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11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(*&)%\"xG\"\"&\" \"\"%\"yG\"\"\"F,*$)F(\"\"#F*\"\"$F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "degree(p,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "coeff(p,x,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand((x+1)^20);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,L*$)%\"x G\"#?\"\"\"\"\"\"*$)F&\"#>F(F'*$)F&\"#=F(\"$!>*$)F&\"# " 0 "" {MPLTEXT 1 0 10 "fa ctor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"F'F'\"#?\" \"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "un polynme alatoire :" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "randpoly(x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,.*$)%\"xG\"\"&\"\"\"!#&)*$)F&\"\"%F(!#b*$)F&\" \"$F(!#P*$)F&\"\"#F(!#NF&\"#(*\"#]\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$)% \"xG\"\"&\"\"\"!#&)*$)F&\"\"%F(!#b*$)F&\"\"$F(!#P*$)F&\"\"#F(!#NF&\"#( *\"#]\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Ceci " }{TEXT 259 6 "prouve" }{TEXT -1 17 " l'irrductibilit." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "f:=(1+x*(1+y))^2/(1-y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&*$),&\"\"\"F)*&%\"xGF),&F)F)%\"yGF)F)F)\"\"#\" \"\"F/,&F)F)*$)F-F.F/!\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "collect(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&*&),&\"\" \"F(%\"yGF(\"\"#\"\"\")%\"xGF*F+F+,&F(F(*$)F)F*F+!\"\"!\"\"F(*&*&,&F*F (F)F*F(F-F(F+F.F2F(*&F+F+F.F2F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "collect(f,x,normal);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&*& ,&\"\"\"F'%\"yGF'F')%\"xG\"\"#\"\"\"F,,&F(F'!\"\"F'!\"\"F.*&F*F,F-F/! \"#*&F,F,,&F.F'*$)F(F+F,F'F/F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Un peu plus de vrai calcul :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "P:=x^10-v*x^9-x+v;Q:=2*x^3+5*u*x^2+2*u^2*x+x+2*u;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"PG,**$)%\"xG\"#5\"\"\"\"\"\"*&%\"vGF+)F(\"\" *F*!\"\"F(F0F-F+" }}{PARA 11 "" 1 "" 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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&\"\"\"F%%\"xG !\"\"\"\"\"*&F%F%,&F&F(F(F(F'!\"\"*&F%F%,(*$)F&\"\"#F%F(F&F(F(F(F'F+*& F%F%*$)F-\"\"#F%F'F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "recherche des racines exactement" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " solve(1/f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(\"\"!!\"\",&#F$\"\"# \"\"\"*&%\"IGF(-%%sqrtG6#\"\"$\"\"\"#F(F',&F&F(F)F&F%F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(a*x^3+b*x^2+c*x+d,x);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6%,(*&*$),**(%\"cG\"\"\"%\"bGF*%\"aGF*\" #O*&%\"dGF*)F,\"\"#\"\"\"!$3\"*$)F+\"\"$F2!\")*(-%%sqrtG6#F6F2-F:6#,,* &)F)F6F2F,F2\"\"%*&)F)F1F2)F+F1F2!\"\"**F)F2F+F2F,F2F/F2!#=*&)F/F1F2F0 F2\"#F*&F/F2F5F2FAF2F,F2\"#7#F*F6F2F2F,!\"\"#F*\"\"'*&,&*&F)F2F,F2F6*$ FDF2FEF2*&F,\"\"\")F'#\"\"\"F6F2FN#!\"#F6*&F+F2F,FN#FEF6,*F$#FEFLFQFMF fnFgn*(%\"IGF*F9F2,&F$FOFQ#F1F6F*#F*F1,*F$FinFQFMFfnFgnFjn#FEF1" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "ou numeriquement" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "fsolve(f=1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`V9fM!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "on peut aussi trouver les racines complexes d'un polynome " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve(numer(f-1),x,complex);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6($!+NW\"fM\"!\"*,&$!+EK,S()!#5\"\"\"%\" IG$!+Sxbf5F%,&F'F*F+$\"+Sxbf5F%,&$!+un)*f7F)F*F+F,,&F2F*F+F/$\"+`V9fMF )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fsolve(numer(f-1),x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!+NW\"fM\"!\"*$\"+`V9fM!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits:=100:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve(numer(f-1),x,complex);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6($!_q\"4^Y1ih9.*)Gx4;\\czbF!p\\O(=%G&[i DpYN.!3>.xF$*y)e:Y;`V9fM\"!#**,&$!_qmzjXI;:T@d&G%RB3%[M*p!=F>*34A#45^& >\\H?qB]W)>$)4hW-eA8+u)!$+\"\"\"\"%\"IG$!_qV'4O[*y/m'[Y$GBa5]I&R*>Hx][ /\"o5^)*HJ;mm&GyxVYO`@YRSxbf5F%,&F'F*F+$\"_qV'4O[*y/m'[Y$GBa5]I&R*>Hx] 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sur un intervalle de " }{TEXT 258 1 "R" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "readlib(sturm):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sturm(sturmseq(x^7+x+1,x),x,-infinity,infinity); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "et quelques autres simplifications sont possibles" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sum(x^10,x=RootOf(x^4+a*x+b, x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"bG\"\"\")%\"aG\"\"#\"\" \"!#5" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 37 "Primitives, equations \+ differentielles" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(1/(x^ 2-2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%%sqrtG6#\"\"#\"\"\"- %(arctanhG6#,$*&%\"xG\"\"\"F%F)#F0F(F0#!\"\"F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "int(exp(x^2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"IG\"\"\"-%%sqrtG6#%#PiGF&-%$erfG6#*&F%\"\"\"%\"xGF/F/#!\" \"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(exp(x^3),x); " }}{PARA 11 "" 1 "" 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