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{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}
{EXCHG {PARA 259 "" 0 "" {TEXT 257 34 "TP 2 - CALCULS LITT\311RAUX - C
ORRIG\311" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "1" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 65 "u:=(1/a+1/b)/(1/a-1/b):A:=(u+1/u)/(u-1/u):
\nA=expand(simplify(A));" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/*&,&*&,&*&\"\"\"F)%\"aG!\"\"F)*&F)F)%\"bGF+F)F),&F(F)F,F+F+F)*&
F'F+F.F)F)F),&F&F)F/F+F+,&*(\"\"#F+F*F+F-F)F)*(F3F+F*F)F-F+F)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Au lieu de tout taper, donnez des \+
noms \340 des expressions identiques !" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 1 "2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand((x+
y+z+t)^4);\n" }{XPPMATH 20 "6#>%\"PG,bo**\"#7\"\"\")%\"yG\"\"#F(%\"zGF
(%\"tGF(F(*(\"\"'F(F)F()F,F+F(F(*(\"\"%F(%\"xGF()F,\"\"$F(F(**F'F(F3F(
F)F(F-F(F(**F'F(F*F(F,F()F-F+F(F(**F'F(F3F(F*F(F8F(F(*(F/F(F0F(F8F(F(*
*F'F(F3F(F,F(F8F(F(**F'F(F3F(F0F(F-F(F(**F'F(F3F(F)F(F,F(F(**F'F(F3F(F
*F(F0F(F(**F'F()F3F+F(F*F(F,F(F(**F'F(F*F(F0F(F-F(F(**F'F(F@F(F*F(F-F(
F(*(F/F(F@F(F8F(F(**F'F(F@F(F,F(F-F(F(*(F2F()F3F5F(F*F(F(*(F2F(F3F()F-
F5F(F(*(F2F()F*F5F(F,F(F(*(F2F(F*F(F4F(F(*(F2F(F4F(F-F(F(*(F/F(F)F(F8F
(F(*(F/F(F@F(F0F(F(*(F2F(FFF(F-F(F(*(F/F(F@F(F)F(F(*(F2F(FJF(F-F(F(*(F
2F(F*F(FHF(F(*(F2F(F,F(FHF(F(*(F2F(F3F(FJF(F(*(F2F(FFF(F,F(F(*$)F3F2F(
F(*$)F*F2F(F(*$)F,F2F(F(*$)F-F2F(F(*,\"#CF(F3F(F*F(F,F(F-F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "P:=expand((x+y+z)^4):collect(P,x);coeff(P,x^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*$)%\"xG\"\"%\"\"\"F(*&,&*&F'F(%\"zG
F(F(*&F'F(%\"yGF(F(F()F&\"\"$F(F(*&,(*(\"#7F(F.F(F,F(F(*&\"\"'F()F,\"
\"#F(F(*&F6F()F.F8F(F(F()F&F8F(F(*&,**(F4F(F:F(F,F(F(*(F4F(F.F(F7F(F(*
&F'F()F.F0F(F(*&F'F()F,F0F(F(F(F&F(F(*(F6F(F:F(F7F(F(*$)F,F'F(F(*(F'F(
FAF(F,F(F(*(F'F(F.F(FCF(F(*$)F.F'F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,(*(\"#7\"\"\"%\"yGF&%\"zGF&F&*&\"\"'F&)F(\"\"#F&F&*&F*F&)F'F,F&F&
" }}}{EXCHG {PARA 260 "" 1 "" {TEXT -1 1 "4" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 93 "S:=a^2*b*(a-b)+b^2*c*(b-c)+c^2*a*(c-a);S2:=subs(a=
y+z,b=x+z,c=x+y,S);\nexpand((S2/(x*y*z)/2));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"SG,(*()%\"aG\"\"#\"\"\"%\"bGF*,&F(F*F+!\"\"F*F**()F
+F)F*%\"cGF*,&F+F*F0F-F*F**()F0F)F*F(F*,&F0F*F(F-F*F*" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#S2G,(*(),&%\"yG\"\"\"%\"zGF*\"\"#F*,&%\"xGF*F+F
*F*,&F)F*F.!\"\"F*F**()F-F,F*,&F.F*F)F*F*,&F+F*F)F0F*F**()F3F,F*F(F*,&
F.F*F+F0F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.%\"yG!\"\"%\"zGF%%\"
xGF%*&F'F%F&\"\"#\"\"\"*&F$F)F&F%F**&F'F)F$F%F*" }}}{EXCHG {PARA 260 "
" 1 "" {TEXT -1 1 "5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "a:=
x*(x+y)*(x+2*y)*(x+3*y)+y^4;factor(a);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"aG,&**%\"xG\"\"\",&F'F(%\"yGF(F(,&F'F(*&\"\"#F(F*F(F(F(,&F'F
(*&\"\"$F(F*F(F(F(F(*$)F*\"\"%F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
*$),(*$)%\"yG\"\"#\"\"\"F**(\"\"$F*%\"xGF*F(F*F**$)F-F)F*F*F)F*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "7" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 134 "A:=factor(x^3+y^3);factor(A,I);allvalues(evala(AFact
or(A)))[1];\nfactor(A,\{I,sqrt(3)\});J:=RootOf(x^2+x+1):alias(j=J):fac
tor(x^3+y^3,j);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&,&%\"yG\"\"
\"%\"xGF(F(,(*$)F)\"\"#F(F(*&F)F(F'F(!\"\"*$)F'F-F(F(F(" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*&,&%\"yG\"\"\"%\"xGF&F&,(*$)F'\"\"#F&F&*&F'F&F%
F&!\"\"*$)F%F+F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"yG\"\"
\"%\"xGF&F&,&F'F&*&,&#F&\"\"#!\"\"*&^##F&F,F&\"\"$F0F&F&F%F&F&F&,&F'F&
*&,&#F&F,F-*&^##F-F,F&F1F0F&F&F%F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,$**\"\"%!\"\",&%\"yG\"\"\"%\"xGF)F),(*&\"\"#F)F*F)F)F(F&*(^#F&F
)F(F)\"\"$#F)F-F)F),(*&F-F)F*F)F)F(F&*(F(F)F0F1^#F)F)F)F)F)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"*&%\"yGF&%\"jGF&F&F&,(F%F&F(!
\"\"F'F+F&,&F(F&F%F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Que de \+
mal pour obtenir : " }{XPPEDIT 18 0 "x^3+y^3 = (x+y)*(x+j*y)(x+j^2*y)!
;" "6#/,&*$%\"xG\"\"$\"\"\"*$%\"yGF'F(*&,&F&F(F*F(F(-%*factorialG6#-,&
F&F(*&%\"jGF(F*F(F(6#,&F&F(*&F3\"\"#F*F(F(F(" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A:=factor(x^3+y^3+z^3);evala(AFacto
r(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,(*$)%\"xG\"\"$\"\"\"F
**$)%\"yGF)F*F**$)%\"zGF)F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)
%\"xG\"\"$\"\"\"F(*$)%\"yGF'F(F(*$)%\"zGF'F(F(" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "x^3+y^3+z^3;" "6#,(*$%\"xG\"\"$\"
\"\"*$%\"yGF&F'*$%\"zGF&F'" }{TEXT -1 0 "" }{MPLTEXT 1 0 1 " " }{TEXT 
-1 0 "" }{MPLTEXT 1 0 16 "est irr\351ductible" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 61 "A:=factor(x^3+y^3+z^3-3*x*y*z);evala(AFactor(A))
;factor(A,j);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&,(%\"yG\"\"\"
%\"xGF(%\"zGF(F(,.*$)F'\"\"#F(F(*&F)F(F'F(!\"\"*&F'F(F*F(F0*&F)F(F*F(F
0*$)F)F.F(F(*$)F*F.F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,(%\"xG
\"\"\"*&,&#F&\"\"#!\"\"*&#F&F*F&-%'RootOfG6#,&\"\"$F&*$)%#_ZGF*F&F&F&F
+F&%\"yGF&F&*&,&#F&F*F+*&#F&F*F&F.F&F&F&%\"zGF&F&F&,(F%F&*&F8F&F6F&F&*
&F(F&F<F&F&F&,(F6F&F%F&F<F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,(%
\"yG\"\"\"%\"xGF&%\"zGF&F&,*F'F&F%!\"\"*&F%F&%\"jGF&F**&F(F&F,F&F&F&,*
F'F&F+F&F(F*F-F*F&" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "x^3+y^3+z
^3-3*xyz = (x+y+z)*(x+j*y+j^2*z)(x+j^2*y+j*z);" "6#/,**$%\"xG\"\"$\"\"
\"*$%\"yGF'F(*$%\"zGF'F(*&F'F(%$xyzGF(!\"\"*&,(F&F(F*F(F,F(F(-,(F&F(*&
%\"jGF(F*F(F(*&F5\"\"#F,F(F(6#,(F&F(*&F5F7F*F(F(*&F5F(F,F(F(F(" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=(x-y)^3+
(y-z)^3+(z-x)^3;factor(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,(
*$),&%\"xG\"\"\"%\"yG!\"\"\"\"$F*F**$),&F+F*%\"zGF,F-F*F**$),&F1F*F)F,
F-F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"$\"\"\",&%\"yGF&%\"z
G!\"\"F&,&%\"xGF&F)F*F&,&F,F&F(F*F&F*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 73 "ce serait quand m\352me plus joli sous la forme : 3(x - y
)(y - z)(z - x) !!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A:=f
actor(x^2+y^2);evala(AFactor(A));factor(A,I);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"AG,&*$)%\"xG\"\"#\"\"\"F**$)%\"yGF)F*F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"*&-%'RootOfG6#,&*$)%#_ZG\"\"#
F&F&F&F&F&%\"yGF&!\"\"F&,&F%F&F'F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#*&,&%\"xG\"\"\"*&^#!\"\"F&%\"yGF&F&F&,&F%F&*&F*F&^#F&F&F&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A:=factor(x^2+y^2+z^2);evala
(AFactor(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,(*$)%\"xG\"\"#
\"\"\"F**$)%\"yGF)F*F**$)%\"zGF)F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,(*$)%\"xG\"\"#\"\"\"F(*$)%\"yGF'F(F(*$)%\"zGF'F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "factor(x^2+y^2+z^2+2*(x*y+y*z+z*x))
;x^2+y^2+z^2+2*(x*y+y*z+z*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),(
%\"xG\"\"\"%\"yGF'%\"zGF'\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.
*$)%\"xG\"\"#\"\"\"F(*$)%\"yGF'F(F(*$)%\"zGF'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 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A:=x^2+y^2+z^2-2*(x*y+y*z+
z*x);evala(AFactor(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,.*$)
%\"xG\"\"#\"\"\"F**$)%\"yGF)F*F**$)%\"zGF)F*F**(F)F*F(F*F-F*!\"\"*(F)F
*F-F*F0F*F2*(F)F*F(F*F0F*F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$)%
\"xG\"\"#\"\"\"F(*$)%\"yGF'F(F(*$)%\"zGF'F(F(*(F'F(F&F(F+F(!\"\"*(F'F(
F+F(F.F(F0*(F'F(F&F(F.F(F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Eto
nnant tout de m\352me que " }{XPPEDIT 18 0 "x^2+y^2+z^2+2*x*y+2*y*z+2*
z*x;" "6#,.*$%\"xG\"\"#\"\"\"*$%\"yGF&F'*$%\"zGF&F'*(F&F'F%F'F)F'F'*(F
&F'F)F'F+F'F'*(F&F'F+F'F%F'F'" }{TEXT -1 39 "  soit \351videmment fact
orisable, et pas " }{XPPMATH 20 "6#,.*$)%\"xG\"\"#\"\"\"F(*$)%\"yGF'F(
F(*$)%\"zGF'F(F(*(F'F(F&F(F+F(!\"\"*(F'F(F+F(F.F(F0*(F'F(F&F(F.F(F0" }
{XPPEDIT 18 0 "%?!;" "6#-%*factorialG6#%#%?G" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 39 "B:=subs(x=x^2,y=y^2,z=z^2,A);factor(B);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG,.*$)%\"xG\"\"%\"\"\"F**$)%\"yGF
)F*F**$)%\"zGF)F*F**(\"\"#F*)F(F2F*)F-F2F*!\"\"*(F2F*F4F*)F0F2F*F5*(F2
F*F3F*F7F*F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,(%\"yG\"\"\"%\"xGF&
%\"zGF&F&,(F'F&F%F&F(!\"\"F&,(F'F&F%F*F(F*F&,(F%F*F'F&F(F&F&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "beaucoup plus joli sous la forme :
 " }{XPPEDIT 18 0 "(x+y+z)(-x+y+z)(x-y+z)(x+y-z);" "6#---,(%\"xG\"\"\"
%\"yGF(%\"zGF(6#,(F'!\"\"F)F(F*F(6#,(F'F(F)F-F*F(6#,(F'F(F)F(F*F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "A:=factor(x^4+y^4);factor(A,
sqrt(2));factor(A,\{sqrt(2),I\});evala(AFactor(A));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"AG,&*$)%\"xG\"\"%\"\"\"F**$)%\"yGF)F*F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*(F'F)%\"yGF)F(#F)F
(F)*$)F+F(F)F)F),(F%F)F*!\"\"F-F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,$*,\"#;!\"\",(*&\"\"#\"\"\"%\"xGF*F**&%\"yGF*F)#F*F)F**(F-F*F)F.^#F*
F*F*F*,(*&F)F*F+F*F*F,F**(^#F&F*F-F*F)F.F*F*,(*&F)F*F+F*F*F,F&F3F*F*,(
*&F)F*F+F*F*F,F&F/F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,&%\"xG
\"\"\"*&)-%'RootOfG6#,&*$)%#_ZG\"\"%F&F&F&F&\"\"$F&%\"yGF&!\"\"F&,&F%F
&*&F)F&F2F&F3F&,&F%F&F5F&F&,&F%F&F'F&F&" }}}{EXCHG {PARA 0 "" 0 "" 
{XPPEDIT 18 0 "x^4+y^4 = (x+uy)(x-uy)(x+conjugate(u)*y)(x-conjugate(u)
*y);" "6#/,&*$%\"xG\"\"%\"\"\"*$%\"yGF'F(---,&F&F(%#uyGF(6#,&F&F(F/!\"
\"6#,&F&F(*&-%*conjugateG6#%\"uGF(F*F(F(6#,&F&F(*&-F76#F9F(F*F(F2" }
{TEXT -1 7 "  avec " }{XPPEDIT 18 0 "u = exp(I*Pi/4);" "6#/%\"uG-%$exp
G6#*(%\"IG\"\"\"%#PiGF*\"\"%!\"\"" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "combine(sin(x)*sin(Pi/3+x)*s
in(Pi/3-x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"%F&-%$s
inG6#,$*&\"\"$F&%\"xGF&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "9
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(cos(7*t));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&\"#k\"\"\")-%$cosG6#%\"tG\"\"(F&F&
*&\"$7\"F&)F(\"\"&F&!\"\"*&\"#cF&)F(\"\"$F&F&*&F,F&F(F&F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "P:=subs(cos(t)=x,%):factor(P+1);sub
s(x=x/2,1-4*x-4*x^2+8*x^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"
xG\"\"\"F&F&F&),*F&F&*&\"\"%F&F%F&!\"\"*&F*F&)F%\"\"#F&F+*&\"\")F&)F%
\"\"$F&F&F.F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"\"F$*&\"\"#F$%
\"xGF$!\"\"*$)F'F&F$F(*$)F'\"\"$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 31 "2cos pi/7 est donc solution de " }{XPPEDIT 18 0 "x^3-x^2-2*x+1;
" "6#,**$%\"xG\"\"$\"\"\"*$F%\"\"#!\"\"*&F)F'F%F'F*F'F'" }{TEXT -1 6 "
  = 0." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(cos(9*t));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&\"$c#\"\"\")-%$cosG6#%\"tG\"\"*F&F
&*&\"$w&F&)F(\"\"(F&!\"\"*&\"$K%F&)F(\"\"&F&F&*&\"$?\"F&)F(\"\"$F&F1*&
F,F&F(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "P:=subs(cos(t
)=x,%):factor(P+1);subs(x=x/2,8*x^3-6*x-1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*(,&%\"xG\"\"\"F&F&F&),&*&\"\"#F&F%F&F&F&!\"\"F*F&),(*&
\"\")F&)F%\"\"$F&F&*&\"\"'F&F%F&F+F&F+F*F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"xG\"\"$\"\"\"F(*&F'F(F&F(!\"\"F(F*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 33 "2cos pi/9 est donc solution de   " }
{XPPEDIT 18 0 "x^3-3*x-1;" "6#,(*$%\"xG\"\"$\"\"\"*&F&F'F%F'!\"\"F'F)
" }{TEXT -1 5 " =0. " }}}}{MARK "1 0 0" 34 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }