@\pCGCv Delboy   # *G8W7taB  dMbP?_"*+%!!1 Geneva1 Geneva1 Geneva1 Geneva1 Geneva1 Geneva1 Geneva&FPage &P&[4d2?'[4d2?(<~?)<~?"PagD <~?<~? @#A# array.0# compA# fixtV General00.00#,##0 #,##0.00#,##0\ _F;\-#,##0\ _F#,##0\ _F;[Red]\-#,##0\ _F#,##0.00\ _F;\-#,##0.00\ _F# #,##0.00\ _F;[Red]\-#,##0.00\ _F#,##0\ "F";\-#,##0\ "F"#,##0\ "F";[Red]\-#,##0\ "F" #,##0.00\ "F";\-#,##0.00\ "F"%"#,##0.00\ "F";[Red]\-#,##0.00\ "F"0%0.00% 0.00E+00 #" "?/? #" "??/?? dd/mm/yy dd\-mmm\-yy dd\-mmm mmm\-yy h:mm\ AM/PMh:mm:ss\ AM/PMhh:mm hh:mm:ssdd/mm/yy\ hh:mm 0.000\1 ##0.0E+0mm:ss@96_-* #,##0\ "F"_-;\-* #,##0\ "F"_-;_-* "-"\ "F"_-;_-@_-63_-* #,##0\ _F_-;\-* #,##0\ _F_-;_-* "-"\ _F_-;_-@_-A>_-* #,##0.00\ "F"_-;\-* #,##0.00\ "F"_-;_-* "-"??\ "F"_-;_-@_->;_-* #,##0.00\ _F_-;\-* #,##0.00\ _F_-;_-* "-"??\ _F_-;_-@_- A, AP- Auto_openenter.root, enter.root, B,  B.0, B.1, B.10,B.11,B.12, B.2,  B.3,  B.4,  B.5, B.6, B.7, B.8, B.9,B_- BASE-  C..,  C.0,& C.1,(C.10,C.11, C.2,  C.3,  C.4,  C.5, C.6, C.7, C.8, C.9,C_-  choleski_factorization,E D, deb,9deg.pol,  dim DP,1 DQ,5 dum E,eigerror,-errfev,Jerror, FindEigVec,I i i.ii-[nim_root-  input_array,I j kkmax, minor N,;nbmin nti,A P, poly@polydial- POLYNOM,PolySour,K Q,ROOT-  t.i tol, varx, XI, xi_values- C C  C  C  C  C C C C C C C C C C C  C  C  C  C "C "TC  @C  C "C  C  C  U } }  } } } } m  l ^bnUlbb w > R  bK0b2APOLYNOM error~ z@~ q@ Solve a polynomial 0" "z TRUETRUEyg^POLYNOM.XLM has found an internal error. It can occur when the roots have already be solved..."v~ ?~ t@~  &@~  P@  OK# POLYNOM.XLM"gB7~ @~ t@~  G@~  P@ Cancel!#"?~ @~ u@~  @j@~  P@  Close"4~ 1@~ ~  @~  @@ C&~ @~ [@~  2@ roots of a polynomialI7D DDADAB% $A5B~ @~ *@~  O@ degree50#N$BXXI$BX$Al TRUETRUETRUE~ @~ ``@~  O@  iterations4"IC9B~ @~ *@~  Y@  tolerance F@C0C9 Enter the coefficient:QHEnter the coefficients for the polynomial by setting first the constant:B AoA(C0)Bh  real root im root~  @~ @W@~ Y@~ \@ h㈵>X F=The value is wrong or missed. Do you want to continue now?..."v^` ND  D AB% $ A5(#&C01"D AlB 45   -0.294 =>tAɿ~  @~ i@~ M@~ @T@~ T@D h02D  " "zB7$ A5B TRUETRUE A -21.4596870543114 2@ (>@ -0.294 =>tA?~ @~ Q@~ N@~ H@~ @ B7$ #.BT 7.97675655698951 '  L' 0.23844 h|?5ֿ~ .@~ @~ e@~ `s@~ W@  xi_values~ ? T@ C7~ @ >  0.23844 h|?5?~ `i@~ s@~ @W@~ V@ Retry $D Al~ ?~ @~ 9@~  @a@  P $D Al~ @~ ``@~   a@  Q?-C9 $A5$A5B~  @~ @Q@~  `@~  K@~  ?<\`iF*#B#B~  @~ `e@~  `@~  K@~  ?x0fX#B = DA"v#B7#BB"DAAl TRUETRUEAuto_ouvrirenter.root$CA5K9D AD AA&B%$ Al$ AlB9'C9 $A5B #>AO@=CF CFCF+Be0SA#"BXB#%"BXC..#A"BX TRUETRUETRUED  $A5D B7C&/  $A5CDM|= CDb? B% $A5AC7 C7d B% $A5""""BP 1>D$BX$CC&C2Al TRUETRUE$A5SAC&  $A5"D  $A5"BC& G:You must put 1 value for the coefficient of the polynomial"v<CD_|= CDt? B%@3The value of TOL must be bounded by 1E-10 and 5E-01"vC7 C7d B%?2You must put for ITER a value bounded by 2 and 100"vUC&6 7*The degrees of the polynomial must be <=20"v"""B#ATbz?(1-P$BXQ$BX$Al$AlTRUETRUETRUETRUE{#BBAA&L+Do you want to erase all the data? (degree:#BRB)"v$A5B$A59'C$  $A5B3?;)D #?A5 B7B.$C$ ?Alru ? #?A5# POLYNOM.XLMBg<$>*CC$C!(\1I$BX$Al TRUETRUE"iB<70O'?*CC$C!~ $ A5B7p1XCF = DA AoXCF3 = DA"v#B^CFi"DAAl#BCF"DAAl TRUETRUETRUE!@C0$:A51B.0$BX$#BAl p value: C<=CDHA A q value: CAkCDvA A Remaining: C7D iterations."z TRUETRUETRUE/9;?CC~ F@<Oa45ֿ*C$?C!U1CB.1$ BX$ #BC<,C7Al TRUETRUE X !"b#%&D'b(\b)*/+,-./q012345hb67a8f9:;F<==>+b? 1XCF = DA+i*DA AoXCFD = DA-i*DA"v#BCF"DAAl#BCF"DAAl TRUETRUETRUE  u5j!1X#3CF"DAAl#30CF;"DAAl TRUETRUE'!KC9 B"$:A5"1B.C6 #C6#"BX#:C6E"#TC6_BC<rB.C6AjCAB.C6AjAl TRUETRUE#A2%2 C.0$&BX$&CAl TRUETRUE~ &F@J'28C.1$(BX$(CC<!C,Al TRUETRUE( G+)KC9 B*82C.C6 #"C6#"BX#":C6E"#TC6_BC<nC.C6}AjCAC.C6AjAl TRUETRUE+Ay,L2gD$-BX$-C.C9AjC.C96AjC.C9PAjAl TRUETRUE-trv@_.h2MD$/BX$/D-B.C9AjC.C96AjAl TRUETRUE/[rv@02DP$1BX$1B.C9AjC.C93AjB.C9NAjC.C9dAjC$}Al TRUETRUE115C>22{DQ$3BX$3B.C9AjC.C9/AjB.C9JAjC.C9dAjAl TRUETRUE3W3>V42DDQ$5BX$5D3B.C9AjC$9Al TRUETRUE5m J>O62=$C< C(Al$CA'C)2Al TRUETRUEb7PC(ACD C)ACD- B% $AA5Bp82^#"Al#!"C<3Al#B"CATAl TRUETRUETRUE9$A54:3"$;C9 AlN$;BX TRUETRUE~ ;9<'C9  $CA5B'=KC9 BM>;#C6"B.C6+AjAl>3B[ POLYNOM.XLM5># r11C1:r13CC&Bm?AL?:D> POLYNOM.XLM D>MQNI.XLM B%BiB)?"-@ l A lB bC D E F bG bH I gJ K L M (N MO P Q MR S 3T bU V W X LY Z 3[ \ ] b^ _ @$A5*@ $  "?@ r11C1BmAA/C0C7  $A5B+Ai#B BB!A real part"`MB;Can't converge after C7 iterations..."v4B"#BC0B"`B r12C1Bm Cdeb5C43#" "z#A5B7 TRUETRUE'C!_"N"m!C imag part"`D$EA5D"igDU#3C0BA "`%#34C0?B"`BD r13C1BmrE`/Do you want to copy the roots on the worksheet?"v  $?A5#OA5B/E!_"N"mE coeff"`Echoleski factorizationFB7FA#F r11C2:r13C8BmkFH3Y$TAl$WAl$[Al$bAl$eAl$iAl$pAl$sAl$wAl&$TRUETRUETRUETRUETRUETRUETRUETRUETRUEG$>A5G r9C3BmCG318l#8lB?#-&BT TRUETRUEIH7"ROOTS OF THE POLYNOMIAL OF DEGREE C&)"`H"2I FindEigVec I#A5I input array*I$"?#J#-BTJerrfev*J$"?J"3vK?dASelect the root to find the corresponding eigenvector (you have: #BHB roots)Bh;K) You have no matrix or no data...BvKPolySourKgKULThe first cell of the array must be stored in the cell $c$3 of the worksheet"vHK36B!_"=dim8l#8lALBX TRUETRUEOL=4The number is wrong or missed. Do you want to retry?"vL3vDKDKADK#BB DK DKAB% $LA5BdimlP#_lALBXVRAILB71L4dim$TBX#-BT TRUETRUE:L@(Put the dimension of the matrixBhVLD8l#8lAL  $L A5" BFL 4+The number of rows (or columns) must be < 9"v4M"DL  $KA5 B7BM$OA51M8l#8l"?MvDL DLDLADL B%C6The dimension of the array must be bounded by 2 and 18"v$OA5BM!^"mM B7N~8l#8lAL8l##28lAM*You must put a squared matrix"v$NA5BN"24N"DM  $LA5 B7B'NiC' B1O8l#8l"?O!^"mOB7*O$"?+O!_DLDL"NBm'OjC' BP"2(Pi.C' BP" P"3P A!_"=PC0 C5 B$=INDEX(A,1,1)^0.5B`XC0F C5U B$` =INDEX(A,C0w,C5 )/INDEX(A,C0,C0)^0.5B`C5C0  B`C0C5 C5  B$ $RA5[C5+C06 C5BC0M B$ $mA5$_A5""""B*Q$"?'QjC' B1Q*#*"?Q$PA5QB7Q${A5Q R"3YRGC1C5 A_#B#DKB"`BR "qR4_ (INDEX(A,C0,C5  )-INDEX(B,C09,C5I)^2)^0.5#!(INDEX(A,4,4)-INDEX(B,4,3)^2)^0.5DS2#3DKB  $NA5BnS\C5 C' $!_C''"N"m!_"N"mB-S!_2"N"mS $TDRAl|Tj!_8l#8lAL8l'#68lAL8lE#T8lAM"N"mTA4T@"8l#8lAL)T!(INDEX(A,4,4)-INDEX(B,4,3)^2)^0.5U"3UAUB $U`4DT(=(Bx$"=(INDEX(A,4,4)-INDEX(B,4,3)^2)^0.5 VcompA!_"=*V$"?_VM!_8l #8lAL8l(#78lAM"N"m@V.C0 $[ $W"DUAl}Wk!_8l#8lAL8l(#78lAL8lF#U8lAM"N"msWa$`Aj$AjAuB73$Xt.C':*x.C'LAlB"Warray.0!_"=*W"=(INDEX(A,4,4)-INDEX(B,4,3)^2)^0.5X$NA5Xt.4*x.4+t.3*x.3+t.2*x.2(Xi.C' B+XkC0 B6Y$dumC' B'YjC' BY4rC6 $W $["Aj)- )-INDEX(B,C0?,C5OC6Z)^2-BxB@=(INDEX(A,4,4)-INDEX(B,4,1)^2-INDEX(B,4,2)^2-INDEX(B,4,3)^2)^0.5RZ,5@DXDXDX+t.C* *x.C*2Bxt.4*x.4+t.3*x.3+t.2*x.2Z!^"mZ $[DYAl[ $XDZAlG[5C1C5  $\A5$]A5BH[@=(INDEX(A,4,4)-INDEX(B,4,1)^2-INDEX(B,4,2)^2-INDEX(B,4,3)^2)^0.59\'C*  $^A5B0\minor.C1 !_"=\A]An]\C5 C' $!_C''"N"m!_"N"mB]D["`A^/DXDXSUM((t.1*x.1+(DX))^2)Bx,*SUM((t.1*x.1+(t.4*x.4+t.3*x.3+t.2*x.2))^2)^A^${A5^ _ $`D^Al_A`_NC5C0 C5C0' B$$zA5B` l a cb xbc d e f Zbg dbh _i j |k Ol m n o p q r "s t ,bu v w x 3y z u{ | } b~ V @0`(somme((t.1+(t.4*x.4+t.3*x.3+t.2*x.2))^2)+`minorC'B`h (INDEX(A,C0,C5  )-INDEX(B,C59,C0I )*INDEX(B,C0f,C0v ))/INDEX(B,C0,C0)75(INDEX(A,2,4)-INDEX(B,4,1)*INDEX(B,2,1))/INDEX(B,2,2)!a=D`"b.a=minor.C8"ba $bD`AlJb8#3DKB $cA5$sA5B'b!_"N"m=b5(INDEX(A,2,4)-INDEX(B,4,1)*INDEX(B,2,1))/INDEX(B,2,2)c compA"?cA$cԋDb(=(Bx86=(INDEX(A,2,4)-INDEX(B,4,1)*INDEX(B,2,1))/INDEX(B,2,2)d!^"m:d( =-SUM(r[-C' ]C:r[-1]C)B`@d.C0 $i $e"DcAl(ei.C' Be s.0!_"=e'fjC' Bf+fkC0 B\gJC1C5 #3 DKBB`B`B4g"!_C' "N"mg|5C6 $e $i"Aj- -INDEX(B,C5=,C0MC6X )*INDEX(B,C0w,C0C6)-Bxnh\C5 C' $!_C''"N"m!_"N"mB9h'!_C'C'"N"mh $iDgAliAi ii!_"=>i6=(INDEX(A,2,4)-INDEX(B,4,1)*INDEX(B,2,1))/INDEX(B,2,2)jAj!^"mjA*k$"?1k|#|"?'kiC' BkDi"`sla$uAj$AjAuB73$mt.C':*x.C'LAlBBl0!_8l#8lAL"N"m'ljC' Bl${A5l mt.4*x.4+t.3*x.3+t.2*x.2m"2Cm1C0C5  B"``mNC5C0 C5C0' B$${A5B6n$dumC' B_nM!_8l#8lAL8l&#58lAM"N"mnn\C5 C' $!_C''"N"m!_"N"mBnD (INDEX(A,C0,C5  )-INDEX(B,C59,C0I )*index(B,C5f,C0z ))/index(B,C5,C0)75(INDEX(A,3,4)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)Ro@DmDmDm+t.C* *x.C*2Bxt.4*x.4+t.3*x.3+t.2*x.2o"3oAo $pDnAlp $mDoAl1p|#|"?pA=p5(INDEX(A,3,4)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)9q'C*  $sA5B`qN!_8l#8lAL8l'#68lAM"N"mq!^"m$qDp(=(Bx86=(INDEX(A,3,4)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)rAr =-compA"bIr7!_C' C' "N"m@r.C0 $w $s"DqAl?sp-DmDm somme((t.1+(Dm))^2)Bx*(somme((t.1+(t.4*x.4+t.3*x.3+t.2*x.2))^2)Bs0'Have you a complex root? y=OK; n=cancelBv/snbminC'B>s6=(INDEX(A,3,4)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)t $uDsAlOt=t.iDs C'#'+BB9t'!_C'C'"N"m+tkC0 B0u(somme((t.1+(t.4*x.4+t.3*x.3+t.2*x.2))^2)9u5'B *#*B? VRAIVRAIZuH =MMULT(array.C:+s.C:* *ii,array.0)BbuC6 $s $w"Aj- -index(B,C5=,C5MC6X )*index(B,C5w,C5C6)-BxRP=(INDEX(A,3,4)-index(B,4,1)*index(B,3,1)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)!v=Du"b$vTIBB  VRAIVRAI0varray.C: !_"=v $wDuAlwB7ewSDvA?2You have no data stored or you have missing values"vBPw>iC:C'C'#C:.BXwP=(INDEX(A,3,4)-index(B,4,1)*index(B,3,1)-INDEX(B,4,2)*index(B,3,2))/index(B,3,3)9x'!_3CC"N"mPx>jC:C'C'#C:.BxAy,yt.CC !_"=y!^"myDw"`zzAGz5C0C5  ${A5$|A5Bz${A5z {'{!_"N"m0{minor.C0 !_"=n{\C5 C' $!_C''"NBm!_"NBmB{ ||B |mC5 C'C: $!_C'8"N"m!_"N"mB|A}}B7}A}A~~A~$` A5'!_"N"mB7 b2b+T0b6b.8Z5#.7$*bTBminorC: C'C''C:2B.=minor.C8"b'!_"N"mAP>=-1/C: *SUM(r[-C'& ]C:r[-1]C)B`,s.C: !_"=2 !_C' "N"mA* $  "?4"polyC'BVDC=  "`=s.C=."`B'!_"N"mA* $  "?3!!_C'"N"m"2 "5&r132C1:r199C18Bm"4B B7= %> 5PPP[4d2?[4d2?<~?<~?m | } b~ VAhT0bbq0bb0bhTbAq0Fq0b mhT0@Hbb]l0bGDl0@Hbbb@blbbqq     "