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2 2 0 0 0 1 }{PSTYLE "_pstyle3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }3 3 0 -1 -1 -1 1 0 1 0 2 2 -1 1 } {CSTYLE "_cstyle3" -1 204 "Times" 1 12 0 0 255 1 0 0 0 2 2 2 0 0 0 1 } {PSTYLE "_pstyle4" -1 203 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }1 1 0 -1 8 4 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle5" -1 204 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_cstyle4" -1 205 "Courier " 1 12 0 0 153 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "_cstyle5" -1 206 "Couri er" 1 12 0 0 204 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "_cstyle6" -1 207 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle7" -1 208 "Couri er" 1 12 204 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "_cstyle8" -1 209 "Cou rier" 1 12 153 0 153 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "_cstyle9" -1 210 "Times" 1 12 255 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle10" -1 211 "Courier" 1 12 0 153 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "_cstyle11" -1 212 "Courier" 1 12 0 0 255 1 0 1 0 2 1 2 0 0 0 1 }{PSTYLE "_pstyle6 " -1 205 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle12" -1 213 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle13" -1 214 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle14" -1 215 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle7" -1 206 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_cstyle15" -1 216 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 8 "restart;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 1 "\n" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 13 "with(linalg);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {TEXT 203 79 "Warning, the protected names norm and trace have been redefined and unprotected" }{TEXT 203 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#7^rI.BlockDiagonalG6\"I,GramSchmidtGF%I,JordanBlockGF%I )LUdecompGF%I)QRdecompGF%I*WronskianGF%I'addcolGF%I'addrowGF%I$adjGF%I (adjointGF%I&angleGF%I(augmentGF%I(backsubGF%I%bandGF%I&basisGF%I'bezo utGF%I,blockmatrixGF%I(charmatGF%I)charpolyGF%I)choleskyGF%I$colGF%I'c oldimGF%I)colspaceGF%I(colspanGF%I*companionGF%I'concatGF%I%condGF%I)c opyintoGF%I*crossprodGF%I%curlGF%I)definiteGF%I(delcolsGF%I(delrowsGF% I$detGF%I%diagGF%I(divergeGF%I(dotprodGF%I*eigenvalsGF%I,eigenvaluesGF %I-eigenvectorsGF%I+eigenvectsGF%I,entermatrixGF%I&equalGF%I,exponenti alGF%I'extendGF%I,ffgausselimGF%I*fibonacciGF%I+forwardsubGF%I*frobeni usGF%I*gausselimGF%I*gaussjordGF%I(geneqnsGF%I*genmatrixGF%I%gradGF%I) hadamardGF%I(hermiteGF%I(hessianGF%I(hilbertGF%I+htransposeGF%I)ihermi teGF%I*indexfuncGF%I*innerprodGF%I)intbasisGF%I(inverseGF%I'ismithGF%I *issimilarGF%I'iszeroGF%I)jacobianGF%I'jordanGF%I'kernelGF%I*laplacian GF%I*leastsqrsGF%I)linsolveGF%I'mataddGF%I'matrixG6$I*protectedGF[pI(_ syslibGF%I&minorGF%I(minpolyGF%I'mulcolGF%I'mulrowGF%I)multiplyGF%I%no rmGFjoI*normalizeGF%I*nullspaceGF%I'orthogGF%I*permanentGF%I&pivotGF%I *potentialGF%I+randmatrixGF%I+randvectorGF%I%rankGF%I(ratformGF%I$rowG F%I'rowdimGF%I)rowspaceGF%I(rowspanGF%I%rrefGF%I*scalarmulGF%I-singula rvalsGF%I&smithGF%I,stackmatrixGF%I*submatrixGF%I*subvectorGF%I)sumbas isGF%I(swapcolGF%I(swaprowGF%I*sylvesterGF%I)toeplitzGF%I&traceGFjoI*t ransposeGF%I,vandermondeGF%I*vecpotentGF%I(vectdimGF%I'vectorGFjoI*wro nskianGF%" }{TEXT 204 0 "" }}}{SECT 1 {PARA 203 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 15 "taille:=proc(A)" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n local t,u,n,p;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n t:=[op(2,evalm(A))];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n n:=op(2,t[1]);p:=op(2,t[2]); " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\n [n,p];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 18 "diagonale:=proc(X)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n local i,j,n,B;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 18 "\n n:=taille(X)[2];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 22 "\n B:=array(1..n,1..n);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 22 "\n for i from 1 to n do" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 40 "\n for j from 1 to n do B[i,j]:=0; od;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 18 "\n B[i,i]:=X[1,i];" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 17 "filtre:=proc(X,r)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 18 "\n local i,j,t,B,C;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n t:=taille(X);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\n B:=a rray(1..r,1..t[2]-r);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n C:= array(1..r,1..r);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n for i f rom 1 to r do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 47 "\n for j fro m 1 to r do C[i,j]:=X[i,j]; od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 53 "\n for j from 1 to t[2]-r do B[i,j]:=X[i,j+r]; od;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 7 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 19 "\nevalm(C),evalm(B);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 25 "Per mut_ligne:=proc(i,j,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nloc al B,k,t;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB:=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 to t[2] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n B[i,k]:=A[j,k]; B[j,k]:=A[i,k];" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "Dilat_ligne:=proc(a,i,A)" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 13 "\nlocal k,t,B;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB: =array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB :=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 t o t[2] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\n B[i,k]:=simplif y(a*A[i,k]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "Transvect_ligne:=proc(i,a,j,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal k,t,B;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:= taille(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB:=array(1..t[1 ],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 to t[2] do" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 36 "\n B[i,k]:=simplify(A[i,k]+a*A [j,k]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 202 31 "CherchePivot_colonne:=proc(A,i)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 12 "\n local t,k;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 16 "\n t:=taille(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\n if is(i>t[1])then RETURN(IMPOSSIBLE); fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 26 "\n for k from i to t[1] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n if is(A[k,i]<>0) then RETURN(k); fi; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n od;" }{MPLTEXT 1 202 0 " " }{MPLTEXT 1 202 13 "\n RETURN(0);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 27 "Permut_colonne:=proc(i,j,A)" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 13 "\nlocal B,k,t;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB: =array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB :=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 t o t[1] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n B[k,i]:=A[k,j]; B[k,j]:=A[k,i];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 202 36 "zero_sur_pivot_historique:=proc(i,A)" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n local t,B,k," }{MPLTEXT 1 205 5 "hist;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 205 11 "hist:=NULL;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n t:= taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n B:=array(1.. t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n B:=evalm(A ); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 75 "\n if is(i>t[2]) or is(i >t[1]) or is(B[i,i]<>1) then RETURN(IMPOSSIBLE); fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 25 "\n for k from 1 to i-1 do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 3 "\n " }{MPLTEXT 1 205 54 " if B[k,i]<>0 then h ist:=hist,[\"Transvection_ligne\",k," }{MPLTEXT 1 206 8 "-B[k,i]," } {MPLTEXT 1 205 7 "i]; fi;" }{TEXT 207 8 " hist c" }{TEXT 207 64 "onti ent la s\351quence des op\351rations \351l\351mentaires effectu\351es \+ sur B" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n B:=Transvect_lign e(k,-B[k,i],i,B); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" } {MPLTEXT 1 208 0 "" }{MPLTEXT 1 208 10 "\nevalm(B)," }{MPLTEXT 1 205 7 "[hist];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 37 "zero_sous_pivot_historiq ue:=proc(i,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n local t,B,k ," }{MPLTEXT 1 205 7 "hist,r;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 3 "\n " }{MPLTEXT 1 205 11 "hist:=NULL;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 17 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n B:=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 14 "\n B:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 74 "\n if is(i>t[2]) or is(i>t[1]) or is(B[i,i]=0) then RETURN(IMP OSSIBLE); fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 25 "\n if (B[i,i ]<>1 ) then " }{MPLTEXT 1 205 43 "hist:=hist,[\"Dilate_ligne\",1/B[i,i ],i]; fi;" }{TEXT 207 1 " " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 36 " \n B:=Dilat_ligne(1/B[i,i],i,B); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 26 "\nfor k from i+1 to t[1] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\n " }{MPLTEXT 1 205 54 " if B[k,i]<>0 then hist:=hist,[\"T ransvection_ligne\",k," }{MPLTEXT 1 206 8 "-B[k,i]," }{MPLTEXT 1 205 7 "i]; fi;" }{TEXT 207 1 " " }{TEXT 207 71 " hist contient la s\351que nce des op\351rations \351l\351mentaires effectu\351es sur B" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 39 "\n B:=Transvect_ligne(k,-B[k ,i],i,B); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 11 "\n evalm(B)," }{MPLTEXT 1 205 7 "[hist] ;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 " " }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 29 "Gauss_historique:=p roc(A,opt)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 18 "\n local T,i,j,t, k," }{MPLTEXT 1 205 7 "hist,r," }{MPLTEXT 1 209 5 "temp;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 205 11 "hist:=NULL;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n T:=array(1..t[1],1..t[2]);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n T:=evalm(A); " }{TEXT 210 1 " " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 26 "\n for j from 1 to t[2] do " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 32 "\n i:=CherchePivot_col onne(T,j);" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 23 "\nif opt=\"colonn es\" then" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 12 "\n k:=j+1; " } {MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 29 "\n while(i=0 and k0 then T:=Permu t_ligne(i,j,T); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n \+ if (i<>j) then " }{MPLTEXT 1 205 37 "hist:=hist,[\"Echange_ligne \",i,j]; fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n \+ " }{MPLTEXT 1 209 39 " temp:=zero_sous_pivot_historique(j,T);" } {MPLTEXT 1 202 2 " " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\n \+ T:=temp[1];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n \+ " }{MPLTEXT 1 206 23 "hist:=hist,op(temp[2]);" }{MPLTEXT 1 202 20 " " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 " \n fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 211 16 "if opt=\"CRAMER\" " }{MPLTEXT 1 202 1 " " }{MPLTEXT 1 211 6 " then " }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 63 "\n if (sum(T[k,k],k=1..t[1])<>t[1]) then RETURN (IMPOSSIBLE) fi; " }{TEXT 207 1 " " }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 35 "\n for j from t[1] to 1 by -1 do " }{TEXT 207 1 " " } {MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 44 "\n temp:=zero_sur_pivot_his torique(j,T); " }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 16 "\n T:=tem p[1];" }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 32 "\n hist:=hist,op(te mp[2]); " }{MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 7 "\n od;" } {MPLTEXT 1 211 0 "" }{MPLTEXT 1 211 4 "\nfi;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 9 "\n [hist];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 " \nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 17 "Ginverse:=proc(A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n local T,B,j,k,q,t,m,hist,texte;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\n T:=array(1..t[1],1..t[2]);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\n B:=array(1..t[1],1..t[2]); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\n for j from 1 to t[1] do " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 49 "\n for k from 1 to t[1] \+ do T[j,k]:=0; od; " }{TEXT 207 46 "tous les coefficients de la l igne j sont nulls" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n T[j,j ]:=1; " }{TEXT 207 21 "sauf celui d'indice j" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 7 "\n od; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 3 "\n " }{TEXT 207 43 "On a a obtenu jusqu'ici la matrice identit\351" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n B:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n hist:=Gauss_historique(A,\"CRAMER\"); \+ " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n m:=nops(hist); " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\n print(B, \"........\" , T); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n for j from 1 to m do" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n q:=hist[j];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 12 "\n if q[1]=\"" }{MPLTEXT 1 209 13 "Echan ge_ligne" }{MPLTEXT 1 202 10 "\" then T:=" }{MPLTEXT 1 209 12 "Permut_ ligne" }{MPLTEXT 1 202 17 "(q[2],q[3],T);B:=" }{MPLTEXT 1 209 12 "Perm ut_ligne" }{MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='L'[q[2]],\"<--->\" ,'L'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n elif q[1]= \"" }{MPLTEXT 1 209 15 "Echange_colonne" }{MPLTEXT 1 202 10 "\" then T :=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 17 "(q[2],q[3] ,T);B:=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 49 "(q[2] ,q[3],B);texte:='C'[q[2]],\"<--->\",'C'[q[3]];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 206 12 "Dilate_ligne " }{MPLTEXT 1 202 10 "\" then T:=" }{MPLTEXT 1 212 11 "Dilat_ligne" } {MPLTEXT 1 202 17 "(q[2],q[3],T);B:=" }{MPLTEXT 1 209 11 "Dilat_ligne" }{MPLTEXT 1 202 54 "(q[2],q[3],B);texte:='L'[q[3]],\"<----\",q[2]*'L' [q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" } {MPLTEXT 1 211 18 "Transvection_ligne" }{MPLTEXT 1 202 10 "\" then T:= " }{MPLTEXT 1 211 15 "Transvect_ligne" }{MPLTEXT 1 202 22 "(q[2],q[3], q[4],T);B:=" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 70 " (q[2],q[3],q[4],B);texte:='L'[q[2]],\"<----\",'L'[q[2]]+q[3]*'L'[q[4]] ; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\n print(B,texte,T);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n e nd:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 14 "Grang:=proc(A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n local B,j,k,q,t,m,hist,r,texte;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 31 "\n B:=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n B:=evalm(A);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 40 "\n hist:=Gauss_historique(A,\"colonnes\"); " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n m:=nops(hist); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n print(\"........\" , B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n for j from 1 to m do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n q:=hist[j];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 12 "\n if q[1]=\"" }{MPLTEXT 1 209 13 "Echange_ligne" }{MPLTEXT 1 202 10 "\" then B:=" }{MPLTEXT 1 209 12 "Permut_ligne" } {MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='L'[q[2]],\"<--->\",'L'[q[3]]; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n elif q[1]=\"" } {MPLTEXT 1 209 15 "Echange_colonne" }{MPLTEXT 1 202 11 "\" then B:=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 49 "(q[2],q[3],B); texte:='C'[q[2]],\"<--->\",'C'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 206 12 "Dilate_ligne" } {MPLTEXT 1 202 11 "\" then B:=" }{MPLTEXT 1 209 11 "Dilat_ligne" } {MPLTEXT 1 202 54 "(q[2],q[3],B);texte:='L'[q[3]],\"<----\",q[2]*'L'[q [3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" } {MPLTEXT 1 211 18 "Transvection_ligne" }{MPLTEXT 1 202 11 "\" then B: =" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 70 "(q[2],q[3] ,q[4],B);texte:='L'[q[2]],\"<----\",'L'[q[2]]+q[3]*'L'[q[4]]; " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n fi;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 18 "\n print(texte,B);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n e nd:" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }} {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "Grang_inverse:=proc(A,C)" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n local B,j,k,q,t,m,hist,r,te xte;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(C); " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n B:=array(1..t[1],1..t[2] );" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n B:=evalm(C);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n hist:=Gauss_historique(A,\" colonnes\"); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n m:=nops(his t); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n print(\"........\" , B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n for j from m to 1 by -1 do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n q:=hist[j];" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 12 "\n if q[1]=\"" }{MPLTEXT 1 209 13 "Echange_ligne" }{MPLTEXT 1 202 10 "\" then B:=" }{MPLTEXT 1 209 12 "Permut_ligne" }{MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='L'[q[2 ]],\"<--->\",'L'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n \+ elif q[1]=\"" }{MPLTEXT 1 209 15 "Echange_colonne" }{MPLTEXT 1 202 11 "\" then B:=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='C'[q[2]],\"<--->\",'C'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 206 12 "Di late_ligne" }{MPLTEXT 1 202 11 "\" then B:=" }{MPLTEXT 1 209 11 "Dila t_ligne" }{MPLTEXT 1 202 58 "(1/q[2],q[3],B);texte:='L'[q[3]],\"<---- \",1/q[2]*'L'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n el if q[1]=\"" }{MPLTEXT 1 211 18 "Transvection_ligne" }{MPLTEXT 1 202 11 "\" then B:=" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 71 "(q[2],-q[3],q[4],B);texte:='L'[q[2]],\"<----\",'L'[q[2]]-q[3]* 'L'[q[4]]; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n fi;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 18 "\n print(texte,B);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 6 "\n end:" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 25 "Gsyst_cramer:=proc(A,X,Y)" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 38 "\n local B,Z,Xt,j,k,q,t,m,hist,r,texte;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n B:=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n B:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n Z:=array(1..t[1],1..1);" }{MPLTEXT 1 202 0 " " }{MPLTEXT 1 202 30 "\n Z:=evalm(transpose([Y]));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\n Xt:=array(1..t[2],1..1);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n Xt:=evalm(transpose([X]) );" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n hist:=Gauss_historique (A,\"CRAMER\"); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n m:=nops( hist); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n print(\"........ \" ,evalm(B&*Xt),\"=\",Z);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 " \n for j from 1 to m do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n \+ q:=hist[j];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nif q[1]=\"" } {MPLTEXT 1 209 13 "Echange_ligne" }{MPLTEXT 1 202 10 "\" then Z:=" } {MPLTEXT 1 209 12 "Permut_ligne" }{MPLTEXT 1 202 17 "(q[2],q[3],Z);B:= " }{MPLTEXT 1 209 12 "Permut_ligne" }{MPLTEXT 1 202 49 "(q[2],q[3],B); texte:='L'[q[2]],\"<--->\",'L'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n elif q[1]=\"" }{MPLTEXT 1 209 15 "Echange_colonne" } {MPLTEXT 1 202 11 "\" then Xt:=" }{MPLTEXT 1 209 14 "Permut_colonne" } {MPLTEXT 1 202 18 "(q[2],q[3],Xt);B:=" }{MPLTEXT 1 209 14 "Permut_colo nne" }{MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='C'[q[2]],\"<--->\",'C'[ q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" } {MPLTEXT 1 206 12 "Dilate_ligne" }{MPLTEXT 1 202 10 "\" then Z:=" } {MPLTEXT 1 212 11 "Dilat_ligne" }{MPLTEXT 1 202 17 "(q[2],q[3],Z);B:=" }{MPLTEXT 1 209 11 "Dilat_ligne" }{MPLTEXT 1 202 54 "(q[2],q[3],B);te xte:='L'[q[3]],\"<----\",q[2]*'L'[q[3]];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 211 18 "Transvection _ligne" }{MPLTEXT 1 202 10 "\" then Z:=" }{MPLTEXT 1 211 15 "Transvect _ligne" }{MPLTEXT 1 202 22 "(q[2],q[3],q[4],Z);B:=" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 70 "(q[2],q[3],q[4],B);texte:='L' [q[2]],\"<----\",'L'[q[2]]+q[3]*'L'[q[4]]; " }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\n fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 35 "\n \+ print(texte,evalm(B&*Xt),\"=\",Z);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n end:" } {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 18 "Gsyst:=proc(A,X,Y)" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 59 "\n local B,Z,Xt,Xd,j,k,q,t,m,r ,hist,texte,param,F,Bc,Zc,Xtc;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n t:=taille(A); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n \+ B:=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 " \n B:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n Z:= array(1..t[1],1..1);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 30 "\n Z :=evalm(transpose([Y]));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\n \+ Xt:=evalm([X]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 23 "\n Xd: =diagonale(Xt);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n hist:=Gau ss_historique(A,\"colonnes\"); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\n m:=nops(hist); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n pr int(\"........\" ,evalm(B&*Xd),\"=\",Z);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 22 "\n for j from 1 to m do" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 14 "\n q:=hist[j];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nif q[1]=\"" }{MPLTEXT 1 209 13 "Echange_ligne" }{MPLTEXT 1 202 10 "\" then Z:=" }{MPLTEXT 1 209 12 "Permut_ligne" }{MPLTEXT 1 202 17 "(q[2],q[3],Z);B:=" }{MPLTEXT 1 209 12 "Permut_ligne" } {MPLTEXT 1 202 49 "(q[2],q[3],B);texte:='L'[q[2]],\"<--->\",'L'[q[3]]; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n elif q[1]=\"" } {MPLTEXT 1 209 15 "Echange_colonne" }{MPLTEXT 1 202 11 "\" then Xt:=" }{MPLTEXT 1 209 10 "Permut_col" }{MPLTEXT 1 202 22 "onne(q[2],q[3],Xt) ;B:=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 49 "(q[2],q[ 3],B);texte:='C'[q[2]],\"<--->\",'C'[q[3]];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 206 12 "Dilate_ligne " }{MPLTEXT 1 202 10 "\" then Z:=" }{MPLTEXT 1 212 11 "Dilat_ligne" } {MPLTEXT 1 202 17 "(q[2],q[3],Z);B:=" }{MPLTEXT 1 209 11 "Dilat_ligne" }{MPLTEXT 1 202 54 "(q[2],q[3],B);texte:='L'[q[3]],\"<----\",q[2]*'L' [q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\"" } {MPLTEXT 1 211 18 "Transvection_ligne" }{MPLTEXT 1 202 10 "\" then Z:= " }{MPLTEXT 1 211 15 "Transvect_ligne" }{MPLTEXT 1 202 22 "(q[2],q[3], q[4],Z);B:=" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 70 " (q[2],q[3],q[4],B);texte:='L'[q[2]],\"<----\",'L'[q[2]]+q[3]*'L'[q[4]] ; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 21 "\n Xd:=diagonale(Xt);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 35 "\n print(texte,evalm(B&*Xd),\"=\",Z);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 37 "\n r:=add(B[i,i],i=1..min(t[1],t[2]));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 100 "\n print(\"Conclusion: Sous la condition d'avoir la compatibilit\351 des\",t[1]-r, \"derni\350res \351quations\");" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 47 "\nfor j from r+1 to t[1] do pr int(Z[j,1]=0); od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 34 "\nparam:= seq(Xt[1,j],j=r+1..t[2]); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 55 " \nprint(\"En prenant alors \",param, \"comme param\351tres\"); " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 66 "\nprint(\"On est donc ramen\35 1 \340 la resolution du syst\350me de CRAMER\");" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\nF:=filtre(B,r);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 82 "\nBc:=F[1];Zc:=evalm(transpose([[seq(Z[j,1],j=1..r) ]])-F[2]&*transpose([[param]]));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 41 "\nXtc:=transpose([[seq(Xt[1,j],j=1..r)]]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 8 "\n#CRAMER" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 39 "\n hist:=Gauss_historique(Bc,\"CRAMER\"); " }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 17 "\n m:=nops(hist); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 43 "\n print(\"........\" ,evalm(Bc&*Xtc),\"=\",Zc);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n for j from 1 to m do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n q:=hist[j];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 10 "\nif q[1]=\"" }{MPLTEXT 1 209 13 "Echange_ligne" } {MPLTEXT 1 202 11 "\" then Zc:=" }{MPLTEXT 1 209 12 "Permut_ligne" } {MPLTEXT 1 202 19 "(q[2],q[3],Zc);Bc:=" }{MPLTEXT 1 209 12 "Permut_lig ne" }{MPLTEXT 1 202 50 "(q[2],q[3],Bc);texte:='L'[q[2]],\"<--->\",'L'[ q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n elif q[1]=\"" } {MPLTEXT 1 209 15 "Echange_colonne" }{MPLTEXT 1 202 12 "\" then Xtc:=" }{MPLTEXT 1 209 12 "Permut_ligne" }{MPLTEXT 1 202 20 "(q[2],q[3],Xtc) ;Bc:=" }{MPLTEXT 1 209 14 "Permut_colonne" }{MPLTEXT 1 202 50 "(q[2],q [3],Bc);texte:='C'[q[2]],\"<--->\",'C'[q[3]];" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 15 "\n elif q[1]=\"" }{MPLTEXT 1 206 12 "Dilate_ligne " }{MPLTEXT 1 202 11 "\" then Zc:=" }{MPLTEXT 1 212 11 "Dilat_ligne" } {MPLTEXT 1 202 19 "(q[2],q[3],Zc);Bc:=" }{MPLTEXT 1 209 11 "Dilat_lign e" }{MPLTEXT 1 202 55 "(q[2],q[3],Bc);texte:='L'[q[3]],\"<----\",q[2]* 'L'[q[3]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n elif q[1]=\" " }{MPLTEXT 1 211 18 "Transvection_ligne" }{MPLTEXT 1 202 11 "\" then \+ Zc:=" }{MPLTEXT 1 211 15 "Transvect_ligne" }{MPLTEXT 1 202 24 "(q[2],q [3],q[4],Zc);Bc:=" }{MPLTEXT 1 209 15 "Transvect_ligne" }{MPLTEXT 1 202 71 "(q[2],q[3],q[4],Bc);texte:='L'[q[2]],\"<----\",'L'[q[2]]+q[3]* 'L'[q[4]]; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n fi;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n print(texte,evalm(Bc&*Xtc) ,\"=\",Zc);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\n od;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n end:" }{MPLTEXT 1 202 0 "" } }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}}{EXCHG {PARA 205 "" 0 "" {TEXT 213 23 "R\351solution d'un syst\350me" }{TEXT 214 0 "" } }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 82 "A:=array(1..4,1..4): f or i from 1 to 4 do for j from 1 to 4 do A[i,j]:=i+j: od:od:" } {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 11 "A =evalm(A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I \"AG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&\"\"#\"\"$\"\"%\"\" &7&F/F0F1\"\"'7&F0F1F3\"\"(7&F1F3F5\"\")" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 29 "Gsyst(A,[x,y,z,t],[6,7,8,9]);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&Q)........6\"- I'matrixG6$I*protectedGF(I(_syslibGF$6#7&7&,$I\"xGF$\"\"#,$I\"yGF$\"\" $,$I\"zGF$\"\"%,$I\"tGF$\"\"&7&,$F.F2,$F1F5,$F4F8,$F7\"\"'7&,$F.F5,$F1 F8,$F4F>,$F7\"\"(7&,$F.F8,$F1F>,$F4FD,$F7\"\")Q\"=F$-F&6#7&7#F>7#FD7#F J7#\"\"*" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\" 6#\"\"\"Q&<----F%,$F##F'\"\"#-I'matrixG6$I*protectedGF/I(_syslibGF%6#7 &7&I\"xGF%,$I\"yGF%#\"\"$F+,$I\"zGF%F+,$I\"tGF%#\"\"&F+7&,$F4F8,$F6\" \"%,$F:F>,$F<\"\"'7&,$F4FB,$F6F>,$F:FE,$F<\"\"(7&,$F4F>,$F6FE,$F:FK,$F <\"\")Q\"=F%-F-6#7&7#F87#FK7#FQ7#\"\"*" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"#Q&<----F%,&F#\"\"\"&F$6#F*!\"$-I' matrixG6$I*protectedGF1I(_syslibGF%6#7&7&I\"xGF%,$I\"yGF%#\"\"$F',$I\" zGF%F',$I\"tGF%#\"\"&F'7&\"\"!,$F8#!\"\"F',$F#F-F'7&,$F6\"\"%,$ F8F@,$F<\"\"',$F>\"\"(7&,$F6F@,$F8FN,$F\"\")Q\"=F%-F/6#7&7#F:7# !\"#7#FV7#\"\"*" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I \"LG6\"6#\"\"$Q&<----F%,&F#\"\"\"&F$6#F*!\"%-I'matrixG6$I*protectedGF1 I(_syslibGF%6#7&7&I\"xGF%,$I\"yGF%#F'\"\"#,$I\"zGF%F:,$I\"tGF%#\"\"&F: 7&\"\"!,$F8#!\"\"F:,$F#!\"$F:7&FB,$F8FE,$FFI7&,$F6F@,$ F8\"\"',$F<\"\"(,$F>\"\")Q\"=F%-F/6#7&7#F'7#FM7#F-7#\"\"*" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"%Q&<----F%,&F# \"\"\"&F$6#F*!\"&-I'matrixG6$I*protectedGF1I(_syslibGF%6#7&7&I\"xGF%,$ I\"yGF%#\"\"$\"\"#,$I\"zGF%F;,$I\"tGF%#\"\"&F;7&\"\"!,$F8#!\"\"F;,$F=F F,$F?#!\"$F;7&FC,$F8FF,$F=!\"#,$F?FJ7&FC,$F8FI,$F=FJ,$F?#!\"*F;Q\"=F%- F/6#7&7#F:7#FN7#!\"%7#!\"'" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"#Q&<----F%,$F#!\"#-I'matrixG6$I*protecte dGF.I(_syslibGF%6#7&7&I\"xGF%,$I\"yGF%#\"\"$F',$I\"zGF%F',$I\"tGF%#\" \"&F'7&\"\"!F5F8,$F;F77&F?,$F5!\"\",$F9F*,$F;!\"$7&F?,$F5#FFF',$F9FF,$ F;#!\"*F'Q\"=F%-F,6#7&7#F77#\"\"%7#!\"%7#!\"'" }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"$Q&<----F%,&F#\"\"\"&F $6#\"\"#F*-I'matrixG6$I*protectedGF1I(_syslibGF%6#7&7&I\"xGF%,$I\"yGF% #F'F-,$I\"zGF%F-,$I\"tGF%#\"\"&F-7&\"\"!F8F:,$F=F'7&FAFAFAFA7&FA,$F8#! \"$F-,$F;FG,$F=#!\"*F-Q\"=F%-F/6#7&7#F'7#\"\"%7#FA7#!\"'" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"%Q&<----F%,&F# \"\"\"&F$6#\"\"##\"\"$F--I'matrixG6$I*protectedGF3I(_syslibGF%6#7&7&I \"xGF%,$I\"yGF%F.,$I\"zGF%F-,$I\"tGF%#\"\"&F-7&\"\"!F:F;,$F>F/7&FBFBFB FBFDQ\"=F%-F16#7&7#F/7#F'7#FBFK" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"CG6\"6#\"\"$Q&<--->F%&F$6#\"\"%-I'matrixG6$I*protec tedGF/I(_syslibGF%6#7&7&I\"xGF%,$I\"yGF%#F'\"\"#,$I\"tGF%#\"\"&F8,$I\" zGF%F87&\"\"!F6,$F:F'F=7&F@F@F@F@FBQ\"=F%-F-6#7&7#F'7#F+7#F@FI" } {TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6%QenConclusion:~Sous~ la~condition~d'avoir~la~compatibilit|dy~des6\"\"\"#Q4derni|cyres~|dyqu ationsF$" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&Q2En~prenant~alors~6\"I\"t GF$I\"zGF$Q1comme~param|dytresF$" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#QXOn~est~donc~ramen|dy~|[y~la~resolution~du~syst|cyme~d e~CRAMER6\"" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&Q).... ....6\"-I'matrixG6$I*protectedGF(I(_syslibGF$6#7$7#,&I\"xGF$\"\"\"I\"y GF$#\"\"$\"\"#7#F0Q\"=F$-F&6#7$7#,(F2F/I\"tGF$#!\"&F3I\"zGF$!\"#7#,(\" \"%F/F;!\"$F>F?" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I \"LG6\"6#\"\"\"Q&<----F%,&F#F'&F$6#\"\"##!\"$F,-I'matrixG6$I*protected GF2I(_syslibGF%6#7$7#I\"xGF%7#I\"yGF%Q\"=F%-F06#7$7#,(F.F'I\"tGF%F,I\" zGF%F'7#,(\"\"%F'F@F.FA!\"#" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {TEXT 215 14 "Calcul du rang" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 91 "A:=array(1..4,1..4): for i from 1 to 4 do for j from 1 to 4 do A[i,j]:=min(i-1,j-1): od:od:" } {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 11 "A =evalm(A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I \"AG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&\"\"!F.F.F.7&F.\"\" \"F0F07&F.F0\"\"#F27&F.F0F2\"\"$" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 9 "Grang(A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6$Q)........6\"-I'matrixG6$I*protectedGF(I(_s yslibGF$6#7&7&\"\"!F-F-F-7&F-\"\"\"F/F/7&F-F/\"\"#F17&F-F/F1\"\"$" } {TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"CG6\"6#\"\"\"Q&< --->F%&F$6#\"\"#-I'matrixG6$I*protectedGF/I(_syslibGF%6#7&7&\"\"!F4F4F 47&F'F4F'F'7&F'F4F+F+7&F'F4F+\"\"$" }{TEXT 204 0 "" }}{PARA 202 "" 1 " " {XPPMATH 20 "6&&I\"LG6\"6#\"\"#Q&<--->F%&F$6#\"\"\"-I'matrixG6$I*pro tectedGF/I(_syslibGF%6#7&7&F+\"\"!F+F+7&F4F4F4F47&F+F4F'F'7&F+F4F'\"\" $" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"LG6\"6#\"\"$ Q&<----F%,&F#\"\"\"&F$6#F*!\"\"-I'matrixG6$I*protectedGF1I(_syslibGF%6 #7&7&F*\"\"!F*F*7&F6F6F6F67&F6F6F*F*7&F*F6\"\"#F'" }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"LG6\"6#\"\"%Q&<----F%,&F#\"\"\"&F $6#F*!\"\"-I'matrixG6$I*protectedGF1I(_syslibGF%6#7&7&F*\"\"!F*F*7&F6F 6F6F67&F6F6F*F*7&F6F6F*\"\"#" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"CG6\"6#\"\"#Q&<--->F%&F$6#\"\"$-I'matrixG6$I*protec tedGF/I(_syslibGF%6#7&7&\"\"\"F4\"\"!F47&F5F5F5F57&F5F4F5F47&F5F4F5F'" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"LG6\"6#\"\"$Q& <--->F%&F$6#\"\"#-I'matrixG6$I*protectedGF/I(_syslibGF%6#7&7&\"\"\"F4 \"\"!F47&F5F4F5F47&F5F5F5F57&F5F4F5F+" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"LG6\"6#\"\"%Q&<----F%,&F#\"\"\"&F$6#\"\"#!\"\" -I'matrixG6$I*protectedGF2I(_syslibGF%6#7&7&F*F*\"\"!F*7&F7F*F7F*7&F7F 7F7F77&F7F7F7F*" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I \"CG6\"6#\"\"$Q&<--->F%&F$6#\"\"%-I'matrixG6$I*protectedGF/I(_syslibGF %6#7&7&\"\"\"F4F4\"\"!7&F5F4F4F57&F5F5F5F57&F5F5F4F5" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&&I\"LG6\"6#\"\"%Q&<--->F%&F$6#\"\"$ -I'matrixG6$I*protectedGF/I(_syslibGF%6#7&7&\"\"\"F4F4\"\"!7&F5F4F4F57 &F5F5F4F57&F5F5F5F5" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {TEXT 215 33 "R\351solution d'un syst\350me de CRAMER" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 87 "A:=array(1.. 4,1..4): for i from 1 to 4 do for j from 1 to 4 do A[i,j]:=min(i,j): o d:od:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 11 "A=evalm(A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#/I\"AG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&\" \"\"F.F.F.7&F.\"\"#F0F07&F.F0\"\"$F27&F.F0F2\"\"%" }{TEXT 204 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 44 "Gsyst_cramer(A,[x1,x2,x3 ,x4],[y1,y2,y3,y4]);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6&Q)........6\"-I'matrixG6$I*protectedGF(I(_syslibGF$6#7& 7#,*I#x1GF$\"\"\"I#x2GF$F/I#x3GF$F/I#x4GF$F/7#,*F.F/F0\"\"#F1F5F2F57#, *F.F/F0F5F1\"\"$F2F87#,*F.F/F0F5F1F8F2\"\"%Q\"=F$-F&6#7&7#I#y1GF$7#I#y 2GF$7#I#y3GF$7#I#y4GF$" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"#Q&<----F%,&F#\"\"\"&F$6#F*!\"\"-I'matrixG6$I*pro tectedGF1I(_syslibGF%6#7&7#,*I#x1GF%F*I#x2GF%F*I#x3GF%F*I#x4GF%F*7#,(F 8F*F9F*F:F*7#,*F7F*F8F'F9\"\"$F:F?7#,*F7F*F8F'F9F?F:\"\"%Q\"=F%-F/6#7& 7#I#y1GF%7#,&I#y2GF%F*FHF-7#I#y3GF%7#I#y4GF%" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"$Q&<----F%,&F#\"\"\"&F$6#F*! \"\"-I'matrixG6$I*protectedGF1I(_syslibGF%6#7&7#,*I#x1GF%F*I#x2GF%F*I# x3GF%F*I#x4GF%F*7#,(F8F*F9F*F:F*7#,(F8F*F9\"\"#F:F?7#,*F7F*F8F?F9F'F: \"\"%Q\"=F%-F/6#7&7#I#y1GF%7#,&I#y2GF%F*FHF-7#,&I#y3GF%F*FHF-7#I#y4GF% " }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"%Q &<----F%,&F#\"\"\"&F$6#F*!\"\"-I'matrixG6$I*protectedGF1I(_syslibGF%6# 7&7#,*I#x1GF%F*I#x2GF%F*I#x3GF%F*I#x4GF%F*7#,(F8F*F9F*F:F*7#,(F8F*F9\" \"#F:F?7#,(F8F*F9F?F:\"\"$Q\"=F%-F/6#7&7#I#y1GF%7#,&I#y2GF%F*FHF-7#,&I #y3GF%F*FHF-7#,&I#y4GF%F*FHF-" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"$Q&<----F%,&F#\"\"\"&F$6#\"\"#!\"\"-I'ma trixG6$I*protectedGF2I(_syslibGF%6#7&7#,*I#x1GF%F*I#x2GF%F*I#x3GF%F*I# x4GF%F*7#,(F9F*F:F*F;F*7#,&F:F*F;F*7#,(F9F*F:F-F;F'Q\"=F%-F06#7&7#I#y1 GF%7#,&I#y2GF%F*FGF.7#,&I#y3GF%F*FJF.7#,&I#y4GF%F*FGF." }{TEXT 204 0 " " }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\"%Q&<----F%,&F#\"\" \"&F$6#\"\"#!\"\"-I'matrixG6$I*protectedGF2I(_syslibGF%6#7&7#,*I#x1GF% F*I#x2GF%F*I#x3GF%F*I#x4GF%F*7#,(F9F*F:F*F;F*7#,&F:F*F;F*7#,&F:F*F;F-Q \"=F%-F06#7&7#I#y1GF%7#,&I#y2GF%F*FGF.7#,&I#y3GF%F*FJF.7#,&I#y4GF%F*FJ F." }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"LG6\"6#\"\" %Q&<----F%,&F#\"\"\"&F$6#\"\"$!\"\"-I'matrixG6$I*protectedGF2I(_syslib GF%6#7&7#,*I#x1GF%F*I#x2GF%F*I#x3GF%F*I#x4GF%F*7#,(F9F*F:F*F;F*7#,&F:F *F;F*7#F;Q\"=F%-F06#7&7#I#y1GF%7#,&I#y2GF%F*FFF.7#,&I#y3GF%F*FIF.7#,&I #y4GF%F*FLF." }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6(&I\"L G6\"6#\"\"\"Q&<----F%,&F#F'&F$6#\"\"%!\"\"-I'matrixG6$I*protectedGF1I( _syslibGF%6#7&7#,(I#x1GF%F'I#x2GF%F'I#x3GF%F'7#,(F8F'F9F'I#x4GF%F'7#,& F9F'F " 0 "" {TEXT 215 33 "Calcul de l'inverse d'une matrice" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 12 "Ginverse(A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6%-I'matrixG6$I*protectedGF&I(_s yslibG6\"6#7&7&\"\"\"F,F,F,7&F,\"\"#F.F.7&F,F.\"\"$F07&F,F.F0\"\"%Q).. ......F(-F$6#7&7&F,\"\"!F8F87&F8F,F8F87&F8F8F,F87&F8F8F8F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF& I(_syslibG6\"6#7&7&\"\"\"F,F,F,7&\"\"!F,F,F,7&F,\"\"#\"\"$F17&F,F0F1\" \"%&I\"LGF(6#F0Q&<----F(,&F4F,&F56#F,!\"\"-F$6#7&7&F,F.F.F.7&F;F,F.F.7 &F.F.F,F.7&F.F.F.F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 " 6'-I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"F,F,F,7&\"\"!F,F, F,7&F.F,\"\"#F07&F,F0\"\"$\"\"%&I\"LGF(6#F2Q&<----F(,&F4F,&F56#F,!\"\" -F$6#7&7&F,F.F.F.7&F;F,F.F.7&F;F.F,F.7&F.F.F.F," }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF&I(_syslibG6 \"6#7&7&\"\"\"F,F,F,7&\"\"!F,F,F,7&F.F,\"\"#F07&F.F,F0\"\"$&I\"LGF(6# \"\"%Q&<----F(,&F3F,&F46#F,!\"\"-F$6#7&7&F,F.F.F.7&F;F,F.F.7&F;F.F,F.7 &F;F.F.F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matri xG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"F,F,F,7&\"\"!F,F,F,7&F.F.F, F,7&F.F,\"\"#\"\"$&I\"LGF(6#F2Q&<----F(,&F3F,&F46#F1!\"\"-F$6#7&7&F,F. F.F.7&F:F,F.F.7&F.F:F,F.7&F:F.F.F," }{TEXT 204 0 "" }}{PARA 202 "" 1 " " {XPPMATH 20 "6'-I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"F, F,F,7&\"\"!F,F,F,7&F.F.F,F,7&F.F.F,\"\"#&I\"LGF(6#\"\"%Q&<----F(,&F2F, &F36#F1!\"\"-F$6#7&7&F,F.F.F.7&F:F,F.F.7&F.F:F,F.7&F.F:F.F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF& I(_syslibG6\"6#7&7&\"\"\"F,F,F,7&\"\"!F,F,F,7&F.F.F,F,7&F.F.F.F,&I\"LG F(6#\"\"%Q&<----F(,&F1F,&F26#\"\"$!\"\"-F$6#7&7&F,F.F.F.7&F:F,F.F.7&F. F:F,F.7&F.F.F:F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'- I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"F,F,\"\"!7&F-F,F,F,7 &F-F-F,F,7&F-F-F-F,&I\"LGF(6#F,Q&<----F(,&F1F,&F26#\"\"%!\"\"-F$6#7&7& F,F-F,F97&F9F,F-F-7&F-F9F,F-7&F-F-F9F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\" \"F,F,\"\"!7&F-F,F,F-7&F-F-F,F,7&F-F-F-F,&I\"LGF(6#\"\"#Q&<----F(,&F1F ,&F26#\"\"%!\"\"-F$6#7&7&F,F-F,F:7&F:F,F,F:7&F-F:F,F-7&F-F-F:F," } {TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protec tedGF&I(_syslibG6\"6#7&7&\"\"\"F,F,\"\"!7&F-F,F,F-7&F-F-F,F-7&F-F-F-F, &I\"LGF(6#\"\"$Q&<----F(,&F1F,&F26#\"\"%!\"\"-F$6#7&7&F,F-F,F:7&F:F,F, F:7&F-F:\"\"#F:7&F-F-F:F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"F,\" \"!F-7&F-F,F,F-7&F-F-F,F-7&F-F-F-F,&I\"LGF(6#F,Q&<----F(,&F1F,&F26#\" \"$!\"\"-F$6#7&7&F,F,F9F-7&F9F,F,F97&F-F9\"\"#F97&F-F-F9F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'-I'matrixG6$I*protectedGF& I(_syslibG6\"6#7&7&\"\"\"F,\"\"!F-7&F-F,F-F-7&F-F-F,F-7&F-F-F-F,&I\"LG F(6#\"\"#Q&<----F(,&F1F,&F26#\"\"$!\"\"-F$6#7&7&F,F,F:F-7&F:F4F:F-7&F- F:F4F:7&F-F-F:F," }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6'- I'matrixG6$I*protectedGF&I(_syslibG6\"6#7&7&\"\"\"\"\"!F-F-7&F-F,F-F-7 &F-F-F,F-7&F-F-F-F,&I\"LGF(6#F,Q&<----F(,&F1F,&F26#\"\"#!\"\"-F$6#7&7& F8F9F-F-7&F9F8F9F-7&F-F9F8F97&F-F-F9F," }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{PARA 206 "" 0 "" {TEXT 216 0 "" }}{PARA 206 "" 0 "" {TEXT 216 0 "" }}{PARA 206 "" 0 "" {TEXT 216 0 "" }}{PARA 206 "" 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 }