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od;" }{MPLTEXT 1 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"\"F(F(" }{TEXT 205 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"#F(F(" }{TEXT 205 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"$F(F(" } {TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 30 "T[1,2] :=a;T[1,3]:=b;T[2,3]:=c;" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"\"\"\"#I\"aGF&" }{TEXT 205 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"\"\"\"$I\"bGF&" } {TEXT 205 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>&I\"TG6\"6$\"\"#\" \"$I\"cGF&" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 9 "print(T);" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#-I'matrixG6\"6#7%7%\"\"\"I\"aGF%I\"bGF%7%F*\"\"#I\"cGF%7%F+F.\" \"$" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 202 9 "EXERICE 2" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 8 "restart:" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 " > " 0 "" {MPLTEXT 1 204 60 "R:=array(1..4,1..4);S:=array(1..4,1..4);T: =array(1..4,1..4);" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"RG6\"-I&arrayGI*protectedGF(6%;\"\"\"\"\"%F*7\"" }{TEXT 205 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"SG6\"-I&arrayGI*protectedG F(6%;\"\"\"\"\"%F*7\"" }{TEXT 205 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"TG6\"-I&arrayGI*protectedGF(6%;\"\"\"\"\"%F*7\"" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "for i from 1 to \+ 4 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 22 "\n for j from 1 to 4 do " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 32 "\n R[i,j]:=is((j-i)/3,int eger);" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 8 "\nod; od;" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 10 "R=eval(R); " }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I\"RG6\"-I' matrixGF%6#7&7&I%trueGI*protectedGF,I&falseGF,F-F+7&F-F+F-F-7&F-F-F+F- F*" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "f or i from 1 to 4 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 22 "\n for j from 1 to 4 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 20 "\n S[i,j]: =is(i " 0 "" {MPLTEXT 1 204 10 "S =eval(S);" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I \"SG6\"-I'matrixGF%6#7&7&I&falseGI*protectedGF,I%trueGF,F-F-7&F+F+F-F- 7&F+F+F+F-7&F+F+F+F+" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "for i from 1 to 4 do" }{MPLTEXT 1 204 0 "" } {MPLTEXT 1 204 22 "\n for j from 1 to 4 do" }{MPLTEXT 1 204 0 "" } {MPLTEXT 1 204 31 "\n T[i,j]:=is(i=j*j or j=i*i);" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 8 "\nod; od;" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 10 "T=eval(T);" }{MPLTEXT 1 204 0 " " }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I\"TG6\"-I'matrixGF%6#7&7&I%true GI*protectedGF,I&falseGF,F-F-7&F-F-F-F+7&F-F-F-F-7&F-F+F-F-" }{TEXT 205 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 203 46 "Pour savoir si la r elation associ\351e au tableau" }{TEXT 206 22 " U n'est pas reflexive" }{TEXT 203 33 " il faut et il suffit de trouver " }{TEXT 206 2 "un" } {TEXT 203 9 " \351l\351ment " }{TEXT 206 22 "false sur la diagonale" } {TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 18 "reflex ive:=proc(U)" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 13 "\nlocal i,j,r;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 9 "\nr:=true;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 21 "\nfor i from 1 to 4 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 38 "\n if (U[i,i]=false) then r:=false; fi;" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 0 "" } {MPLTEXT 1 204 3 "\nr;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nend: " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 3 "\n " }{MPLTEXT 1 204 0 "" } }}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 26 "R_reflexive=reflexive( R); " }{TEXT 207 15 "R est r\351flexive" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I,R_reflexiveG6\"I%trueGI*protectedGF'" } {TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 26 "S_refl exive=reflexive(S); " }{TEXT 207 21 "S n'est pas r\351flexive" } {MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I,S_reflexiveG 6\"I&falseGI*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 26 "T_reflexive=reflexive(T); " }{TEXT 207 21 "T n'e st pas r\351flexive" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I,T_reflexiveG6\"I&falseGI*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 203 31 "La relation associ\351e au tableau" }{TEXT 206 27 " U n'est pas antisym\351trque " }{TEXT 203 20 " si et seulemen t si " }{TEXT 206 2 "un" }{TEXT 206 8 " couple " }{TEXT 203 11 "d'\351 l\351ments " }{TEXT 206 38 "sym\351triques par rapport \340 la diagona le" }{TEXT 203 30 " (en dehors de celle-ci) sont " }{TEXT 206 18 "simu ltan\351ment true" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 23 "antisymetrique:=proc(U)" }{MPLTEXT 1 204 0 "" } {MPLTEXT 1 204 13 "\nlocal i,j,r;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 9 "\nr:=true;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 21 "\nfor i fr om 1 to 3 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 25 "\n for j from i +1 to 4 do " }{TEXT 207 29 "on ne parcourt que les cases " }{TEXT 208 25 "au dessus de la diagonale" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 43 "\n if U[i,j] and U[j,i] then r:=false; fi; " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 11 "\nod; od; r;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 204 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 36 "R_antisymetrique=antisymetrique (R); " }{TEXT 207 26 "R n'est pas antisym\351trique" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I1R_antisymetriqueG6\"I&false GI*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 36 "S_antisymetrique=antisymetrique(S); " }{TEXT 207 20 "S est antisym\351trique" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I1S_antisymetriqueG6\"I%trueGI*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 36 "T_antisymetr ique=antisymetrique(T); " }{TEXT 207 26 "T n'est pas antisym\351trique " }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I1T_antisym etriqueG6\"I&falseGI*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 203 31 "La relation associ\351e au tableau" }{TEXT 206 24 " U n'est pa s transitive " }{TEXT 203 20 " si et seulement si " }{TEXT 203 36 "un \+ triplet U[i,j] U[j,k] et U[i,k] " }{TEXT 203 56 "d'\351l\351ments ne \+ v\351rifie pas l'implication de transitivit\351 " }{TEXT 203 1 " " } {TEXT 206 66 " U[i,j] et U[j,k] sont simultan\351ment true et pourtant U[i,k] false" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 19 "transitive:=proc(U)" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 15 "\nlocal i,j,k,r;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 9 "\nr:=tru e;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 21 "\nfor i from 1 to 4 do" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 22 "\n for j from 1 to 4 do" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 23 "\n for k from 1 to 4 do" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 60 "\n if U[i,j] and U[j,k] and \+ U[i,k]=false then r:=false; fi;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 10 "\nod;od;od;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 3 "\nr;" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 204 0 "" }} }{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 28 "R_transitive=transitive (R); " }{TEXT 207 16 "R est transitive" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I-R_transitiveG6\"I%trueGI*protectedGF'" } {TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 28 "S_tran sitive=transitive(S); " }{TEXT 207 16 "S est transitive" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I-S_transitiveG6\"I%trueG I*protectedGF'" }{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 28 "T_transitive=transitive(T); " }{TEXT 207 22 "T n'es t pas transitive" }{MPLTEXT 1 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I-T_transitiveG6\"I&falseGI*protectedGF'" }{TEXT 205 0 "" }}} {EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{PARA 205 "" 0 "" {TEXT 209 0 "" }}{PARA 205 "" 0 "" {TEXT 209 0 "" }}{PARA 205 "" 0 "" {TEXT 209 0 "" }}{PARA 205 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }