0*F=$\"&j^*F5%'matrixG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$md5GL(7(\"\"!$\"&Kq'!\"&F'F'F'F'7($
\"\"\"F'F'$\"&kO)F*F'F'F'7(F'$\"&oH$F*F'$\"&!f\"*F*F'F'7(F'F'$\"&Oj\"F
*F'$\"&_l*F*F'7(F'F'F'$\"&&4%)!\"'F'$\"&++\"!\"%7(F'F'F'F'$\"&&[MF=F'%
'matrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 379 "ma5 := matrix(
[[0, .71429, 0, 0, 0], [1., .21978, .76923, 0, 0], [0, .54945e-1, .192
31, .83333, 0], [0, .99900e-2, .34965e-1, .15152, .90909], [0, .99900e
-3, .34965e-2, .15152e-1, .90909e-1]]);\nmb5 := matrix([[0, .71429, 0,
 0, 0, 0], [1., 0, .76923, 0, 0, 0], [0, .28571, 0, .83333, 0, 0], [0,
 0, .23077, 0, .90909, 0], [0, 0, 0, .16667, 0, 1.0000], [0, 0, 0, 0, \+
.90909e-1, 0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ma5GL'7'\"\"!$
\"&H9(!\"&F'F'F'7'$\"\"\"F'$\"&y>#F*$\"&Bp(F*F'F'7'F'$\"&X\\&!\"'$\"&J
#>F*$\"&LL)F*F'7'F'$\"&+***!\"($\"&l\\$F5$\"&_^\"F*$\"&44*F*7'F'$F<!\"
)$F?F=$FAF5$FCF5%'matrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$mb5GL(
7(\"\"!$\"&H9(!\"&F'F'F'F'7($\"\"\"F'F'$\"&Bp(F*F'F'F'7(F'$\"&r&GF*F'$
\"&LL)F*F'F'7(F'F'$\"&xI#F*F'$\"&44*F*F'7(F'F'F'$\"&nm\"F*F'$\"&++\"!
\"%7(F'F'F'F'$F9!\"'F'%'matrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 271 "ma4 := matrix([[0, .76923, 0, 0], [1., .19231, .83333, 0], [0
, .34965e-1, .15152, .90909], [0, .34965e-2, .15152e-1, .90909e-1]]);
\nmb4 := matrix([[0, .76923, 0, 0, 0], [1., 0, .83333, 0, 0], [0, .230
77, 0, .90909, 0], [0, 0, .16667, 0, 1.0000], [0, 0, 0, .90909e-1, 0]]
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ma4GL&7&\"\"!$\"&Bp(!\"&F'F'7
&$\"\"\"F'$\"&J#>F*$\"&LL)F*F'7&F'$\"&l\\$!\"'$\"&_^\"F*$\"&44*F*7&F'$
F4!\"($F7F5$F9F5%'matrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$mb4GL'
7'\"\"!$\"&Bp(!\"&F'F'F'7'$\"\"\"F'F'$\"&LL)F*F'F'7'F'$\"&xI#F*F'$\"&4
4*F*F'7'F'F'$\"&nm\"F*F'$\"&++\"!\"%7'F'F'F'$F4!\"'F'%'matrixG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "fonz:= 'font' = ['TIMES', 'R
OMAN', 15];fony:= 'font' = ['TIMES', 'ROMAN', 25];" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%fonzG/%%fontG7%%&TIMESG%&ROMANG\"#:" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%%fonyG/%%fontG7%%&TIMESG%&ROMANG\"#D" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "ro:=0.17; K:=20; roo:= evalf
(ro*19/15,2); soy := x-> (1-x)*x*1.1; " }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#roG$\"#<!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG\"#?" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rooG$\"#A!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$soyG:6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&,&\"\"\"F/
9$!\"\"F/F0F/$\"#6F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
142 "show:= proc(zz::uneval);\nif show_bool then display(eval(zz), sca
ling=constrained, axes=boxed, title=zz, titlefont= [TIMES,ITALIC,20]) \+
fi; end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "pl_cir0:= disp
lay(polygonplot([seq([ro*cos(2*Pi*k/K),ro*sin(2*Pi*k/K) ], k=0..K)], c
olor= green, thickness=2), \n textplot([0,0,`centre`]), fony): if show
_bool then display(plot(soy(t),t=0..1), show(pl_cir0)) fi; " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "pl_pte:= polygonplot([[-0.9,
-1.8],[0,0],[0.9,-1.8],[-0.9,-1.8]], color=red): show(pl_pte);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "fsolve( soy(ro*cos(t))=ro*si
n(t), t=0..1): cutg:= ro*cos(\"); cutd:= 1-\";" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%cutgG$\"+r@,B7!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%%cutdG$\"+Hy)px)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "
fac_pte:= 0.05: xf:= 0.82; rotate(pl_pte, Pi+arctan(-1/D(soy)(xf))):\n
pl_pte1:= transform((x,y)->[x*fac_pte+cutd,y*fac_pte+soy(cutd)])(\"): \+
show(pl_pte1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xfG$\"##)!\"#" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 "pl_arc_up:= plot(soy(t), t
=cutg..cutd, numpoints=K, adaptive=false, thickness=2, color=black): \+
\npl_leg_up:= textplot([0.5, soy(0.5),`centre`], fonz): \nif show_bool
 then display(show(pl_arc_up), pl_leg_up); fi;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "pl_fle_up:= display(pl_arc_up, pl_pte1): show(
pl_fle_up);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "pl_arc_do:=
 transform((x,y)->[1-x,-y])(pl_arc_up): pl_leg_do:= transform((x,y)->[
1-x,-y])(pl_leg_up): show(pl_arc_do);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "pl_fle_do:= transform((x,y)->[1-x,-y])(pl_fle_up): sh
ow(pl_fle_do);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "pl_ptr:= \+
rotate(pl_pte, 0.95):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "y
la:=1.7: pl_pte0:= transform((x,y)->[x*fac_pte-roo*sqrt(0.5),y*fac_pte
-roo*(yla+sqrt(0.5))])(pl_ptr): # show(pl_pte0);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 186 "pl_fle_0:= display(plot([seq([roo*sin(2*Pi*k/K), roo
*cos(2*Pi*k/K)-roo*yla ], k=1..K-1)], thickness=2, color=black), \n  t
extplot([0, -yla*roo,`centre`], fonz), pl_pte0): show(pl_fle_0); " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "mk_cir:= proc(k,tt) local f
; f:= transform(unapply( (evalc@[Re,Im])(x+I*y+ k), x, y)):\n f( subs(
`centre`= sprintf(`%d`, tt), pl_cir0)); \" end:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 115 "if show_bool then display(show(pl_fle_0), mk_
cir(1,1), mk_cir(0,0), pl_fle_up, pl_fle_do, scaling=constrained); fi;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 774 "mk_par:= proc(p1,p2,va
l) local f, sub, xla, a, b; \nsub:= `centre`= `if`(val=1., `1.0000`, s
printf(`%1.5f`, val));\nif val=0 then NULL  \nelif p1=p2 then f:= tran
sform(unapply( [x+p1,y], x,y)); f( subs(sub, pl_fle_0))  \nelif p2 < p
1 then \n xla:= unapply(a*x+b,x): \{xla(cutg)=p2+cutg , xla(cutd)=p1-c
utg\}; assign(solve(\", \{a,b\}));\n transform(unapply( [xla(x), a*y+(
1-a)*soy(cutg)], x, y))( pl_fle_do),\n transform(unapply( [xla(x), a*y
+(1-a)*soy(cutg)+0.10], x, y))( subs(sub, pl_leg_do)) \nelse  \n xla:=
 unapply(a*x+b,x): \{xla(cutg)=p1+cutg , xla(cutd)=p2-cutg\}; assign(s
olve(\", \{a,b\}));\n transform(unapply( [xla(x), a*y+(1-a)*soy(cutg)]
, x, y))( `if`(p2=p1+1,pl_fle_up,pl_arc_up)),\n transform(unapply( [xl
a(x), a*y+(1-a)*soy(cutg)-0.11], x, y))( subs(sub, pl_leg_up))  \nfi; \+
end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "mk_fleches:= proc(
mm, fu) local j,k; display( \n seq( mk_cir(k,fu(k)), k= 1..rowdim(mm))
, seq(seq(mk_par(j,k, mm[k,j]), k=1..rowdim(mm)), j=1..coldim(mm)),\n \+
 scaling=constrained, axes=none); end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 80 "mx:=4: mark.mx:= mk_fleches(ma.mx, id-1):\"; nivo.mx:
= mk_fleches(mb.mx, id-1):\";" }}{PARA 13 "" 1 "" {INLPLOT "6I-%)POLYG
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