{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "He lp Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 "" 1 24 0 0 104 0 1 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Ou tput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "B ullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 17 "TP PASCAL 922 n\2601" } }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Exemples de tests" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "P:=X^4-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG,&*$%\"XG\"\"%\"\"\"!\"\"F)" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 37 "Entr\351e de l'expression du polyn\364me P." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Q:=X-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG,&%\"XG\"\"\"!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "R:=3*X^7+9*X^5-18*X^3+81*X^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG,**$%\"XG\"\"(\"\"$*$F'\"\"&\"\"**$F'F)!#=*$F'\" \"#\"#\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "S:=X^5+3*X^3-6 *X+27;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG,**$%\"XG\"\"&\"\"\"*$ F'\"\"$F+F'!\"'\"#FF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ex pand(P^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"XG\"#;\"\"\"*$F% \"#7!\"%*$F%\"\")\"\"'*$F%\"\"%F*F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "expand permet de d\351velopper une expression, ici P puis sance 4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "expand(Q^10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,8*$%\"XG\"#5\"\"\"*$F%\"\"*!#5*$F% \"\")\"#X*$F%\"\"(!$?\"*$F%\"\"'\"$5#*$F%\"\"&!$_#*$F%\"\"%F3*$F%\"\"$ F0*$F%\"\"#F-F%F*F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ex pand(R^3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,>*$%\"XG\"\"(!'%Ha$*$F% \"\"'\"'T9`*$F%\"#;\"%(=#*$F%\"#7!%hl*$F%\"#5!&K(y*$F%\"\")\"&K(y*$F% \"\"*\"':8<*$F%\"#9\"&AJ\"*$F%\"#6\"&(zn*$F%\"#@\"#F*$F%\"#>\"$V#*$F% \"# " 0 "" {MPLTEXT 1 0 12 "expand(P*Q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"XG\"\"& \"\"\"*$F%\"\"%!\"\"F%F*F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "expand(R*Q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*$%\"XG\"\")\" \"$*$F%\"\"(!\"$*$F%\"\"'\"\"**$F%\"\"&!\"**$F%\"\"%!#=*$F%F'\"#***$F% \"\"#!#\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand(subs(X =Q,P)); # PoQ" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"XG\"\"%\"\"\"* $F%\"\"$!\"%*$F%\"\"#\"\"'F%F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "subs permet de \"substituer\" \340 l'ind\351termin\351e X de P le pol yn\364me Q, d'o\371 la valeur de PoQ ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand(subs(X=R,Q)); # QoR" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"XG\"\"(\"\"$*$F%\"\"&\"\"**$F%F'!#=*$F%\"\"#\"# \")!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand(su bs(X=R,P)); # PoR" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,J*$%\"XG\"#;\"(W K@#*$F%\"#?!&J%G*$F%\"#7!)3'\\E\"*$F%\"#5\")%eaF\"*$F%\"\")\")@n/V*$F% \"\"*!)_PEQ*$F%\"#9!(MGF\"*$F%\"#B\"%[()*$F%\"#=\"'#y1%*$F%\"#G\"#\")* $F%\"#E\"$s**$F%\"#C\"%IC*$F%\"#A!%[()*$F%\"#6\")3BC<*$F%\"#@\"&K(y*$F %\"#>FQ*$F%\"# " 0 "" {MPLTEXT 1 0 14 "simplify(R/S);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,$*$%\"XG\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 121 "simplify permet de \"simplifier\" l'expression R/S. Le r \351sultat rendu sinon serait une fraction rationnelle non simplifi \351e." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(P/Q);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"XG\"\"$\"\"\"*$F%\"\"#F'F%F'F' F'" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 23 "Polyn\364mes cyclotomique s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(numtheory);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7fn%\"BG%\"FG%&GIgcdG%\"JG%\"LG%\"MG%* bernoulliG%)bigomegaG%&cfracG%)cfracpolG%+cyclotomicG%)divisorsG%&eule rG%)factorEQG%*factorsetG%'fermatG%(ifactorG%)ifactorsG%)imagunitG%&in dexG%)invcfracG%'invphiG%'isolveG%(isprimeG%*issqrfreeG%)ithprimeG%'ja cobiG%*kroneckerG%'lambdaG%)legendreG%)mcombineG%)mersenneG%*minkowski G%(mipolysG%%mlogG%'mobiusG%&mrootG%&msqrtG%)nearestpG%*nextprimeG%*nt hconverG%)nthdenomG%)nthnumerG%'nthpowG%&orderG%)pdexpandG%$phiG%*ppri mrootG%*prevprimeG%)primrootG%(quadresG%+rootsunityG%*safeprimeG%&sigm aG%*sq2factorG%(sum2sqrG%$tauG%%thueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 218 "with permet de charger une biblioth\350que de fonctions. Ici les polyn\364mes cyclotomiques, qui interviennent en th\351orie d es nombres, peuvent \352tre obtenus directement en appelant la fonctio n cyclotomic du package numtheory." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "?cyclotomic" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "? permet d'obtenir de l'aide sur une fonction. Ici on obtient :" }} {PARA 0 "" 0 "" {TEXT 26 10 "Function: " }{TEXT -1 55 "numtheory[cyclo tomic] - calculate cyclotomic polynomial" }}{PARA 0 "" 0 "usage" {TEXT 26 17 "Calling Sequence:" }{TEXT -1 20 "\n cyclotomic(n, t)" } }{PARA 0 "" 0 "" {TEXT 26 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT 23 4 "n - " }{TEXT -1 23 "non-negative integer\n " }{TEXT 23 4 "t - " } {TEXT -1 8 "variable" }}{PARA 0 "" 0 "synopsis" {TEXT 26 12 "Descripti on:" }}{PARA 15 "" 0 "" {TEXT -1 78 "The function cyclotomic(n, t) wil l return the nth cyclotomic polynomial in t. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "cyclotomic(0,X);cyclotomic(1,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"XG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"XG\" \"\"!\"\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "cyclotomic(2 ,X);cyclotomic(3,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"XG\"\"\"F %F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"XG\"\"#\"\"\"F%F'F'F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "cyclotomic(4,X);cyclotomic (5,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"XG\"\"#\"\"\"F'F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"XG\"\"%\"\"\"*$F%\"\"$F'*$F%\" \"#F'F%F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "cyclotomic (10,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"XG\"\"%\"\"\"*$F%\" \"$!\"\"*$F%\"\"#F'F%F*F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "\{coeffs(\")\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "cyclotomic(13,X); #13 est premier dc le resultat est tres simple" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,<*$%\"XG\"#7\"\"\"*$F%\"#6F'*$F%\"#5F'*$F%\"\"*F'*$F%\"\")F'*$F %\"\"(F'*$F%\"\"'F'*$F%\"\"&F'*$F%\"\"%F'*$F%\"\"$F'*$F%\"\"#F'F%F'F'F '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "\{coeffs(\")\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Pour obtenir l'ensemble des coefficients du polyn\364me p r\351c\351dent." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cyclotom ic(104,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,<*$%\"XG\"#[\"\"\"*$F% \"#W!\"\"*$F%\"#SF'*$F%\"#OF**$F%\"#KF'*$F%\"#GF**$F%\"#CF'*$F%\"#?F** $F%\"#;F'*$F%\"#7F**$F%\"\")F'*$F%\"\"%F*F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cyclotomic(105,X);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,^o\"\"\"F$%\"XGF$*$F%\"\"(!\"#*$F%\"\"&!\"\"*$F%\"\"#F$*$F%\"#7 F$*$F%\"\"*F+*$F%\"\")F+*$F%\"\"'F+*$F%\"#[F$*$F%\"#SF+*$F%\"#OF$*$F% \"#KF$*$F%\"#GF+*$F%\"#CF+*$F%\"#?F+*$F%\"#;F$*$F%\"#9F$*$F%\"#8F$*$F% \"#NF$*$F%\"#EF+*$F%\"#AF+*$F%\"#YF$*$F%\"#ZF$*$F%\"#JF$*$F%\"# " 0 "" {MPLTEXT 1 0 40 "seq(\{coeffs(cyclotomic(k,X ))\},k=0..105);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6fq<#\"\"\"<$!\"\"F$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%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%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%F#F%<%F&F $!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "seq permet d'obtenir une liste des coefficients des polyn\364mes cyclotomiques pour n<=105." } }}}}{MARK "2 16 0 0" 88 }{VIEWOPTS 1 1 0 1 1 1803 }