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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 56 "Utilisation des
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(Groebner);" }}{PARA 12 "" 1 "
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ilbertdimG%,hilbertpolyG%.hilbertseriesG%-inter_reduceG%*is_finiteG%,i
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
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"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "read \"C:/Documents an
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{XPPMATH 20 "6#>&%(voisinsG6#%'bresilG7,%'guyaneG%(surinamG%'guyanaG%*
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amG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(voisinsG6#%(surinamG7#%'guy
anaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(voisinsG6#%'guyanaG7#%*ven
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(voisinsG6#%(uruguayG7\"" }}{PARA 
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0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "P:=m->mul(X-i,i=1..m
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{PARA 257 "" 0 "" {TEXT 257 10 "Conclusion" }{TEXT -1 64 " : il n'y a \+
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0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 84 "Il y a donc au m
oins une solution pour le 4-coloriage. On va remonter une solution :" 
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{PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 55 "On pe
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{XPPMATH 20 "6%\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
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\"%\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "G:=gbasis(eqns
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),(*&\"\"(F(%'guyanaGF(F)*$)F5F,F(F(\"#7F(,&%(surinamGF(F,F),&%'guyane
GF(\"\"$F),&%'bresilGF(F(F),(*$)%)equateurGF,F(F(*&F=F(FCF(F)F,F(,(*$)
%*argentineGF,F(F(*&F4F(FHF(F)F8F(,(%)paraguayGF(FHF(F4F),&%)colombieG
F(F=F),**&F5F(%*venezuelaGF(F(*&F=F(FPF(F)*&F,F(F5F(F)\"\"'F(,(*$)FPF,
F(F(*&FSF(FPF(F)\"\")F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
solve(G[9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(G[12]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "solve(G[13]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%'guyanaG\"\"$
/%*venezuelaGF(<$/F%F%/F(\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 227 "G:=gbasis(eqns(4) union \{bresil-1\} union \{chili-1\} union
\{surinam-2\} union \{guyane-3\} union \{colombie-3\} union \{uruguay-
2\} union\{bolivie-2\} union \{guyana-3\} union\{paraguay-3\} union\{e
quateur-1\} union\{venezuela-2\},plex(op(pays)));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%\"GG7/,&%&chiliG\"\"\"F(!\"\",&%(uruguayGF(\"\"#F),&%
(bolivieGF(F,F),&%&perouGF(\"\"%F),&%'guyanaGF(\"\"$F),&%(surinamGF(F,
F),&%'guyaneGF(F4F),&%'bresilGF(F(F),&%)equateurGF(F(F),&%*argentineGF
(F1F),&%)paraguayGF(F4F),&%)colombieGF(F4F),&%*venezuelaGF(F,F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "nops(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nops(pays);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"#8" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}
{PARA 257 "" 0 "" {TEXT -1 39 "On a obtenu un 4-coloriage de la carte.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 6 "Sudoku" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "read \+
\"C:/Documents and Settings/Richard/Bureau/Sudoku.mpl\";" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%'sudokuG<?,&&%\"xG6$\"\"\"F*F*\"\"&!\"\",&&F(6
$\"\"#F0F*\"\"*F,,&&F(6$\"\"$F*F*\"\"%F,,&&F(6$F5F5F*\"\"(F,,&&F(6$F0
\"\"'F*F+F,,&&F(6$F*F+F*\"\")F,,&&F(6$F5F6F*F*F,,&&F(6$F*FBF*F6F,,&&F(
6$F0F:F*F:F,,&&F(6$F0FBF*F*F,,&&F(6$F>F*F*F1F,,&&F(6$F>F5F*FBF,,&&F(6$
F6F+F*F5F,,&&F(6$F+F+F*F>F,,&&F(6$F6F1F*F6F,,&&F(6$F:F>F*FBF,,&&F(6$F>
F1F*F>F,,&&F(6$F:F5F*F1F,,&&F(6$FBF0F*F6F,,&&F(6$F1F5F*F5F,,&&F(6$FBF+
F*F:F,,&&F(6$F1F6F*F6F,,&&F(6$F1F+F*F*F,,&&F(6$F1F>F*F>F,,&&F(6$FBF:F*
F+F,,&&F(6$F1F:F*F1F,,&&F(6$F1FBF*FBF,,&&F(6$F+FBF*F:F,,&&F(6$F>F:F*F5
F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:=9:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "lignes:=\{seq(\{seq(x[i,j],j=1..n)
\},i=1..n)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "colonnes:=
\{seq(\{seq(x[i,j],i=1..n)\},j=1..n)\}:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "blocs:=\{seq(seq(\{seq(seq(x[i*3+ii,j*3+jj],ii=1..3),
jj=1..3)\},i=0..3-1),j=0..3-1)\}:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "sys1:=\{seq(seq(subs(\{X=x[i,j]\},P(n)),i=1..n),j=1..
n)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "sys2:=\{seq(seq(s
eq(subs(\{X=pt1,Y=pt2\},Q(n)),pt1=rel),pt2=rel),rel= lignes union colo
nnes union blocs)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st \+
:= time();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#stG$\"&Ge&!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "G:=gbasis(sys1 union sys2 un
ion sudoku, tdeg(seq(seq(x[i,j],j=1..n),i=1..n))):\nst2:=time() - st;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$st2G$\"'r1!)!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "G;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#7#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "7 9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }