{VERSION 7 1 "Linux" "7.1" } {USTYLETAB {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1 " -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 12 40 120 40 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "MS Serif" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS Serif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Orde red List 4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Wa rning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "He ading 1" -1 3 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 2" -1 204 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 } {CSTYLE "Equation Label" -1 200 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Page Number" -1 33 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Serif" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{PSTYLE "" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 66 "Sz\303\241m\303\255t\303 \263g\303\251pes sz\303\241melm\303\251let" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 18 "J\303\241rai Antal" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 68 "Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\2 41lnak" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 59 "1. A pr\303\255mek el oszl\303\241sa, szit\303\241l\303\241s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 63 "2. Egyszer\305\261 faktoriz\303\241l\303\241si m\303\263 dszerek" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 64 "3. Egyszer\305\261 pr\303\255mtesztel\303\251si m\303\26 3dszerek" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 18 "4. Lucas-sorozatok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 23 "5. Alkalmaz\30 3\241sok " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 36 "6. Sz\303\241mok \303\251s polinomok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 45 "7. Gyors Four ier-transzform\303\241ci\303\263" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 38 "8. Elliptikus f\303\274ggv\303\2 51nyek" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 59 "9. Sz\303\241mol\303\241s elliptikus g\303\266rb\303\251 ken" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 65 "10. Faktoriz\303\241l\303\241s elliptikus g\303\274rb\303\251 kkel" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 55 "11. Pr\303\255mteszt elliptikus g\303\266rb\303\251kkel" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 37 "12. Polinomfaktoriz\303\241l \303\241s" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "restart; with(PolynomialTools);" }}{PARA 11 "" 1 "" {XPPMATH 20 "73I0CoefficientListG6\"I2CoefficientVectorGF$I-GcdFreeBas isGF$I?GreatestFactorialFactorizationGF$I(HurwitzGF$I1IsSelfReciprocal GF$I2MinimalPolynomialGF$I0PDEToPolynomialGF$I0PolynomialToPDEGF$I0Shi ftEquivalentGF$I7ShiftlessDecompositionGF$I(ShortenGF$I(ShorterGF$I%So rtGF$I&SplitGF$I'SplitsGF$I*TranslateGF$" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "12.1. " }{TEXT 206 57 "Polinomfaktoriz\303\241l\303\241s \+ modulo egy pr\303\255m." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 17 "12.2 . Visszavezet" }{TEXT 206 8 "\303\251" }{TEXT 206 3 "s n" }{TEXT 206 8 "\303\251" }{TEXT 206 19 "gyzetmentes esetre." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "SquareFree: =proc(a,x,p) local i,out,b,c,y,z,w;\n" }{MPLTEXT 1 0 36 "i:=1; out:=[] ; b:=diff(a,x) mod p;\n" }{MPLTEXT 1 0 67 "if b=0 then error \"zero de rivative; substitute x^p with p\"; fi;\n" }{MPLTEXT 1 0 41 "c:=Gcd(a,b ) mod p; w:=Quo(a,c,x) mod p;\n" }{MPLTEXT 1 0 23 "while degree(c)<>0 \+ do\n" }{MPLTEXT 1 0 22 " y:=Gcd(w,c) mod p;\n" }{MPLTEXT 1 0 24 " z: =Quo(w,y,x) mod p;\n" }{MPLTEXT 1 0 21 " out:=[op(out),z];\n" } {MPLTEXT 1 0 11 " i:=i+1;\n" }{MPLTEXT 1 0 30 " w:=y; c:=Quo(c,y,x) \+ mod p;\n" }{MPLTEXT 1 0 28 "od; out:=[c,op(out),w]; end;" }}{PARA 11 " " 1 "" {XPPMATH 20 "f*6%I\"aG6\"I\"xGF%I\"pGF%6)I\"iGF%I$outGF%I\"bGF% I\"cGF%I\"yGF%I\"zGF%I\"wGF%F%F%C*>F)\"\"\">F*7\">F+-I$modGF%6$-I%diff G%*protectedG6$F$F&F'@$/F+\"\"!YQGzero~derivative;~substitute~x^p~with ~pF%>F,-F76$-I$GcdGF%6$F$F+F'>F/-F76$-I$QuoGF%6%F$F,F&F'?(F%F2F2F%0-I' degreeGF;6#F,F?C(>F--F76$-FF6$F/F,F'>F.-F76$-FL6%F/F-F&F'>F*7$-I#opGF; 6#F*F.>F),&F)F2F2F2>F/F->F,-F76$-FL6%F,F-F&F'>F*7%F,FjnF/F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "`mod`:=mods; x:='x'; a:=x^15 -1; debug(SquareFree); SquareFree(a,x,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%modsG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"x G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"#:\"\"\"F(F(!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "I+SquareFreeG6\"" }}{PARA 9 "" 1 "" {TEXT 207 43 "\{--> enter SquareFree, args = x^15-1, x, 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 9 "" 1 "" {TEXT 207 85 "< -- ERROR in SquareFree (now at top level) = zero derivative; substitut e x^p with p\}" }}{PARA 8 "" 1 "" {TEXT 208 61 "Error, (in SquareFree) zero derivative; substitute x^p with p" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "SquareFree(a,x,11);" }}{PARA 9 "" 1 "" {TEXT 207 44 " \{--> enter SquareFree, args = x^15-1, x, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&\"\"%\"\"\")I\"xG6\"\"#9F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\" \"#:\"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",&*$)I\"x G6\"\"#:F#F#F#!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 54 "<-- exit SquareFr ee (now at top level) = [1, x^15-1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",&*$)I\"xG6\"\"#:F#F#F#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "SquareFree(x^3+3*x^2+3*x+1,x,11);" }}{PARA 9 "" 1 "" {TEXT 207 53 "\{--> enter SquareFree, args = x^3+3*x^2+3*x+1, x, 11" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"$\"\"\")I\"xG6\"\"\"#F%F %*&\"\"&F%F'F%!\"\"F$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\" \"\"#\"\"\"F(*&F'F(F%F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG 6\"\"\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"F%F%" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I \"xG6\"\"\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"F%F %" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"\"F#F#,&I \"xG6\"F#F#F#" }}{PARA 9 "" 1 "" {TEXT 207 57 "<-- exit SquareFree (no w at top level) = [1, 1, 1, x+1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7& \"\"\"F#F#,&I\"xG6\"F#F#F#" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 7 "1 2.3. V" }{TEXT 206 8 "\303\251" }{TEXT 206 11 "ges testek." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "n:= 8; RijndaelPoly:=Nextprime(Z^n,Z) mod 2; alpha:=Z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"ZG6\"\"\" )\"\"\"F(*$)F%\"\"%F(F(*$)F%\"\"$F(F(F%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"ZG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "x: =234; xx:=convert(x,base,2); xxx:=add(xx[i]*Z^(i-1),i=1..nops(xx));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$M#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*\"\"!\"\"\"F#F$F#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,I\"ZG6 \"\"\"\"*$)F#\"\"$F%F%*$)F#\"\"&F%F%*$)F#\"\"'F%F%*$)F#\"\"(F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "y:=111; yy:=convert(y,base,2 ); yyy:=add(yy[i]*Z^(i-1),i=1..nops(yy));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7)\"\"\"F#F#F#\" \"!F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"\"\"F#I\"ZG6\"F#*$)F$\"\" #F#F#*$)F$\"\"$F#F#*$)F$\"\"&F#F#*$)F$\"\"'F#F#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 68 "zzz:=modpol(xxx+yyy,RijndaelPoly,Z,2); zz:=Coe fficientList(zzz,Z);\n" }{MPLTEXT 1 0 36 "z:=add(zz[i]*2^(i-1),i=1..no ps(zz));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"ZG6\"\"\"(\"\"\"F(F( F(*$)F%\"\"#F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*\"\"\"\"\"!F#F$F$F $F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$L\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "zzz:=modpol(xxx*yyy,RijndaelPoly,Z,2); zz:=Coeff icientList(zzz,Z);\n" }{MPLTEXT 1 0 38 "z:=add(zz[i]*2^(i-1),i=1..nops (zz));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*$)I\"ZG6\"\"\"'\"\"\"F(*$ )F%\"\"&F(F(*$)F%\"\"%F(F(*$)F%\"\"$F(F(*$)F%\"\"#F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7)\"\"\"\"\"!F#F#F#F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$D\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "zzz: =modpol(1/xxx,RijndaelPoly,Z,2); zz:=CoefficientList(zzz,Z);\n" } {MPLTEXT 1 0 36 "z:=add(zz[i]*2^(i-1),i=1..nops(zz));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*$)I\"ZG6\"\"\"(\"\"\"F(*$)F%\"\"'F(F(*$)F%\"\"%F(F (*$)F%\"\"#F(F(F%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*\"\"\"F#F# \"\"!F#F$F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$:#" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "12.4. Fak" }{TEXT 206 33 "toriz\303\241l \303\241s k\303\274" }{TEXT 206 1 "l" }{TEXT 206 8 "\303\266" }{TEXT 206 2 "nb" }{TEXT 206 8 "\303\266" }{TEXT 206 1 "z" }{TEXT 206 8 "\305 \221" }{TEXT 206 4 " fok" }{TEXT 206 8 "\303\272" }{TEXT 206 12 " fakt orokra." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "PartialFactorDD:=proc(a,x,p) local aa,L,aaa,w,i;\n" } {MPLTEXT 1 0 27 "i:=1; w:=x; aa:=a; L:=[];\n" }{MPLTEXT 1 0 26 "while \+ i<=degree(aa)/2 do\n" }{MPLTEXT 1 0 27 " w:=Rem(w^p,aa,x) mod p;\n" } {MPLTEXT 1 0 27 " aaa:=Gcd(aa,w-x) mod p;\n" }{MPLTEXT 1 0 19 " L:=[ op(L),aaa];\n" }{MPLTEXT 1 0 18 " if aaa<>1 then\n" }{MPLTEXT 1 0 30 " aa:=Quo(aa,aaa,x) mod p:\n" }{MPLTEXT 1 0 27 " w:=Rem(w,aa,x) \+ mod p;\n" }{MPLTEXT 1 0 15 " fi; i:=i+1;\n" }{MPLTEXT 1 0 23 "od; L:= [op(L),aa]; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"aG6\"I\"xGF%I \"pGF%6'I#aaGF%I\"LGF%I$aaaGF%I\"wGF%I\"iGF%F%F%C(>F-\"\"\">F,F&>F)F$> F*7\"?(F%F0F0F%1F-,$*&#F0\"\"#F0-I'degreeG%*protectedG6#F)F0F0C'>F,-I$ modGF%6$-I$RemG6$F=I(_syslibGF%6%)F,F'F)F&F'>F+-FB6$-I$GcdGFF6$F),&F,F 0F&!\"\"F'>F*7$-I#opGF=6#F*F+@$0F+F0C$>F)-FB6$-I$QuoGFF6%F)F+F&F'>F,-F B6$-FE6%F,F)F&F'>F-,&F-F0F0F0>F*7$FTF)F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "`mod`:=mods; x:='x'; a:=x^15-1; debug(PartialFact orDD); PartialFactorDD(a,x,11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%mod sG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"xG6\"" }}{PARA 11 " " 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"#:\"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I0PartialFactorDDG6\"" }}{PARA 9 "" 1 "" {TEXT 207 49 "\{--> enter PartialFactorDD, args = x^15-1, x, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"xG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"#:\"\"\"F(F(!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$) I\"xG6\"\"#6\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"& \"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#,&*$)I\"xG6\"\"\"& \"\"\"F)F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"#5\"\" \"F(*$)F%\"\"&F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\" \"\"'\"\"\"!\"\"F%F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"xG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$ )I\"xG6\"\"#5\"\"\"F(*$)F%\"\"&F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*$)I\"xG6\"\"\"&\"\"\"F)F)!\"\",(*$)F&\"#5F)F)F$F)F)F)" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*$)I\"xG6\"\"\"&\"\"\"F)F)!\"\",(*$)F&\"#5F)F)F$F)F)F )F)" }}{PARA 9 "" 1 "" {TEXT 207 70 "<-- exit PartialFactorDD (now at \+ top level) = [x^5-1, x^10+x^5+1, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*$)I\"xG6\"\"\"&\"\"\"F)F)!\"\",(*$)F&\"#5F)F)F$F)F)F)F)" }}}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "12.5. Has" }{TEXT 206 8 "\303\255 " }{TEXT 206 1 "t" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Pa rtialFactorSplit:=proc(a,x,d,p) local t,i;\n" }{MPLTEXT 1 0 69 "t:=ran d(); t:=convert(t,base,p); t:=add(t[i]*x^(i-1),i=1..nops(t));\n" } {MPLTEXT 1 0 55 "t:=modpol(t,a,x,p); t:=modpol(t^((p^d-1)/2)-1,a,x,p); \n" }{MPLTEXT 1 0 45 "t:=Gcd(t,a) mod p; [t,Quo(a,t,x) mod p]; end;" } }{PARA 11 "" 1 "" {XPPMATH 20 "f*6&I\"aG6\"I\"xGF%I\"dGF%I\"pGF%6$I\"t GF%I\"iGF%F%F%C)>F*-I%randGF%F%>F*-I(convertG%*protectedG6%F*I%baseGF% F(>F*-I$addGF36$*&&F*6#F+\"\"\")F&,&F+F=F=!\"\"F=/F+;F=-I%nopsGF36#F*> F*-I'modpolG6$F3I(_syslibGF%6&F*F$F&F(>F*-FH6&,&)F*,&*&#F=\"\"#F=)F(F' F=F=FSF@F=F=F@F$F&F(>F*-I$modGF%6$-I$GcdGFI6$F*F$F(7$F*-FX6$-I$QuoGFI6 %F$F*F&F(F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "debug(Pa rtialFactorSplit); PartialFactorSplit(x^5-1,x,1,11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I3PartialFactorSplitG6\"" }}{PARA 9 "" 1 "" {TEXT 207 54 "\{--> enter PartialFactorSplit, args = x^5-1, x, 1, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-M0')=dR" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\" \")\"\"!\"#5\"\"'F#F%F&F$\"\"*\"\"#\"\"%\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",6\"\")\"\"\"*&\"#5F$)I\"xG6\"\"\"#F$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(F8F$F$*&F1F$)F(F&F$F$*$)F(\"#6F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"#\"\"\"!\"\"*&\"\"%F()F%\"\"$F(F(*$)F%F+ F(F)*&F+F(F%F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&\"\"&\"\"\")I\"x G6\"\"\"%F%!\"\"*$)F'\"\"$F%F%*&\"\"#F%)F'F/F%F**&F)F%F'F%F*F%F*" }} {PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"\"#\"\"\"F(*&\"\"&F(F%F(! \"\"\"\"%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"#\"\" \"F)*&\"\"&F)F&F)!\"\"\"\"%F),**$)F&\"\"$F)F)*&F+F)F%F)F)F&F,F1F," }} {PARA 9 "" 1 "" {TEXT 207 77 "<-- exit PartialFactorSplit (now at top \+ level) = [x^2-5*x+4, x^3+5*x^2-x-3]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"#\"\"\"F)*&\"\"&F)F&F)!\"\"\"\"%F),**$)F&\"\"$F)F) *&F+F)F%F)F)F&F,F1F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "exp and((x^2+2*x-2)*(x^3-2*x^2-5*x-5)) mod 11;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"&\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "PartialFactorSplit(x^2+2*x-2,x,1,11);\n" } {MPLTEXT 1 0 43 "PartialFactorSplit(x^3-2*x^2-5*x-5,x,1,11);" }}{PARA 9 "" 1 "" {TEXT 207 58 "\{--> enter PartialFactorSplit, args = x^2+2*x -2, x, 1, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-:k\")RJ>" }}{PARA 11 "" 1 "" {XPPMATH 20 "7-\"\"(\"\"*F#\"\"$F%\"\"%\"\"\"\"\"!\"#5F&F#" }} {PARA 11 "" 1 "" {XPPMATH 20 ",6\"\"(\"\"\"*&\"\"*F$I\"xG6\"F$F$*&F#F$ )F'\"\"#F$F$*&\"\"$F$)F'F-F$F$*&F-F$)F'\"\"%F$F$*&F1F$)F'\"\"&F$F$*$)F '\"\"'F$F$*&\"#5F$)F'\"\")F$F$*&F1F$)F'F&F$F$*&F#F$)F'F9F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"#!\"\"*&\"\"&\"\"\"I\"xG6\"F'F$" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"!\"\"\"\"$\"\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",( *$)I\"xG6\"\"\"#F#F#*&F)F#F'F#F#F)!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 65 "<-- exit PartialFactorSplit (now at top level) = [1, x^2+2*x-2]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",(*$)I\"xG6\"\"\"#F#F#*&F)F#F 'F#F#F)!\"\"" }}{PARA 9 "" 1 "" {TEXT 207 64 "\{--> enter PartialFacto rSplit, args = x^3-2*x^2-5*x-5, x, 1, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\",l/ " 0 "" {MPLTEXT 1 0 61 "expand((x- 4)*(x-5)) mod 11; expand((x+2)*(x^2-4*x+3)) mod 11;" }}{PARA 11 "" 1 " " {XPPMATH 20 ",(*$)I\"xG6\"\"\"#\"\"\"F(*&F'F(F%F(F(F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&\"\"#F()F%F*F(!\" \"*&\"\"&F(F%F(F,F.F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Pa rtialFactorSplit(x^2-4*x+3,x,1,11);" }}{PARA 9 "" 1 "" {TEXT 207 58 " \{--> enter PartialFactorSplit, args = x^2-4*x+3, x, 1, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-fW[(=+)" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\" \"!\"\"$\"\"'\"\"*\"\"(\"#5\"\"#F(F$F&\"\")F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",8*&\"\"$\"\"\"I\"xG6\"F%F%*&\"\"'F%)F&\"\"#F%F%*&\"\"*F% )F&F$F%F%*&\"\"(F%)F&\"\"%F%F%*&\"#5F%)F&\"\"&F%F%*&F+F%)F&F)F%F%*&F4F %)F&F0F%F%*&F$F%)F&\"\")F%F%*&F-F%)F&F-F%F%*&F=F%)F&F4F%F%*&F+F%)F&\"# 6F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I\"xG6\"F%!\"\" \"\"&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"!\"\"\"\"\"F&" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"xG6\"\"\"\"F&!\"\",&F$F&\"\"$F'" }}{PARA 9 "" 1 "" {TEXT 207 61 "<-- exit PartialFactorSplit (now at top level) = [x -1, x-3]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"xG6\"\"\"\"F&!\"\", &F$F&\"\"$F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "PartialFact orSplit(x^2-4*x+3,x,1,11);" }}{PARA 9 "" 1 "" {TEXT 207 58 "\{--> ente r PartialFactorSplit, args = x^2-4*x+3, x, 1, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-po0_vU" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"$F#\"\"& \"\")\"\"*\"#5\"\"\"\"\"'F#F$F$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",: \"\"$\"\"\"*&F#F$I\"xG6\"F$F$*&\"\"&F$)F&\"\"#F$F$*&\"\")F$)F&F#F$F$*& \"\"*F$)F&\"\"%F$F$*&\"#5F$)F&F)F$F$*$)F&\"\"'F$F$*&F8F$)F&\"\"(F$F$*& F#F$)F&F-F$F$*&F)F$)F&F0F$F$*&F)F$)F&F4F$F$*$)F&\"#6F$F$" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&\"\"%\"\"\"I\"xG6\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"\"# \"\"\"F(*&\"\"%F(F%F(!\"\"\"\"$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$, (*$)I\"xG6\"\"\"#\"\"\"F)*&\"\"%F)F&F)!\"\"\"\"$F)F)" }}{PARA 9 "" 1 " " {TEXT 207 65 "<-- exit PartialFactorSplit (now at top level) = [x^2- 4*x+3, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"#\"\" \"F)*&\"\"%F)F&F)!\"\"\"\"$F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "expand((x-3)*(x-1)) mod 11; " }}{PARA 11 "" 1 "" {XPPMATH 20 " ,(*$)I\"xG6\"\"\"#\"\"\"F(*&\"\"%F(F%F(!\"\"\"\"$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "PartialFactorSplit(x^10+x^5+1,x,2,11);" }} {PARA 9 "" 1 "" {TEXT 207 59 "\{--> enter PartialFactorSplit, args = x ^10+x^5+1, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-UWoAE%)" }} {PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"!\"\"%F$\"\"\"\"#5\"\"&\"\"*F(\"\" $F'F&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",8*&\"\"%\"\"\"I\"xG6\"F%F %*&F$F%)F&\"\"#F%F%*$)F&\"\"$F%F%*&\"#5F%)F&F$F%F%*&\"\"&F%)F&F2F%F%*& \"\"*F%)F&\"\"'F%F%*&F5F%)F&\"\"(F%F%*&F-F%)F&\"\")F%F%*&F2F%)F&F5F%F% *&F/F%)F&F/F%F%*&F*F%)F&\"#6F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",6*& \"\"&\"\"\")I\"xG6\"\"\"*F%F%*&\"\"$F%)F'\"\")F%F%*&\"\"#F%)F'\"\"(F%! \"\"*&\"\"%F%)F'\"\"'F%F2*&F$F%)F'F$F%F2*$)F'F4F%F2*$)F'F+F%F%*&F4F%)F 'F/F%F%*&F/F%F'F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*&\"\"$\"\" \")I\"xG6\"\"\"*F%!\"\"*&F$F%)F'\"\"(F%F**&\"\"%F%)F'\"\"'F%F**$)F'F$F %F%*&F$F%)F'\"\"#F%F*F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"xG6 \"\"\"%\"\"\"F(*&\"\"#F()F%\"\"$F(!\"\"*&\"\"&F()F%F*F(F-*&F'F(F%F(F(F 'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I\"xG6\"\"\"%\"\"\"F)*&\" \"#F))F&\"\"$F)!\"\"*&\"\"&F))F&F+F)F.*&F(F)F&F)F)F(F),0*$)F&\"\"'F)F) *&F+F))F&F0F)F)*&F+F)F%F)F.F*F)*&F(F)F1F)F)*&F-F)F&F)F.F-F)" }}{PARA 9 "" 1 "" {TEXT 207 109 "<-- exit PartialFactorSplit (now at top level) = [x^4-2*x^3-5*x^2+4*x+4, x^6+2*x^5-2*x^4+2*x^3+4*x^2-3*x+3]\}" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I\"xG6\"\"\"%\"\"\"F)*&\"\"#F))F& \"\"$F)!\"\"*&\"\"&F))F&F+F)F.*&F(F)F&F)F)F(F),0*$)F&\"\"'F)F)*&F+F))F &F0F)F)*&F+F)F%F)F.F*F)*&F(F)F1F)F)*&F-F)F&F)F.F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "expand((x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5)*( x^4+2*x^3+x^2-5*x-2)) mod 11;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I \"xG6\"\"#5\"\"\"F(*$)F%\"\"&F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "PartialFactorSplit(x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5,x, 2,11);\n" }{MPLTEXT 1 0 47 "PartialFactorSplit(x^4+2*x^3+x^2-5*x-2,x,2 ,11);" }}{PARA 9 "" 1 "" {TEXT 207 80 "\{--> enter PartialFactorSplit, args = x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-SeG'G7%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"!\"\"% \"\")F#\"\"&\"\"*F%\"\"$F'F'F$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,6*&\"\"%\"\"\"I\"xG6\"F%F%*&\"\")F%)F&\"\"#F%F%*&\"\"&F%)F&F$F%F%*&\" \"*F%)F&F-F%F%*&F)F%)F&\"\"'F%F%*&\"\"$F%)F&\"\"(F%F%*&F0F%)F&F)F%F%*& F0F%)F&F0F%F%*&F$F%)F&\"#5F%F%*$)F&\"#6F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&\"\"$\"\"\")I\"xG6\"\"\"&F%F%*&\"\"%F%)F'F+F%!\"\"*&F +F%)F'F$F%F-*&F+F%)F'\"\"#F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",, *&\"\"&\"\"\")I\"xG6\"F$F%F%*&\"\"#F%)F'\"\"%F%!\"\"*$)F'\"\"$F%F-*&F$ F%)F'F*F%F%F'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"xG6\"\"\"%\" \"\"F(*&F'F()F%\"\"$F(F(*&\"\"#F()F%F-F(F(F%F(F-!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I\"xG6\"\"\"%\"\"\"F)*&F(F))F&\"\"$F)F)*&\"\"# F))F&F.F)F)F&F)F.!\"\",(*$F/F)F)*&\"\"&F)F&F)F)F,F)" }}{PARA 9 "" 1 "" {TEXT 207 83 "<-- exit PartialFactorSplit (now at top level) = [x^4+4 *x^3+2*x^2+x-2, x^2+5*x+3]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I \"xG6\"\"\"%\"\"\"F)*&F(F))F&\"\"$F)F)*&\"\"#F))F&F.F)F)F&F)F.!\"\",(* $F/F)F)*&\"\"&F)F&F)F)F,F)" }}{PARA 9 "" 1 "" {TEXT 207 68 "\{--> ente r PartialFactorSplit, args = x^4+2*x^3+x^2-5*x-2, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-!=9sT'**" }}{PARA 11 "" 1 "" {XPPMATH 20 "7. \"\"$\"\")\"\"*\"\"%\"#5\"\"&F'F#\"\"'F&F(F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",:\"\"$\"\"\"*&\"\")F$I\"xG6\"F$F$*&\"\"*F$)F'\"\"#F$F$*& \"\"%F$)F'F#F$F$*&\"#5F$)F'F.F$F$*&\"\"&F$)F'F4F$F$*&F1F$)F'\"\"'F$F$* &F#F$)F'\"\"(F$F$*&F8F$)F'F&F$F$*&F.F$)F'F*F$F$*&F4F$)F'F1F$F$*&F#F$)F '\"#6F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"%\"\"\"I\"xG6\"F%! \"\"*&\"\"#F%)F&\"\"$F%F(*&F,F%)F&F*F%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\"xG6\"\"\"%F#F#*&\"\"#F#)F'\"\"$F#F#*$)F'F +F#F#*&\"\"&F#F'F#!\"\"F+F2" }}{PARA 9 "" 1 "" {TEXT 207 75 "<-- exit \+ PartialFactorSplit (now at top level) = [1, x^4+2*x^3+x^2-5*x-2]\}" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\"xG6\"\"\"%F#F#*&\"\"#F#) F'\"\"$F#F#*$)F'F+F#F#*&\"\"&F#F'F#!\"\"F+F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "expand((x^2+3*x-2)*(x^4-5*x^3-2*x^2-3*x+3)) mod 1 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*$)I\"xG6\"\"\"'\"\"\"F(*&\"\"#F ()F%\"\"&F(!\"\"*&\"\"$F()F%\"\"%F(F(*$)F%F/F(F(*&F*F()F%F*F(F-*&F1F(F %F(F(F,F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "PartialFactorS plit(x^4-5*x^3-2*x^2-3*x+3,x,2,11);\n" }{MPLTEXT 1 0 47 "PartialFactor Split(x^4+2*x^3+x^2-5*x-2,x,2,11);" }}{PARA 9 "" 1 "" {TEXT 207 70 "\{ --> enter PartialFactorSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-]uI3kQ" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"!\"\"%\"\"'\"\"$F%F$\"\"*F%F'F'F&\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",8*&\"\"%\"\"\"I\"xG6\"F%F%*&\"\"'F%)F&\"\"#F%F% *&\"\"$F%)F&F-F%F%*&F)F%)F&F$F%F%*&F$F%)F&\"\"&F%F%*&\"\"*F%)F&F)F%F%* &F)F%)F&\"\"(F%F%*&F5F%)F&\"\")F%F%*&F5F%)F&F5F%F%*&F-F%)F&\"#5F%F%*$) F&\"#6F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*\"\"\"!\"\"I\"xG6\"F#*& \"\"%F#)F%\"\"$F#F#*&\"\"#F#)F%F,F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"xG6\"\"\"%\"\"\"F(*&\" \"&F()F%\"\"$F(!\"\"*&\"\"#F()F%F/F(F-*&F,F(F%F(F-F,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I\"xG6\"\"\"%\"\"\"F)*&\"\"&F))F&\"\"$F)!\"\" *&\"\"#F))F&F0F)F.*&F-F)F&F)F.F-F)F)" }}{PARA 9 "" 1 "" {TEXT 207 77 " <-- exit PartialFactorSplit (now at top level) = [x^4-5*x^3-2*x^2-3*x+ 3, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,,*$)I\"xG6\"\"\"%\"\"\"F)* &\"\"&F))F&\"\"$F)!\"\"*&\"\"#F))F&F0F)F.*&F-F)F&F)F.F-F)F)" }}{PARA 9 "" 1 "" {TEXT 207 68 "\{--> enter PartialFactorSplit, args = x^4+2*x^ 3+x^2-5*x-2, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-l#*=2Yp" }} {PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"!\"\"#\"\"\"\"\"(F%F&\"\"$\"\"%\" \"'\"\")F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",8*&\"\"#\"\"\"I\"xG6\"F %F%*$)F&F$F%F%*&\"\"(F%)F&\"\"$F%F%*$)F&\"\"%F%F%*&F+F%)F&\"\"&F%F%*&F -F%)F&\"\"'F%F%*&F0F%)F&F+F%F%*&F6F%)F&\"\")F%F%*&F;F%)F&\"\"*F%F%*&F0 F%)F&\"#5F%F%*&F$F%)F&\"#6F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*\"\" #\"\"\"I\"xG6\"!\"\"*&\"\"%F$)F%\"\"$F$F$*&F)F$)F%F#F$F'" }}{PARA 11 " " 1 "" {XPPMATH 20 "!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\"xG6\"\"\"%F#F#*&\"\"#F#) F'\"\"$F#F#*$)F'F+F#F#*&\"\"&F#F'F#!\"\"F+F2" }}{PARA 9 "" 1 "" {TEXT 207 75 "<-- exit PartialFactorSplit (now at top level) = [1, x^4+2*x^3 +x^2-5*x-2]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\"xG6\"\" \"%F#F#*&\"\"#F#)F'\"\"$F#F#*$)F'F+F#F#*&\"\"&F#F'F#!\"\"F+F2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "expand((x^2+4*x+5)*(x^2-2*x+ 4)) mod 11;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"xG6\"\"\"%\"\"\"F (*&\"\"#F()F%\"\"$F(F(*$)F%F*F(F(*&\"\"&F(F%F(!\"\"F*F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "PartialFactorSplit(x^4-5*x^3-2*x^2- 3*x+3,x,2,11);" }}{PARA 9 "" 1 "" {TEXT 207 70 "\{--> enter PartialFac torSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-B+)H,t(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"*\"#5\" \"\"\"\"(\"\"%F&\"\")F%F#F(F&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",: \"\"*\"\"\"*&\"#5F$I\"xG6\"F$F$*$)F'\"\"#F$F$*&\"\"(F$)F'\"\"$F$F$*&\" \"%F$)F'F1F$F$*&F-F$)F'\"\"&F$F$*&\"\")F$)F'\"\"'F$F$*$)F'F-F$F$*&F#F$ )F'F7F$F$*&F7F$)F'F#F$F$*&F-F$)F'F&F$F$*&F+F$)F'\"#6F$F$" }}{PARA 11 " " 1 "" {XPPMATH 20 ",*\"\"%!\"\"I\"xG6\"F$*&\"\"#\"\"\")F%\"\"$F)F)*&F #F))F%F(F)F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\" xG6\"\"\"%F#F#*&\"\"&F#)F'\"\"$F#!\"\"*&\"\"#F#)F'F0F#F.*&F-F#F'F#F.F- F#" }}{PARA 9 "" 1 "" {TEXT 207 77 "<-- exit PartialFactorSplit (now a t top level) = [1, x^4-5*x^3-2*x^2-3*x+3]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\",,*$)I\"xG6\"\"\"%F#F#*&\"\"&F#)F'\"\"$F#!\"\"*& \"\"#F#)F'F0F#F.*&F-F#F'F#F.F-F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11);" }}{PARA 9 "" 1 "" {TEXT 207 70 "\{--> enter PartialFactorSplit, args = x^4-5*x^3 -2*x^2-3*x+3, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-YHH;1t" }} {PARA 11 "" 1 "" {XPPMATH 20 "7.\"\"\"\"\"%\"\"(\"\"*\"\"$F&F#F$F&F#\" \"'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",:\"\"\"F#*&\"\"%F#I\"xG6\"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#*$)F&F-F#F#*&F 7F#)F&\"#5F#F#*&F+F#)F&\"#6F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*\" \"%\"\"\"*&F#F$I\"xG6\"F$F$*&\"\"&F$)F&\"\"$F$!\"\"*&F+F$)F&\"\"#F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$\"\"\")I\"xG6\"F$F%!\"\"F%F% " }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"\"#\"\"\"F(*&\"\"&F(F %F(F(\"\"$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"#\"\" \"F)*&\"\"&F)F&F)F)\"\"$F),(F$F)F&F)F)F)" }}{PARA 9 "" 1 "" {TEXT 207 71 "<-- exit PartialFactorSplit (now at top level) = [x^2+5*x+3, x^2+x +1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"#\"\"\"F)*& \"\"&F)F&F)F)\"\"$F),(F$F)F&F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11);" }} {PARA 9 "" 1 "" {TEXT 207 70 "\{--> enter PartialFactorSplit, args = x ^4-5*x^3-2*x^2-3*x+3, x, 2, 11" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-dO0 2l5" }}{PARA 11 "" 1 "" {XPPMATH 20 "7-\"\"%\"#5\"\")\"\"!F&\"\"&F'\" \"*\"\"\"F)F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",4\"\"%\"\"\"*&\"#5F$I \"xG6\"F$F$*&\"\")F$)F'\"\"#F$F$*&\"\"&F$)F'F.F$F$*&F.F$)F'\"\"'F$F$*& \"\"*F$)F'\"\"(F$F$*$)F'F*F$F$*$)F'F4F$F$*&F#F$)F'F&F$F$" }}{PARA 11 " " 1 "" {XPPMATH 20 ",*\"\"\"!\"\"*&\"\"&F#I\"xG6\"F#F#*&\"\"%F#)F'\"\" #F#F$*&F*F#)F'\"\"$F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$\"\" \")I\"xG6\"F$F%F%F$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6 \"\"\"#\"\"\"F(F%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6 \"\"\"#\"\"\"F)F&F)F)F),(F$F)*&\"\"&F)F&F)F)\"\"$F)" }}{PARA 9 "" 1 "" {TEXT 207 71 "<-- exit PartialFactorSplit (now at top level) = [x^2+x +1, x^2+5*x+3]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,(*$)I\"xG6\"\"\"# \"\"\"F)F&F)F)F),(F$F)*&\"\"&F)F&F)F)\"\"$F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "expand((x^2+x+1)*(x^2+5*x+3)) mod 11;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$)I\"xG6\"\"\"%\"\"\"F(*&\"\"&F()F%\"\"$F(!\" \"*&\"\"#F()F%F/F(F-*&F,F(F%F(F-F,F(" }}}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "13. Az AKS-teszt" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 36 "14. A szita m\303\263dszerek alapjai" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} }{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 201 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }