{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "" 0 1 0 0 0 0 0 0 0 0 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 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "#Exercice 3 :\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7ir%#&xG%$AddG%(AdjointG%3BackwardSubs tituteG%+BandMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalFormG%-Bilinear FormG%%CAREG%5CharacteristicMatrixG%9CharacteristicPolynomialG%'Column G%0ColumnDimensionG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatrixG% 0ConditionNumberG%/ConstantMatrixG%/ConstantVectorG%%CopyG%2CreatePerm utationG%-CrossProductG%%DAREG%-DeleteColumnG%*DeleteRowG%,Determinant G%)DiagonalG%/DiagonalMatrixG%*DimensionG%+DimensionsG%+DotProductG%6E igenConditionNumbersG%,EigenvaluesG%-EigenvectorsG%&EqualG%2ForwardSub stituteG%.FrobeniusFormG%4GaussianEliminationG%2GenerateEquationsG%/Ge nerateMatrixG%(GenericG%2GetResultDataTypeG%/GetResultShapeG%5GivensRo tationMatrixG%,GramSchmidtG%-HankelMatrixG%,HermiteFormG%3HermitianTra nsposeG%/HessenbergFormG%.HilbertMatrixG%2HouseholderMatrixG%/Identity MatrixG%2IntersectionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*I sUnitaryG%2JordanBlockMatrixG%+JordanFormG%1KroneckerProductG%(LA_Main G%0LUDecompositionG%-LeastSquaresG%,LinearSolveG%.LyapunovSolveG%$MapG %%Map2G%*MatrixAddG%2MatrixExponentialG%/MatrixFunctionG%.MatrixInvers eG%5MatrixMatrixMultiplyG%+MatrixNormG%,MatrixPowerG%5MatrixScalarMult iplyG%5MatrixVectorMultiplyG%2MinimalPolynomialG%&MinorG%(ModularG%)Mu ltiplyG%,NoUserValueG%%NormG%*NormalizeG%*NullSpaceG%3OuterProductMatr ixG%*PermanentG%&PivotG%*PopovFormG%0QRDecompositionG%-RandomMatrixG%- RandomVectorG%%RankG%6RationalCanonicalFormG%6ReducedRowEchelonFormG%$ RowG%-RowDimensionG%-RowOperationG%)RowSpaceG%-ScalarMatrixG%/ScalarMu ltiplyG%-ScalarVectorG%*SchurFormG%/SingularValuesG%*SmithFormG%8Stron glyConnectedBlocksG%*SubMatrixG%*SubVectorG%)SumBasisG%0SylvesterMatri xG%/SylvesterSolveG%/ToeplitzMatrixG%&TraceG%*TransposeG%0TridiagonalF ormG%+UnitVectorG%2VandermondeMatrixG%*VectorAddG%,VectorAngleG%5Vecto rMatrixMultiplyG%+VectorNormG%5VectorScalarMultiplyG%+ZeroMatrixG%+Zer oVectorG%$ZipG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M:=Matrix (2,2,[4,-1,4,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'RTABLEG6 %\"*ONc^\"-%'MATRIXG6#7$7$\"\"%!\"\"7$F.\"\"!%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Eigenvectors(M);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%-EigenvectorsG6#-%'RTABLEG6%\"*ONc^\"-%'MATRIXG6#7$ 7$\"\"%!\"\"7$F/\"\"!%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "#M n'est pas diagonalisable : l'espace engendr\351 par les vec teurs propres n'est que de dimension 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "P:=Matrix(2,2,[1,1,2,0]); #On prend comme premier vec teur de base le vecteur propre." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"PG-%'RTABLEG6%\"*#Rd::-%'MATRIXG6#7$7$\"\"\"F.7$\"\"#\"\"!%'MatrixG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "PM:=P^(-1).M.P;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PMG-%'RTABLEG6%\"*O(e::-%'MATRIXG6# 7$7$\"\"#F.7$\"\"!F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "PP:=Matrix(2,2,[2,0,0,1]); #On conjugue par une dilatation pour \+ ramener le coefficient \340 1." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P PG-%'RTABLEG6%\"*+)e::-%'MATRIXG6#7$7$\"\"#\"\"!7$F/\"\"\"%'MatrixG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "PP^(-1).PM.PP;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*K'f::-%'MATRIXG6#7$7$\"\"#\" \"\"7$\"\"!F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "M 2:=Matrix(2,2,[35,-116,10,-33]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #M2G-%'RTABLEG6%\"*'pf::-%'MATRIXG6#7$7$\"#N!$;\"7$\"#5!#L%'MatrixG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Eigenvectors(M2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%-EigenvectorsG6#-%'RTABLEG6%\"*'pf:: -%'MATRIXG6#7$7$\"#N!$;\"7$\"#5!#L%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "#M2 est diagonalisable dans C. Elle n'est pas dia gonalisable dans R car elle a des valeurs propres non r\351elles." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "V1:=Matrix(2,1,[17+I,5]); V2 :=Matrix(2,1,[17-I,5]); #Les vecteurs propres de M2 dans C." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#V1G-%'RTABLEG6%\"*g(f::-%'MATRIXG6#7$7#^$ \"#<\"\"\"7#\"\"&%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#V2G-% 'RTABLEG6%\"*C)f::-%'MATRIXG6#7$7#^$\"# " 0 "" {MPLTEXT 1 0 159 "P2:=Matrix([(V1+V2)/2,(V1-V 2)/(2*I)]); #On prend pour vecteurs de base la partie r\351elle et la \+ partie imaginaire d'un des vecteurs propres (ils sont conjugu\351s)." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P2G-%'RTABLEG6%\"*/6c^\"-%'MATRIX G6#7$7$\"#<\"\"\"7$\"\"&\"\"!%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "PM2:=P2^(-1).M2.P2;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$PM2G-%'RTABLEG6%\"*O>c^\"-%'MATRIXG6#7$7$\"\"\"\"\"#7$!\"#F.%'Mat rixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "PM2/sqrt(5);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+?c^\"-%'MATRIXG6#7$7$, $*&\"\"&!\"\"F.#\"\"\"\"\"#F1,$*(F2F1F.F/F.F0F17$,$*(F2F1F.F/F.F0F/F,% 'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "#(1/sqrt(5))^2 +(2/sqrt(5))^2=1 donc il existe theta tel que cos(theta)=1/sqrt(5) et \+ sin(theta)=2/sqrt(5) ; en posant a=sqrt(5), la matrice est bien de la \+ forme demand\351e." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "M3:=M atrix(4,4,[\n[3,0,-1,0],\n[-1,2,0,1],\n[0,0,3,0],\n[-1,-1,-1,4]\n]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M3G-%'RTABLEG6%\"*k?c^\"-%'MATRIX G6#7&7&\"\"$\"\"!!\"\"F/7&F0\"\"#F/\"\"\"7&F/F/F.F/7&F0F0F0\"\"%%'Matr ixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "M4:=Matrix(4,4,[\n[2 ,-3,-2,-2],\n[0,4,1,1],\n[1,2,4,1],\n[0,-1,-1,2]\n]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M4G-%'RTABLEG6%\"*G@c^\"-%'MATRIXG6#7&7&\"\"#! \"$!\"#F07&\"\"!\"\"%\"\"\"F47&F4F.F3F47&F2!\"\"F7F.%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Eigenvectors(M3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%-EigenvectorsG6#-%'RTABLEG6%\"*k?c^\"-%'MA TRIXG6#7&7&\"\"$\"\"!!\"\"F07&F1\"\"#F0\"\"\"7&F0F0F/F07&F1F1F1\"\"%%' MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Eigenvectors(M4) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%-EigenvectorsG6#-%'RTABLEG6%\"* G@c^\"-%'MATRIXG6#7&7&\"\"#!\"$!\"#F17&\"\"!\"\"%\"\"\"F57&F5F/F4F57&F 3!\"\"F8F/%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "#M3 et M4 ne sont pas diagonalisables, leurs espaces engendr\351s par les vecteurs propres sont de dimension 2, mais on ne peut pas conclure qu ant \340 la similitude de M3 et M4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "e1:=Matrix(4,1,[-1,1,0,0]); e3:=Matrix(4,1,[1,0,0,1]) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G-%'RTABLEG6%\"*#>i::-%'MATR IXG6#7&7#!\"\"7#\"\"\"7#\"\"!F1%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e3G-%'RTABLEG6%\"*cAc^\"-%'MATRIXG6#7&7#\"\"\"7#\"\"!F/F-%'Ma trixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Id:=IdentityMatrix (4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IdG-%/IdentityMatrixG6#\"\" %" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "e2:=LinearSolve(M3-3*I d,e1,free='s');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G-%,LinearSolv eG6%-%'RTABLEG6%\"*wDc^\"-%'MATRIXG6#7&7&,&*&\"\"$\"\"\"-%/IdentityMat rixG6#\"\"%F4!\"\"F3F4\"\"!F9F:7&F9,&*&F3F4F5F4F9\"\"#F4F:F47&F:F:F1F: 7&F9F9F9,&*&F3F4F5F4F9F8F4%'MatrixG-F)6%\"*#>i::-F-6#7&7#F97#F47#F:FLF C/%%freeG%\"sG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "e2:=eval( e2,[s[1,1]=0,s[2,1]=1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G-%,L inearSolveG6%-%'RTABLEG6%\"*wDc^\"-%'MATRIXG6#7&7&,&*&\"\"$\"\"\"-%/Id entityMatrixG6#\"\"%F4!\"\"F3F4\"\"!F9F:7&F9,&*&F3F4F5F4F9\"\"#F4F:F47 &F:F:F1F:7&F9F9F9,&*&F3F4F5F4F9F8F4%'MatrixG-F)6%\"*#>i::-F-6#7&7#F97# F47#F:FLFC/%%freeG%\"sG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " e4:=LinearSolve(M3-3*Id,e3,free='s');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e4G-%,LinearSolveG6%-%'RTABLEG6%\"*KGc^\"-%'MATRIXG6#7&7&,&*&\" \"$\"\"\"-%/IdentityMatrixG6#\"\"%F4!\"\"F3F4\"\"!F9F:7&F9,&*&F3F4F5F4 F9\"\"#F4F:F47&F:F:F1F:7&F9F9F9,&*&F3F4F5F4F9F8F4%'MatrixG-F)6%\"*cAc^ \"-F-6#7&7#F47#F:FKFJFC/%%freeG%\"sG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "e4:=eval(e4,[s[1,1]=0,s[2,1]=1]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#e4G-%,LinearSolveG6%-%'RTABLEG6%\"*KGc^\"-%'MATRIX G6#7&7&,&*&\"\"$\"\"\"-%/IdentityMatrixG6#\"\"%F4!\"\"F3F4\"\"!F9F:7&F 9,&*&F3F4F5F4F9\"\"#F4F:F47&F:F:F1F:7&F9F9F9,&*&F3F4F5F4F9F8F4%'Matrix G-F)6%\"*cAc^\"-F-6#7&7#F47#F:FKFJFC/%%freeG%\"sG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 26 "P3:=Matrix([e1,e2,e3,e4]);" }}{PARA 8 "" 1 " " {TEXT -1 200 "Error, (in Matrix) this entry is too tall or too short : LinearSolve(Matrix(4, 4, [[...],[...],[...],[...]], datatype = anyth ing),Matrix(4, 1, [[...],[...],[...],[...]], datatype = anything),free = s)\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Rank(P3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%%RankG6#%#P3G" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "P3^(-1).M3.P3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\".G6%*&\"\"\"F'%#P3G!\"\"-%'RTABLEG6%\"*k?c^\"-%'MATRIXG6#7&7 &\"\"$\"\"!F)F47&F)\"\"#F4F'7&F4F4F3F47&F)F)F)\"\"%%'MatrixGF(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "#Le polyn\364me minimal de M 3 est donc (X-3)^2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Eige nvectors(M4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%-EigenvectorsG6#-%' RTABLEG6%\"*G@c^\"-%'MATRIXG6#7&7&\"\"#!\"$!\"#F17&\"\"!\"\"%\"\"\"F57 &F5F/F4F57&F3!\"\"F8F/%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "f1:=Matrix(4,1,[1,-1,0,1]);f4:=Matrix(4,1,[1,-1,1,0]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G-%'RTABLEG6%\"*'*Gc^\"-%'MATRIXG 6#7&7#\"\"\"7#!\"\"7#\"\"!F-%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f4G-%'RTABLEG6%\"*gHc^\"-%'MATRIXG6#7&7#\"\"\"7#!\"\"F-7#\"\"!%' MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f2:=LinearSolve( M4-3*Id,f1,free='s');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G-%,Line arSolveG6%-%'RTABLEG6%\"*;Kc^\"-%'MATRIXG6#7&7&,&*&\"\"$\"\"\"-%/Ident ityMatrixG6#\"\"%F4!\"\"\"\"#F4!\"$!\"#F<7&\"\"!,&*&F3F4F5F4F9F8F4F4F4 7&F4F:F?F47&F>F9F9F1%'MatrixG-F)6%\"*'*Gc^\"-F-6#7&7#F47#F97#F>FJFC/%% freeG%\"sG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f2:=eval(f2,[ s[2,1]=-1,s[1,1]=0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G-%,Line arSolveG6%-%'RTABLEG6%\"*;Kc^\"-%'MATRIXG6#7&7&,&*&\"\"$\"\"\"-%/Ident ityMatrixG6#\"\"%F4!\"\"\"\"#F4!\"$!\"#F<7&\"\"!,&*&F3F4F5F4F9F8F4F4F4 7&F4F:F?F47&F>F9F9F1%'MatrixG-F)6%\"*'*Gc^\"-F-6#7&7#F47#F97#F>FJFC/%% freeG%\"sG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f3:=LinearSol ve(M4-3*Id,f2,free='s');" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#f3G-%,L inearSolveG6%-%'RTABLEG6%\"*sMc^\"-%'MATRIXG6#7&7&,&*&\"\"$\"\"\"-%/Id entityMatrixG6#\"\"%F4!\"\"\"\"#F4!\"$!\"#F<7&\"\"!,&*&F3F4F5F4F9F8F4F 4F47&F4F:F?F47&F>F9F9F1%'MatrixG-F&6%-F)6%\"*;Kc^\"F,FC-F)6%\"*'*Gc^\" -F-6#7&7#F47#F97#F>FOFC/%%freeG%\"sGFR" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f3:=eval(f3,[s[2,1]=1,s[1,1]=0]);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%#f3G-%,LinearSolveG6%-%'RTABLEG6%\"*sMc^\"-%'MATRIX G6#7&7&,&*&\"\"$\"\"\"-%/IdentityMatrixG6#\"\"%F4!\"\"\"\"#F4!\"$!\"#F <7&\"\"!,&*&F3F4F5F4F9F8F4F4F47&F4F:F?F47&F>F9F9F1%'MatrixG-F&6%-F)6% \"*;Kc^\"F,FC-F)6%\"*'*Gc^\"-F-6#7&7#F47#F97#F>FOFC/%%freeG%\"sGFR" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "P4:=Matrix([f1,f2,f3,f4]); " }}{PARA 8 "" 1 "" {TEXT -1 200 "Error, (in Matrix) this entry is too tall or too short: LinearSolve(Matrix(4, 4, [[...],[...],[...],[...]] , datatype = anything),Matrix(4, 1, [[...],[...],[...],[...]], datatyp e = anything),free = s)\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Rank(P4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%RankG6#%#P4G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "P4^(-1).M4.P4;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%\".G6%*&\"\"\"F'%#P4G!\"\"-%'RTABLEG6%\"*G@c^ \"-%'MATRIXG6#7&7&\"\"#!\"$!\"#F57&\"\"!\"\"%F'F'7&F'F3F8F'7&F7F)F)F3% 'MatrixGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "#Le polyn\364 me minimal de M4 est (X-3)^3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "#M3 et M4 n'ont pas le m\352me polyn\364me minimal, donc ne sont pas semblables." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } {RTABLE_HANDLES 151563536 151557392 151558736 151558800 151559632 151559696 151559760 151559824 151561104 151561936 151562000 151562064 151562128 151562192 151562256 151562576 151562832 151562896 151562960 151563216 151563472 }{RTABLE M7R0 I6RTABLE_SAVE/151563536X,%)anythingG6"F%[gl!"%!!!#%"#"#""%F&!""""!F% } {RTABLE M7R0 I6RTABLE_SAVE/151557392X,%)anythingG6"F%[gl!"%!!!#%"#"#"""""#F&""!F% } {RTABLE M7R0 I6RTABLE_SAVE/151558736X,%)anythingG6"F%[gl!"%!!!#%"#"#""#""!F&F&F% } {RTABLE M7R0 I6RTABLE_SAVE/151558800X,%)anythingG6"F%[gl!"%!!!#%"#"#""#""!F'"""F% } {RTABLE M7R0 I6RTABLE_SAVE/151559632X,%)anythingG6"F%[gl!"%!!!#%"#"#""#""!"""F&F% } {RTABLE M7R0 I6RTABLE_SAVE/151559696X,%)anythingG6"F%[gl!"%!!!#%"#"#"#N"#5!$;"!#LF% } {RTABLE M7R0 I6RTABLE_SAVE/151559760X,%)anythingG6"F%[gl!"%!!!##"#""^$"#<"""""&F% } {RTABLE M7R0 I6RTABLE_SAVE/151559824X,%)anythingG6"F%[gl!"%!!!##"#""^$"#