{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "MS Serif" 1 10 128 0 0 1 0 0 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 0 0 0 128 1 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 1 9 0 0 1 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 20 255 0 0 1 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 128 1 2 2 2 2 2 2 1 1 1 1 } 3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE " R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 } {PSTYLE "Maple Output" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 261 1 {CSTYLE "" -1 -1 "Times" 1 36 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Normal" -1 262 1 {CSTYLE "" -1 -1 "Times" 1 18 255 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart; kernelopts( ASSERT=true):" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 35 "Fichier de tes t de \"Pldx (v678.27)\"" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 258 "" 0 "" {TEXT -1 63 "Copyright (c) 1996-2006 Pierre L . Douillet " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 258 "" 0 "" {TEXT -1 11 "Licence GPL" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 283 "libre reproduction pour un u sage universitaire sous reserve d'une copie compl\350te,\navec reprodu ction du programme source dont, en particulier, la pr\351sente mention \n \naucune garantie de fiabilit\351. \nen particulier, toute utilisat ion dans un contexte industriel est vivement d\351conseill\351e\n" }}} {EXCHG {PARA 258 "" 0 "" {TEXT 256 37 "chargement par la commande with (pldx)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(pldx): " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%[ppldx~v68-27~~;~~author~:~~~;~~last~modif~(v68)~:~20/06/2006~G" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "xmani p_sommes" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 6 "Parit\351" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "xmanip_sommes():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "13+Sum(p*x^p, p=1..13); %=(xchimpr+xchpai r-xchnull)(%);\n(ASSERT@value)(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,&\"#8\"\"\"-%$SumG6$*&%\"pGF%)%\"xGF*F%/F*;F%F$F%" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/,&\"#8\"\"\"-%$SumG6$*&%\"pGF&)%\"xGF+F&/F+;F&F%F&,( F%F&-F(6$*&,&F+\"\"#F&!\"\"F&)F-F4F&/F+;F&\"\"(F&-F(6$,$*&F+F&)F-,$F+F 5F&F5/F+;F&\"\"'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "cos(t )+Sum(p*x^p, p=1..infinity): %=(xchimpr+xchpair-xchnull)(%);\n(ASSERT@ simplify@value)(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%$cosG6#%\" tG\"\"\"-%$SumG6$*&%\"pGF))%\"xGF.F)/F.;F)%)infinityGF),(F%F)-F+6$*&,& F.\"\"#F)!\"\"F))F0F8F)F1F)-F+6$,$*&F.F))F0,$F.F9F)F9F1F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "l'op\351rateur de parit\351 s'applique au ssi aux constantes" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "(xchimpr+xchp air-xchnull)(13);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "xmanip _sommes(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(xsplit1G6#-%$SumG6$ )%\"xG%\"kG/F,;\"\"#\"\"),&-F(6$F*/F,;F/\"\"(\"\"\"*$)F+F0F7F7" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(ysplit1G6#-%$SumG6$)%\"xG%\"kG/F,; \"\"#\"\"),&-F(6$F*/F,;F/\"\"*\"\"\"*$)F+F6F7!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%)xsplit_1G6#-%$SumG6$)%\"xG%\"kG/F,;\"\"#\"\"),&-F (6$F*/F,;\"\"$F0\"\"\"*$)F+F/F7F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ -%)ysplit_1G6#-%$SumG6$)%\"xG%\"kG/F,;\"\"#\"\"),&-F(6$F*/F,;\"\"\"F0F 6F+!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(xavanceG6#-%$SumG6$)% \"xG%\"kG/F,;\"\"#\"\"),(-F(6$)F+,&F,\"\"\"F6F6F-F6*$)F+F/F6F6*$)F+\" \"*F6!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(xreculeG6#-%$SumG6$) %\"xG%\"kG/F,;\"\"#\"\"),(-F(6$)F+,&F,\"\"\"F6!\"\"F-F6F+F7*$)F+F0F6F6 " }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 15 "xcauchy, xsplit" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 146 "La proc\351dure xsplit0 \351value les so mmes dont les bornes sont connues.\nCela permet un meilleur fonctionne ment de xsplit1 (etc) dans une double somme" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 82 "La proc\351dure xcauchy g\350re les conflits d'indices \+ ainsi que les bornes de sommation" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Sum(z^n*sin(n*t), n=1..infinity); xcauchy (%,%), xcauchy(%,%, xcombipo@combine);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*&)%\"zG%\"nG\"\"\"-%$sinG6#*&F)F*%\"tGF*F*/F);F*%)infi nityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%$SumG6$-F$6$*(-%$sinG6#*&% \"kG\"\"\"%\"tGF.F.-F*6#*&,&%\"nGF.F-!\"\"F.F/F.F.)%\"zGF4F./F-;F.,&F4 F.F.F5/F4;\"\"#%)infinityG-F$6$-F$6$,&*&-%$cosG6#,&F,!\"#*&F4F.F/F.F.F .F6F.#F.F=*&#F.F=F.*&-FF6#FJF.F6F.F.F5F8F;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 93 "Sum(z^n*sin(n*t), n=1..infinity); xcauchy(%,%); (xs plit0@xsplit_1)(%); (xsplit0@xsplit_1)(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*&)%\"zG%\"nG\"\"\"-%$sinG6#*&F)F*%\"tGF*F*/F) ;F*%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$-F$6$*(-%$s inG6#*&%\"kG\"\"\"%\"tGF.F.-F*6#*&,&%\"nGF.F-!\"\"F.F/F.F.)%\"zGF4F./F -;F.,&F4F.F.F5/F4;\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,&-%$SumG6$-F%6$*(-%$sinG6#*&%\"kG\"\"\"%\"tGF/F/-F+6#*&,&%\"nGF/F.!\" \"F/F0F/F/)%\"zGF5F//F.;F/,&F5F/F/F6/F5;\"\"$%)infinityGF/*&)-F+6#F0\" \"#F/)F8FDF/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%$SumG6$-F%6$*(-% $sinG6#*&%\"kG\"\"\"%\"tGF/F/-F+6#*&,&%\"nGF/F.!\"\"F/F0F/F/)%\"zGF5F/ /F.;F/,&F5F/F/F6/F5;\"\"%%)infinityGF/**\"\"#F/-F+6#F0F/-F+6#,$F0FAF/) F8\"\"$F/F/*&)FBFAF/)F8FAF/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "Sum(z^k*cos(k*t), k=0..infinity),Sum(z^k*cos(k*t), k=1..infinit y); xcauchy(%);\n(xsplit0@xsplit_1)(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%$SumG6$*&)%\"zG%\"kG\"\"\"-%$cosG6#*&F)F*%\"tGF*F*/F);\"\"!%)i nfinityG-F$6$F&/F);F*F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$-F $6$*(-%$cosG6#*&,&%\"nG\"\"\"%\"kG!\"\"F/%\"tGF/F/)%\"zGF.F/-F*6#*&F0F /F2F/F//F0;\"\"!,&F.F/F/F1/F.;F/%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$SumG6$-F%6$*(-%$cosG6#*&,&%\"nG\"\"\"%\"kG!\"\"F0% \"tGF0F0)%\"zGF/F0-F+6#*&F1F0F3F0F0/F1;\"\"!,&F/F0F0F2/F/;\"\"#%)infin ityGF0*&-F+6#F3F0F5F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Int \351grales" }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 39 "id1:=proc(j) op tion inline; j end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$id1Gf*6 #%\"jG6\"6#%'inlineGF(9$F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 959 "xfubini0:= proc(expr)\nlocal quia, quib, su1, su2, vara, su11, varb, expr0, expr_;\noption `Copyright Pierre L. Douillet`;\n if type match(expr,\n su2::anyfunc(su1::anyfunc(expr_::anything, vara::\{equat ion, name\}), varb::equation))\n then\n if type(vara, name) then quia := vara else quia := lhs(vara) end if;\n if type(varb, name) then qu ib := varb else quib := lhs(varb) end if;\n if has(vara, quib) or has (varb, quia) then\n error vara, varb, \"not a genuine rectangle\"\n \+ end if;\n op(0, su1)( procnamee(op(0, su2)(expr_, varb)), vara)\n el if\n typematch(expr, su2::anyfunc(su1::`*`, varb::equation)) and has(s u1, \{Int, Sum\})\n then\n expr0 := select(has, su1, \{Int, Sum\});\n if typematch(expr0, su11::anyfunc(expr_::anything, vara::equation)) \+ then\n subs(su11 = op(0, su11)(expr_*remove(has, su1, \{Int, Sum\}), vara), expr0);\n procname(op(0, su2)(%, varb))\n else expr\n end \+ if\n elif has(expr, \{Int, Sum\}) \n then\n map(procname, expr)\n else expr\n end if\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 102 "xfubini:= subs(procnamee=id1, eval(xfubini0)): \nxxfubini:= subs( procnamee=procname, eval(xfubini0)): \n" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 58 "xvalval : \351valuation de la somme/int\351grale la plus \+ interne" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Agit m^eme s'il n'y a q u'une couche" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Sum(z^n, n=0..infin ity): %= xvalval(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$)%\" zG%\"nG/F);\"\"!%)infinityG,$*&\"\"\"F0,&F(F0F0!\"\"F2F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Sinon, agit sur la couche la plus int\351 rieure" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "tmp:= Sum(y^m*Sum(z^n, n= 0..m), m=0..infinity): %= xvalval(%);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Sum(y^m*Sum(Int(z^n, z=A..1), n=0..m), m=0..infinity): %= xvalva l(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&)%\"yG%\"mG\"\"\" -F%6$)%\"zG%\"nG/F0;\"\"!F*F+/F*;F3%)infinityG-F%6$*&F(F+,&*&)F/,&F*F+ F+F+F+,&F/F+F+!\"\"F?F+*&F+F+F>F?F?F+F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&)%\"yG%\"mG\"\"\"-F%6$-%$IntG6$)%\"zG%\"nG/F2;%\"AGF +/F3;\"\"!F*F+/F*;F9%)infinityG-F%6$*&F(F+-F%6$,$*&,&!\"\"F+)F6,&F3F+F +F+F+F+FGFEFEF7F+F:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "xvalval et Dirac" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "tmp:= Sum(z^n*Dirac(n-4), n=4..infi nity); xvalval(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tmpG-%$SumG6$ *&)%\"zG%\"nG\"\"\"-%&DiracG6#,&F+F,\"\"%!\"\"F,/F+;F1%)infinityG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"zG\"\"%\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Sum(tmp*t^p, p=0..infinity); xvalval(%); \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*&-F$6$*&)%\"zG%\"nG\"\" \"-%&DiracG6#,&F,F-\"\"%!\"\"F-/F,;F2%)infinityGF-)%\"tG%\"pGF-/F9;\" \"!F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*&)%\"zG\"\"%\"\"\") %\"tG%\"pGF*/F-;\"\"!%)infinityG" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "xfubini" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Erreur sur les bornes" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 218 "Sum(y^m*Sum(z^n, n=0..m), m=0..infinity): \+ \ntry %=xfubini(%); detected:= false:\ncatch: detected:= true; print(d etected_error_with_message=lasterror);\nend try:\nif not detected then error \"bad rectangle not detected\"; fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/% " 0 "" {MPLTEXT 1 0 153 "Sum(y^m*Sum( z^n, n=0..infinity), m=0..infinity): %=xfubini(%);\nSum(y^m*Sum(z^n, n =0..5), m=3..12): %= (yjoli@xjoli@xfubini)(%); (ASSERT@expand@value)(% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&)%\"yG%\"mG\"\"\"-F% 6$)%\"zG%\"nG/F0;\"\"!%)infinityGF+/F*F2-F%6$-F%6$*&F.F+F(F+F5F1" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&)%\"yG%\"mG\"\"\"-F%6$)%\" zG%\"nG/F0;\"\"!\"\"&F+/F*;\"\"$\"#7-F%6$*&F.F+-F%6$F(F5F+F1" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Quand l'expression n'est pas du ty pe anything(produit, equation), rien ne se passe " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 145 "vazy(y^m+Sum(z^n, n=0..infinity), m=0..infinity): \+ %=xfubini(%);ASSERT(%):\nvazy(y^m+Sum(z^n, n=0..infinity), 0..infinity ): %=xfubini(%);ASSERT(%):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%vazy G6$,&)%\"yG%\"mG\"\"\"-%$SumG6$)%\"zG%\"nG/F1;\"\"!%)infinityGF+/F*F3F $" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%vazyG6$,&)%\"yG%\"mG\"\"\"-%$ SumG6$)%\"zG%\"nG/F1;\"\"!%)infinityGF+F3F$" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 163 "Quand l'expression est du type anything(produit, equat ion) : rentre tout et rejoue\nEn effet, combine ne rentre pas tous les facteurs sous le signe le plus interne " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "vazy(A*y^m*Sum(z^n, n=0..infinity), m=0..infinity): % =xfubini(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%vazyG6$*(%\"AG\"\" \")%\"yG%\"mGF)-%$SumG6$)%\"zG%\"nG/F2;\"\"!%)infinityGF)/F,F4-F.6$-F% 6$*(F0F)F(F)F*F)F7F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 19 "xvalval et xxfubini" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Probl\350me \340 r\351soudre" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "Sum(x^n*Sum(y^m*cos(n*m*t), m=0..infinity), n=0..infinity):\ntmp: = Int(%, t=-Pi..+Pi);\nxfubini(tmp)= xxfubini(%); " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 294 "xvalval(%); subs(sin(Pi*n*m)=Pi*Dirac(n*m)*(n*m), \+ %);\n(xchimpr+xchpair)(lhs(%))=rhs(%); (xvalval)(%): \n(factor@subs)(t an(Pi*n)=0, tan(1/2*Pi*(2*n-1))=AA, sqrt((y+1)^2*(y-1)^2)=(y+1)*(1-y), \nsqrt((-1+y^2)^2)=(1-y^2), %);\nlimit(%, AA=infinity): subs(csgn((y+ 1)*(-1+conjugate(y)))=-1,%); value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tmpG-%$IntG6$-%$SumG6$*&)%\"xG%\"nG\"\"\"-F)6$*&)%\"yG%\"mGF/ -%$cosG6#*(F.F/F5F/%\"tGF/F//F5;\"\"!%)infinityGF//F.FF:FC" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$-%$IntG6$*()%\"xG%\"nG\"\"\" ,&*&%\"yGF.-%$cosG6#*&F-F.%\"tGF.F.F.F.!\"\"F.,(F0\"\"#F.F7*$)F1F9F.F7 F7/F6;,$%#PiGF7F?/F-;\"\"!%)infinityG-F%6$-F%6$,$*,-%$sinG6#*(F?F.F-F. %\"mGF.F.)F1FNF.F+F.F-F7FNF7F9/FNFAF@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$-%$IntG6$*()%\"xG%\"nG\"\"\",&*&%\"yGF.-%$cosG6#*&F-F.%\" tGF.F.F.F.!\"\"F.,(F0\"\"#F.F7*$)F1F9F.F7F7/F6;,$%#PiGF7F?/F-;\"\"!%)i nfinityG-F%6$-F%6$,$**F?F.-%&DiracG6#*&F-F.%\"mGF.F.)F1FNF.F+F.F9/FNFA F@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%$SumG6$-%$IntG6$*()%\"xG,&% \"nG\"\"#\"\"\"!\"\"F1,&*&%\"yGF1-%$cosG6#*&F.F1%\"tGF1F1F1F1F2F1,(F4F 0F1F2*$)F5F0F1F2F2/F:;,$%#PiGF2FA/F/;F1%)infinityGF1-F&6$-F)6$*()F-,$F /F0F1,&*&F5F1-F76#,$*&F/F1F:F1F0F1F1F1F2F1,(FMF0F1F2F/F/;\"\"!F DF1-F&6$-F&6$,$**FAF1-%&DiracG6#*&F/F1%\"mGF1F1)F5FjnF1)F-F/F1F0/FjnFT FS" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%$SumG6$,$*0)%\"xG%\"nG\"\"# ,&%\"yG\"\"\"F0!\"\"F0,&F/F0F0F0F0,&-%'arctanG6#%#AAGF0-F56#*(F7F0F2F- *&)F2F-F0)F.F-F0#F1F-F0F0F+F1,&F,F-F0F1F1F;F>!\"#/F,;F0%)infinityGF0-F &6$\"\"!/F,;FFFCF0-F&6$,$*&%#PiGF0F*F0F-FG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%$SumG6$,$*2)%\"xG%\"nG\"\"#,&%\"yG\"\"\"F0!\"\"F0, &F/F0F0F0F0%#PiGF0,&F0F0-%%csgnG6#*&)F2F-F0-%*conjugateG6#*$-%%sqrtG6# *&F9F0)F.F-F0F0F0F0F0F+F1,&F,F-F0F1F1FA#F1F-F1/F,;F0%)infinityGF0-F&6$ \"\"!/F,;FJFGF0-F&6$,$*&F3F0F*F0F-FK" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/,$*.%#PiG\"\"\",&%\"yGF'F'F'F',&F)F'F'!\"\"F',&F'F'-%%csgnG6#*&)F( \"\"#F'-%*conjugateG6#*$-%%sqrtG6#*&F1F')F*F2F'F'F'F'F'F:#F+F2-%#lnG6# *&,&F'F'%\"xGF'F',&F'F'FBF+F+F'F<,$*&F&F',&FBF'F'F+F+!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "Sum(cos(n*t)*z^n, n=0..infinity)-1: xsplit_1(%): \nsu mz, sumy:= %, subs(n=m, z=y, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6 $%%sumzG%%sumyG6$-%$SumG6$*&-%$cosG6#*&%\"nG\"\"\"%\"tGF1F1)%\"zGF0F1/ F0;F1%)infinityG-F)6$*&-F-6#*&%\"mGF1F2F1F1)%\"yGF>F1/F>F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "tmp:= 1+sumz+sumy+ (yjoli@xjoli@yjo li@xjoli@combine@xcauchy)(sumz,sumy);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tmpG,,\"\"\"F&-%$SumG6$*&-%$cosG6#*&%\"nGF&%\"tGF&F&)%\"zGF/F&/F /;F&%)infinityGF&-F(6$*&-F,6#*&%\"mGF&F0F&F&)%\"yGF,&F/F&FI!\"\"F&-F,6#,&*&FIF&F0F&!\"#F.F&F& /FI;F&,&F/F&F&FL/F/;FBF5F&F&*&FAF&-F(6$*&F+F&-F(6$*&FHF&FJF&FRF&FUF&F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "(yjoli@xjoli@Int)(tmp, \+ t=-Pi..Pi): \ntmpa0, tmpb0:= selectremove(has,%,\{-2*k*t+n*t, -(-2*k*t +n*t)\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>6$%&tmpa0G%&tmpb0G6$,$-% $IntG6$-%$SumG6$-F-6$*()%\"zG%\"kG\"\"\")%\"yG,&%\"nGF5F4!\"\"F5-%$cos G6#,&*&F4F5%\"tGF5!\"#*&F9F5F@F5F5F5/F4;F5,&F9F5F5F:/F9;\"\"#%)infinit yG/F@;,$%#PiGF:FM#F5FH,*-F*6$F5FJF5-F*6$-F-6$*&-F<6#FBF5)F3F9F5/F9;F5F IFJF5-F*6$-F-6$*&-F<6#*&%\"mGF5F@F5F5)F7F^oF5/F^oFenFJF5*&FNF5-F*6$-F- 6$*&FWF5-F-6$*&F2F5F6F5FCF5FFFJF5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "(xjoli@xfubini)(tmpb0); (xvalval)(%); tmpb:= (value@s ubs)(sin(Pi*n)=0, sin(Pi*m)=0, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,*-%$IntG6$\"\"\"/%\"tG;,$%#PiG!\"\"F,F'-%$SumG6$*&-%!G6#)%\"zG%\"nGF' -F%6$-%$cosG6#*&F7F'F)F'F(F'/F7;F'%)infinityGF'-F/6$*&-F36#)%\"yG%\"mG F'-F%6$-F;6#*&FHF'F)F'F(F'/FHF?F'*&-F36##F'\"\"#F'-F/6$*&-F36#-F/6$*&) F6%\"kGF')FG,&F7F'FgnF-F'/Fgn;F',&F7F'F'F-F'F8F'/F7;FSF@F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%#PiG\"\"#-%$SumG6$,$*(-%!G6#)%\"zG%\"nG\" \"\"-%$sinG6#*&F$F1F0F1F1F0!\"\"F%/F0;F1%)infinityGF1-F'6$,$*(-F,6#)% \"yG%\"mGF1-F36#*&F$F1FBF1F1FBF6F%/FBF8F1*&-F,6##F1F%F1-F'6$,$*(-F,6#, &**)FAF0F1)*&F/F1FAF6F0F1FAF1,&F/F1FAF6F6F1*(FSF1F/F1FVF6F6F1F2F1F0F6F %/F0;F%F9F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tmpbG,$%#PiG\"\"# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 232 "((xchpair+xchimpr)@xxf ubini)(tmpa0); \n(eval@subs)(cos=proc(Z) cos(t*A(normal(-Z/t))) end,%) ; (combine@xvalval)(%); \nsubs( sin(Pi*A(2*k-2*n+1))=0, sin(Pi*A(2*k-2 *n))=(Pi*A(2*k-2*n))*Dirac(2*k-2*n), %);\nxvalval(%); tmpa:= value(%); \n\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$SumG6$-F%6$-%$IntG6$*()% \"zG%\"kG\"\"\")%\"yG,&%\"nG\"\"#F/!\"\"F0-%$cosG6#,&*&F/F0%\"tGF0!\"# *(F5F0F4F0F,(F9F7F1F:F6F:F 1FOF:/F6;F1,&F9F7F7F:/F9;F7FFF1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&- %$SumG6$,$-F%6$,$**%#PiG\"\"\"-%&DiracG6#,&%\"kG!\"#*&\"\"#F-%\"nGF-F- F-)%\"zGF2F-)%\"yG,&F6F5F2!\"\"F-F5/F2;F-,&F6F5F-F<#F-F5/F6;F-%)infini tyGF--F%6$-F%6$\"\"!/F2;F-,&F6F5F5F%%tmpaG,$**%#PiG\"\"\"%\"zGF(%\"y GF(,&!\"\"F(*&F)F(F*F(F(F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "normal((tmpa+tmpb)/Pi); ASSERT(%=(z*y-2)/(z*y-1));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*&,&*&%\"zG\"\"\"%\"yGF'F'\"\"#!\"\"F',&F*F'F%F' F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 8 "xpar frac" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Int(1/mul(x-a, a=1. .3),x=a..b):%= xparfrac(%);\nInt(Int(1/mul(x-a, a=1..3),x=a..f(t)), t= q..e):%= xparfrac(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*& \"\"\"F(*(,&%\"xGF(F(!\"\"F(,&F+F(\"\"#F,F(,&F+F(\"\"$F,F(F,/F+;%\"aG% \"bG-F%6$,(*&F(F(F*F,#F(F.*&F(F(F-F,F,*&F9F(F/F,F(F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$-F%6$*&\"\"\"F**(,&%\"xGF*F*!\"\"F*,&F-F* \"\"#F.F*,&F-F*\"\"$F.F*F./F-;%\"aG-%\"fG6#%\"tG/F9;%\"qG%\"eG-F%6$-F% 6$,(*&F*F*F,F.#F*F0*&F*F*F/F.F.*&FDF*F1F.F*F3F:" }}}}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 " " 0 "" {TEXT -1 40 "Deux listes d'objets (pour quoi faire ?)" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "liste1:= [Diag, Entries, Ev alm, Matrice, Tr, Xpand, arrdim, displayf, evalmm, id, lires, matrice, xcombipo, xintparts, xlap, xmarch, xoption, xprint, xunassign, xwith, yjoli];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'liste1G77%%DiagG%(Entri esG%&EvalmG%(MatriceG%#TrG%&XpandG%'arrdimG%)displayfG%'evalmmG%#idG%& liresG%(matriceG%)xcombipoG%*xintpartsG%%xlapG%'xmarchG%(xoptionG%'xpr intG%*xunassignG%&xwithG%&yjoliG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 265 "liste2:= [Xtens, `convert/D2`, isdiag, sinsin, xHosp ital, xclone, xcol, xcol3, xcollect, xcolor, xcs, xdchvar, xeig, xeigg , xfenetre, xfubini, xjoli, xmanip_sommes, xmk_piv, xplif, xpurge, xpu t, xreg_falsi, xres_ini, xreverse, xtens, xtree, xtrig, zmanip_product s];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'liste2G7?%&XtensG%+convert/D 2G%'isdiagG%'sinsinG%*xHospitalG%'xcloneG%%xcolG%&xcol3G%)xcollectG%'x colorG%$xcsG%(xdchvarG%%xeigG%&xeiggG%)xfenetreG%(xfubiniG%&xjoliG%.xm anip_sommesG%(xmk_pivG%&xplifG%'xpurgeG%%xputG%+xreg_falsiG%)xres_iniG %)xreverseG%&xtensG%&xtreeG%&xtrigG%0zmanip_productsG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 6 "Linalg" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "macro(L inalg=LinearAlgebra);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'LinalgG" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Diag (par opposition, " } {XPPEDIT 18 0 "DiagonalMatrix;" "6#%/DiagonalMatrixG" }{TEXT -1 19 " u tilise une liste)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "(''Diag''=Dia g)(1,2,x+1,Matrix([[a,b],[c,d]])); \n(ASSERT@Linalg[Equal]) (rhs(%), \+ Matrix([[1, 0, 0,0,0], [0, 2, 0,0,0], [0, 0, x+1,0,0], [0, 0, 0,a,b], \+ [0, 0, 0,c,d]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiagG6&\"\"\" \"\"#,&F'F'%\"xGF'-%'RTABLEG6$\")!y%G9-%'MATRIXG6#7$7$%\"aG%\"bG7$%\"c G%\"dG-F,6$\"))3\"G7-F06#7'7'F'\"\"!F@F@F@7'F@F(F@F@F@7'F@F@F)F@F@7'F@ F@F@F4F57'F@F@F@F7F8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Entries ( n'existait pas)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "tmp:= [sin(x),a ,b,12+1,tan,Pi,-12, [1,2]]: Matrix(matrix(2,4,tmp)): (''Entries''=Entr ies)(%);\nASSERT(convert(tmp,set) = \{rhs(%)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(EntriesG6#-%'RTABLEG6$\")?WC9-%'MATRIXG6#7$7&-%$sin G6#%\"xG%\"aG%\"bG\"#87&%$tanG%#PiG!#77$\"\"\"\"\"#6*F0F9F:F8F4F;F6F5 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Evalm. Gestion des vecteurs ? " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "x*< | >; Evalm(%); wh attype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\"-%'RTABLEG6 $\")))p#Q\"-%'MATRIXG6#7$7$%\"aG%\"bG7$%\"cG%\"dGF%" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%'RTABLEG6$\")'*eI9-%'MATRIXG6#7$7$*&%\"xG\"\"\"%\"a GF.*&F-F.%\"bGF.7$*&F-F.%\"cGF.*&F-F.%\"dGF." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'MatrixG" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 " " 0 "" {TEXT -1 5 "xplif" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 " exo:= Int(1/(z^2-2*z*x+1)/sqrt(1-x^2), x=-1..1); \nxplif(%, [z, RealRa nge(0,1)]); x, z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$exoG-%$IntG6$* &\"\"\"F)*&,(*$)%\"zG\"\"#F)F)*(F/F)F.F)%\"xGF)!\"\"F)F)F)-%%sqrtG6#,& F)F)*$)F1F/F)F2F)F2/F1;F2F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%#P iG\"\"\",&*$)%\"zG\"\"#F&F&F&!\"\"F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "value(s ubs(z=1/2, exo));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"%\"\" $" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 14284780 12281088 14244420 13826988 14305896 }{RTABLE M7R0 I5RTABLE_SAVE/14284780X,%)anythingG6"6"[gl!"%!!!#%"#"#%"aG%"cG%"bG%"dGF& } {RTABLE M7R0 I5RTABLE_SAVE/12281088X,%)anythingG6"6"[gl!"%!!!#:"&"&"""""!F(F(F(F(""#F(F(F(F( F(,&F'F'%"xGF'F(F(F(F(F(%"aG%"cGF(F(F(%"bG%"dGF& } {RTABLE M7R0 I5RTABLE_SAVE/14244420X,%)anythingG6"6"[gl!"%!!!#)"#"%-%$sinG6#%"xG%$tanG%"aG%# PiG%"bG!#7"#87$"""""#F& } {RTABLE M7R0 I5RTABLE_SAVE/13826988X,%)anythingG6"6"[gl!"%!!!#%"#"#%"aG%"cG%"bG%"dGF& } {RTABLE M7R0 I5RTABLE_SAVE/14305896X,%)anythingG6"6"[gl!"%!!!#%"#"#*&%"xG"""%"aGF)*&F(F)%"cG F)*&F(F)%"bGF)*&F(F)%"dGF)F& }