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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 43 "10. Faktoriz\303\241l\303\241s elliptikus g" }{TEXT 205 8 "\3 03\266" }{TEXT 205 14 "rb\303\251kkel" }}{PARA 0 "" 0 "" {TEXT 201 0 " " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 55 "11. Pr\303\255mteszt ellipt ikus g\303\266rb\303\251kkel" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 37 "12. Polinomfaktoriz\303\241l\303\241s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 16 "13. Az AKS-teszt" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 36 "14. A szita m\303\263dszerek alapjai" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart; with(numtheo ry);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7QI&GIgcdG6\"I)bigomegaGF$I&cfra cGF$I)cfracpolGF$I+cyclotomicGF$I)divisorsGF$I)factorEQGF$I*factorsetG F$I'fermatGF$I)imagunitGF$I&indexGF$I/integral_basisGF$I)invcfracGF$I' invphiGF$I*issqrfreeGF$I'jacobiGF$I*kroneckerGF$I'lambdaGF$I)legendreG F$I)mcombineGF$I)mersenneGF$I(migcdexGF$I*minkowskiGF$I(mipolysGF$I%ml ogGF$I'mobiusGF$I&mrootGF$I&msqrtGF$I)nearestpGF$I*nthconverGF$I)nthde nomGF$I)nthnumerGF$I'nthpowGF$I&orderG%*protectedGI)pdexpandGF$I$phiGF $I#piGF$I*pprimrootGF$I)primrootGF$I(quadresGF$I+rootsunityGF$I*safepr imeGF$I&sigmaGF$I*sq2factorGF$I(sum2sqrGF$I$tauGF$I%thueGF$" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 13 "14.1. Dixon v" }{TEXT 206 8 "\303\251" }{TEXT 206 8 "letlen n" }{TEXT 206 8 "\303\251" }{TEXT 206 7 "gyzet m " }{TEXT 206 8 "\303\263" }{TEXT 206 7 "dszere." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "n:=nextprim e(7*10^2)*prevprime(14*10^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'*p!) *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "B:=20; F:=[];\n" } {MPLTEXT 1 0 27 "for j from 2 while j" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "rnd:=rand(2..n-2); rnd(); if actors(%^2 mod n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6\"F#F#F#,&-f*F# F#6#I(builtinGF#F#\"$$RF#F#F#I%FAILG%*protectedG6%\"\"'\"''p!)*\"#?\" \"\"\"\"#F0F#F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'-N6" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"7%7$\"\"#F&7$\"\"&F#7$\"&(47F#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "R:=[];\n" }{MPLTEXT 1 0 28 "w hile nops(R)=B then next else R:=[op(R),[x,y]] fi;\n" }{MPLTEXT 1 0 3 "od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 2 "R;" }}{PARA 11 "" 1 "" {XPPMATH 20 "7/7$\"'d[%) 7'7$\"\"#F'7$\"\"&\"\"\"7$\"\"(F'7$\"#8F*7$\"#F*7$\"'&>d#7&7$F'\"\"*7$\"\"$F*7$F,F*F- 7$\"'Cu()7&7$F'F,FB7$F)FCF-7$\"$?#7%7$F'\"\"%7$F)F'7$F6F'7$\"'Z(3*7%F4 7$F6FC7$F " 0 "" {MPLTEXT 1 0 558 "Rc:=[[21 475, [[3, 2], [5, 1], [17, 2], [19, 1]]], [855183, [[2, 4], [3, 4], [5 , 1], [7, 2]]], [164912, [[3, 1], [5, 2], [11, 1], [13, 1], [19, 1]]], [728436, [[2, 1], [3, 2], [11, 1], [13, 1], [17, 1]]], [362222, [[3, \+ 2], [19, 1]]], [297430, [[5, 1], [19, 4]]], [744161, [[3, 3], [5, 1], \+ [11, 1], [13, 1], [19, 1]]], [495370, [[2, 8], [3, 6], [5, 1]]], [5771 06, [[2, 1], [11, 1], [13, 2], [19, 1]]], [699549, [[7, 4]]], [689811, [[5, 4], [13, 1], [17, 1]]], [695704, [[3, 2], [5, 1], [11, 4]]], [31 5384, [[2, 4], [3, 1], [5, 1], [11, 1], [13, 1], [19, 1]]]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "7/7$\"&v9#7&7$\"\"$\"\"#7$\"\"&\"\"\"7$\"#F+7$\"'$=b)7&7$F(\"\"%7$F'F4F)7$\"\"(F(7$\"'7\\;7'7$F'F+7$F*F(7$ \"#6F+7$\"#8F+F.7$\"'O%G(7'7$F(F+F&F=F?7$F-F+7$\"'AAO7$F&F.7$\"'IuH7$F )7$F/F47$\"'hTu7'7$F'F'F)F=F?F.7$\"'q`\\7%7$F(\"\")7$F'\"\"'F)7$\"'1rd 7&FDF=7$F@F(F.7$\"'\\&*p7#7$F7F47$\"'6)*o7%7$F*F4F?FE7$\"'/dp7%F&F)7$F >F47$\"'%Q:$7(F3F;F)F=F?F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7^rI.BlockDiagonalG 6\"I,GramSchmidtGF$I,JordanBlockGF$I)LUdecompGF$I)QRdecompGF$I*Wronski anGF$I'addcolGF$I'addrowGF$I$adjGF$I(adjointGF$I&angleGF$I(augmentGF$I (backsubGF$I%bandGF$I&basisGF$I'bezoutGF$I,blockmatrixGF$I(charmatGF$I )charpolyGF$I)choleskyGF$I$colGF$I'coldimGF$I)colspaceGF$I(colspanGF$I *companionGF$I'concatGF$I%condGF$I)copyintoGF$I*crossprodGF$I%curlGF$I )definiteGF$I(delcolsGF$I(delrowsGF$I$detGF$I%diagGF$I(divergeGF$I(dot prodGF$I*eigenvalsGF$I,eigenvaluesGF$I-eigenvectorsGF$I+eigenvectsGF$I ,entermatrixGF$I&equalGF$I,exponentialGF$I'extendGF$I,ffgausselimGF$I* fibonacciGF$I+forwardsubGF$I*frobeniusGF$I*gausselimGF$I*gaussjordGF$I (geneqnsGF$I*genmatrixGF$I%gradGF$I)hadamardGF$I(hermiteGF$I(hessianGF $I(hilbertGF$I+htransposeGF$I)ihermiteGF$I*indexfuncGF$I*innerprodGF$I )intbasisGF$I(inverseGF$I'ismithGF$I*issimilarGF$I'iszeroGF$I)jacobian GF$I'jordanGF$I'kernelGF$I*laplacianGF$I*leastsqrsGF$I)linsolveGF$I'ma taddGF$I'matrixGF$I&minorGF$I(minpolyGF$I'mulcolGF$I'mulrowGF$I)multip lyGF$I%normGF$I*normalizeGF$I*nullspaceGF$I'orthogGF$I*permanentGF$I&p ivotGF$I*potentialGF$I+randmatrixGF$I+randvectorGF$I%rankGF$I(ratformG F$I$rowGF$I'rowdimGF$I)rowspaceGF$I(rowspanGF$I%rrefGF$I*scalarmulGF$I -singularvalsGF$I&smithGF$I,stackmatrixGF$I*submatrixGF$I*subvectorGF$ I)sumbasisGF$I(swapcolGF$I(swaprowGF$I*sylvesterGF$I)toeplitzGF$I&trac eGF$I*transposeGF$I,vandermondeGF$I*vecpotentGF$I(vectdimGF$I'vectorGF $I*wronskianGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "RM:=matr ix(nops(R),nops(F),0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+m odulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q#RMF'/%'italicGQ%t rueF'/%,mathvariantGQ'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ& falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.mov ablelimitsGF=/%'accentGF=/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF' /%'rspaceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6%-F# 6#-I'mtableGF$6/-I$mtrGF$6*-I$mtdGF$6#-I#mnGF$6$Q\"0F'F9F]oF]oF]oF]oF] oF]oF]oFjnFjnFjnFjnFjnFjnFjnFjnFjnFjnFjnFjn/%%openGQ\"[F'/%&closeGQ\"] F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i to nops(Rc) do \n" }{MPLTEXT 1 0 16 " v:=Rc[i][2];\n" }{MPLTEXT 1 0 23 " for j to n ops(v) do\n" }{MPLTEXT 1 0 15 " vv:=v[j];\n" }{MPLTEXT 1 0 66 " \+ for k to nops(F) do if vv[1]=F[k] then RM[i,k]:=vv[2] fi od;\n" } {MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(RM);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(m fencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I%mrowGF$6#-I'm tableGF$6/-I$mtrGF$6*-I$mtdGF$6#-I#mnGF$6$Q\"0F'/%,mathvariantGQ'norma lF'-F56#-F86$Q\"2F'F;-F56#-F86$Q\"1F'F;F4F4F4F>FC-F26*-F56#-F86$Q\"4F' F;FJFCF>F4F4F4F4-F26*F4FCF>F4FCFCF4FC-F26*FCF>F4F4FCFCFCF4-F26*F4F>F4F 4F4F4F4FC-F26*F4F4FCF4F4F4F4FJ-F26*F4-F56#-F86$Q\"3F'F;FCF4FCFCF4FC-F2 6*-F56#-F86$Q\"8F'F;-F56#-F86$Q\"6F'F;FCF4F4F4F4F4-F26*FCF4F4F4FCF>F4F C-F26*F4F4F4FJF4F4F4F4-F26*F4F4FJF4F4FCFCF4-F26*F4F>FCF4FJF4F4F4-F26*F JFCFCF4FCFCF4FC/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "x:=Rc[10][1]; y:=7^2; x^2-y^2 mod n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'\\&*p" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#\\" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "igcd(n,x-y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%*R\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "RM:=addrow(RM,4,9,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,Typesetti ngGI(_syslibGF'6%-I#miGF$6%Q#RMF'/%'italicGQ%trueF'/%,mathvariantGQ'it alicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/% )stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF =/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ \"1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6%-F#6#-I'mtableGF$6/-I$mtrGF $6*-I$mtdGF$6#-I#mnGF$6$Q\"0F'F9-F^o6#-Fao6$Q\"2F'F9-F^o6#-Fao6$FTF9F] oF]oF]oFdoFio-F[o6*-F^o6#-Fao6$Q\"4F'F9F_pFioFdoF]oF]oF]oF]o-F[o6*F]oF ioFdoF]oFioFioF]oFio-F[o6*FioFdoF]oF]oFioFioFioF]o-F[o6*F]oFdoF]oF]oF] oF]oF]oFio-F[o6*F]oF]oFioF]oF]oF]oF]oF_p-F[o6*F]o-F^o6#-Fao6$Q\"3F'F9F ioF]oFioFioF]oFio-F[o6*-F^o6#-Fao6$Q\"8F'F9-F^o6#-Fao6$Q\"6F'F9FioF]oF ]oF]oF]oF]o-F[o6*FdoFdoF]oF]oFdoF^qFioFio-F[o6*F]oF]oF]oF_pF]oF]oF]oF] o-F[o6*F]oF]oF_pF]oF]oFioFioF]o-F[o6*F]oFdoFioF]oF_pF]oF]oF]o-F[o6*F_p FioFioF]oFioFioF]oFio/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "RM:=addrow(RM,3,7,1): RM:=addrow(RM,3,13,1) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,Typese ttingGI(_syslibGF'6%-I#miGF$6%Q#RMF'/%'italicGQ%trueF'/%,mathvariantGQ 'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF =/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accen tGF=/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsiz eGQ\"1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6%-F#6#-I'mtableGF$6/-I$mt rGF$6*-I$mtdGF$6#-I#mnGF$6$Q\"0F'F9-F^o6#-Fao6$Q\"2F'F9-F^o6#-Fao6$FTF 9F]oF]oF]oFdoFio-F[o6*-F^o6#-Fao6$Q\"4F'F9F_pFioFdoF]oF]oF]oF]o-F[o6*F ]oFioFdoF]oFioFioF]oFio-F[o6*FioFdoF]oF]oFioFioFioF]o-F[o6*F]oFdoF]oF] oF]oF]oF]oFio-F[o6*F]oF]oFioF]oF]oF]oF]oF_p-F[o6*F]oF_p-F^o6#-Fao6$Q\" 3F'F9F]oFdoFdoF]oFdo-F[o6*-F^o6#-Fao6$Q\"8F'F9-F^o6#-Fao6$Q\"6F'F9FioF ]oF]oF]oF]oF]o-F[o6*FdoFdoF]oF]oFdoF^qFioFio-F[o6*F]oF]oF]oF_pF]oF]oF] oF]o-F[o6*F]oF]oF_pF]oF]oFioFioF]o-F[o6*F]oFdoFioF]oF_pF]oF]oF]o-F[o6* F_pFdoF^qF]oFdoFdoF]oFdo/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "RM:=addrow(RM,2,1,1): RM:=addrow(RM ,2,6,1): RM:=addrow(RM,2,7,1):\n" }{MPLTEXT 1 0 66 "RM:=addrow(RM,2,8, 1): RM:=addrow(RM,2,12,1):RM:=addrow(RM,2,13,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I #miGF$6%Q#RMF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$60Q#: =F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symm etricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%%formGQ&infixF'/ %'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)i nfinityF'-I(mfencedGF$6%-F#6#-I'mtableGF$6/-I$mtrGF$6*-I$mtdGF$6#-I#mn GF$6$Q\"4F'F9-F^o6#-Fao6$Q\"6F'F9-F^o6#-Fao6$Q\"2F'F9Fio-F^o6#-Fao6$Q \"0F'F9F^pFio-F^o6#-Fao6$FTF9-F[o6*F]oF]oFcpFioF^pF^pF^pF^p-F[o6*F^pFc pFioF^pFcpFcpF^pFcp-F[o6*FcpFioF^pF^pFcpFcpFcpF^p-F[o6*F^pFioF^pF^pF^p F^pF^pFcp-F[o6*F]oF]oFioFioF^pF^pF^pF]o-F[o6*F]o-F^o6#-Fao6$Q\"8F'F9F] oFioFioFioF^pFio-F[o6*-F^o6#-Fao6$Q#12F'F9-F^o6#-Fao6$Q#10F'F9FioFioF^ pF^pF^pF^p-F[o6*FioFioF^pF^pFio-F^o6#-Fao6$Q\"3F'F9FcpFcp-F[o6*F^pF^pF ^pF]oF^pF^pF^pF^p-F[o6*F^pF^pF]oF^pF^pFcpFcpF^p-F[o6*F]oFdoFioFioF]oF^ pF^pF^p-F[o6*FcqFdoF]oFioFioFioF^pFio/%%openGQ\"[F'/%&closeGQ\"]F'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "RM:=addrow(RM,1,5,1): RM:=a ddrow(RM,1,9,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulen ameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q#RMF'/%'italicGQ%trueF'/ %,mathvariantGQ'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF '/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movableli mitsGF=/%'accentGF=/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rsp aceGFO/%(minsizeGQ\"1F'/%(maxsizeGQ)infinityF'-I(mfencedGF$6%-F#6#-I'm tableGF$6/-I$mtrGF$6*-I$mtdGF$6#-I#mnGF$6$Q\"4F'F9-F^o6#-Fao6$Q\"6F'F9 -F^o6#-Fao6$Q\"2F'F9Fio-F^o6#-Fao6$Q\"0F'F9F^pFio-F^o6#-Fao6$FTF9-F[o6 *F]oF]oFcpFioF^pF^pF^pF^p-F[o6*F^pFcpFioF^pFcpFcpF^pFcp-F[o6*FcpFioF^p F^pFcpFcpFcpF^p-F[o6*F]o-F^o6#-Fao6$Q\"8F'F9FioFioF^pF^pFioFio-F[o6*F] oF]oFioFioF^pF^pF^pF]o-F[o6*F]oF_qF]oFioFioFioF^pFio-F[o6*-F^o6#-Fao6$ Q#12F'F9-F^o6#-Fao6$Q#10F'F9FioFioF^pF^pF^pF^p-F[o6*FdoF_qFioFioFio-F^ 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L" }{TEXT 206 8 "\303\241" }{TEXT 206 3 "nct" }{TEXT 206 8 "\303\266" }{TEXT 206 5 "rtek." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 26 "14.3. Kvadratikus irracion" }{TEXT 206 8 "\303\241" }{TEXT 206 6 "lis sz" }{TEXT 206 8 "\303\241" }{TEXT 206 5 "mok l" }{TEXT 206 8 "\303\241" }{TEXT 206 3 "nct" }{TEXT 206 8 "\30 3\266" }{TEXT 206 10 "rt alakja." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "14.4. Fak" }{TEXT 206 33 "toriz\303\241l\303\241s l\303\241" } {TEXT 206 3 "nct" }{TEXT 206 8 "\303\266" }{TEXT 206 8 "rtekkel." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 7 "14.5. N" }{TEXT 206 8 "\303\251" }{TEXT 206 14 "gyzetes szita." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "n:=nextprime(7*10 ^5)*prevprime(14*10^5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"-****p++)*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "n mod 8; n:=23*n; n mod \+ 8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"/x**4;+aA" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "m:=2000; B:=50; T:=2.; b:=ce il(sqrt(n));\n" }{MPLTEXT 1 0 39 "F:=[[2,floor(0.5+2.*log[2.](2)),1]]; \n" }{MPLTEXT 1 0 27 "for j from 3 while jF*\"\"' 7%\"#HF+\"#77%\"#JF+F17%\"#PF+\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "S:= rtable(0..2*m,0) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,Typese ttingGI(_syslibGF'6%-I#miGF$6%Q\"SF'/%'italicGQ%trueF'/%,mathvariantGQ 'italicF'-I#moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF =/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accen tGF=/%%formGQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsiz eGQ\"1F'/%(maxsizeGQ)infinityF'-I(mactionGF$6$-I(mfencedGF$6%-I'mtable GF$6&-I$mtrGF$6#-I$mtdGF$6#-F#6$-F,6%Q,~0~..~4000~F'F/F2-F,6%Q&ArrayF' F/F2-F\\o6#-F_o6#-F#6$-F,6%Q,Data~Type:~F'F/F2-F,6%Q)anythingF'F/F2-F \\o6#-F_o6#-F#6$-F,6%Q*Storage:~F'F/F2-F,6%Q,rectangularF'F/F2-F\\o6#- F_o6#-F#6$-F,6%Q(Order:~F'F/F2-F,6%Q.Fortran_orderF'F/F2/%%openGQ\"[F' /%&closeGQ\"]F'/%+actiontypeGQ-browsertableF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "p:=F[1][1]; lp:=F[1][2]; x:=modp(m-b+F[1][3],p); \n" }{MPLTEXT 1 0 42 "while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for j from 2 to nops(F) do\n" }{MPLTEXT 1 0 37 " ppp:=F[j]; p:=ppp[1]; lp:=ppp[2];\n" }{MPLTEXT 1 0 26 " x:=modp(m-b +ppp[3],p);\n" }{MPLTEXT 1 0 46 " while x<=2*m do S[x]:=S[x]+lp; x:=x +p; od:\n" }{MPLTEXT 1 0 26 " x:=modp(m-b-ppp[3],p);\n" }{MPLTEXT 1 0 46 " while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:\n" }{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "R:=[]; TT:=floor(lo g[2.](2*m*b)/T);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "fo r j from 0 to 2*m do if S[j]>=TT then R:=[op(R),j-m] fi od:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "R;" }}{PARA 11 "" 1 "" {XPPMATH 20 "7,!%+=!%/6!$%e!$K%!$;\"!\"#\"%m8\"%1:\"%9<\"%M<" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "map(y->ifactors((y+b)^2-n),R );" }}{PARA 11 "" 1 "" {XPPMATH 20 "7,7$!\"\"7)7$\"\"#\"\"$7$F(\"\"\"7 $\"#>F*7$\"#HF*7$\"#JF*7$\"#rF*7$\"$(eF*7$F$7(F&F)7$\"#8F*F+F-7$\"&`4' F*7$F$7)F&F)F7F+F/7$\"#`F*7$\"$p&F*7$F$7(F&F)F+F-7$\"#PF*7$\"%x$)F*7$F $7(7$F'\"\"(F)F7F+FC7$\"$8$F*7$F$7(F&7$F(F'F7F+F-F/7$F*7)F&FOF7F+F-7$ \"$R\"F*7$\"$\"=F*7$F*7)7$F'\"\"&F)F7F+F-F17$\"$$HF*7$F*7(7$F'\"\"'F)F 7F-FC7$\"%zgF*7$F*7(F&7$F(F(F+F/FC7$\"%*\\$F*" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 7 "14.6. T" }{TEXT 206 8 "\303\266" }{TEXT 206 13 "bbpo linomos n" }{TEXT 206 8 "\303\251" }{TEXT 206 14 "gyzetes szita." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "n:=nextprime(7*10^7)*prevprime(14*10^7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"1d(***\\J++)*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "n mod 8; n:=37*n; n mod 8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\" &" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"345**\\l6+EO" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "m:=1 0000; B:=100; T:=1.5;\n" }{MPLTEXT 1 0 39 "F:=[[2,floor(0.5+2.*log[2.] (2)),1]]; \n" }{MPLTEXT 1 0 27 "for j from 3 while jF-F*7%\"#BF'\"#67%\"#HF'F27%\" #TF'\"#97%\"#Z\"\"'F-7%\"#`F:F27%\"#fF:\"#A7%\"#rF:\"\")7%\"#(*F*\"#n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "dd:=floor((2*n/m^2)^(1/4.)): if type(dd,odd) then dd: =dd+1; fi:\n" }{MPLTEXT 1 0 11 "dd:=dd..dd;" }}{PARA 11 "" 1 "" {XPPMATH 20 ";\"$#HF#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "if abs(op(1,dd)-(2*n/m^2)^(1/4.))3 or jacobi(d,n)<>1 do\n" }{MPLTEXT 1 0 22 " d:=prev prime(d);\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 20 " dd:=d..op(2 ,dd);\n" }{MPLTEXT 1 0 6 "else\n" }{MPLTEXT 1 0 27 " d:=nextprime(op( 2,dd));\n" }{MPLTEXT 1 0 43 " while modp(d,4)<>3 or jacobi(d,n)<>1 do \n" }{MPLTEXT 1 0 22 " d:=nextprime(d);\n" }{MPLTEXT 1 0 7 " od;\n " }{MPLTEXT 1 0 20 " dd:=op(1,dd)..d;\n" }{MPLTEXT 1 0 5 "fi:\n" } {MPLTEXT 1 0 6 "d; dd;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$6$" }} {PARA 11 "" 1 "" {XPPMATH 20 ";\"$r#\"$6$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "a:=d^2; h0:=n&^((d-3)/4) mod d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&@n*" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#`" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "h1:=n*h0 mod d; (n-h1^2)/d; h2:=%*h 0*((d+1)/2) mod d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$B#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"1![sMx;f;\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" #D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b:=mods(h1+h2*d,a); b ^2-n mod a; c:=(b^2-n)/a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%)*z" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "! .09`G*[P" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "S:= rtable(0..2 *m,0); p:=F[1][1]; lp:=F[1][2]; x:=modp(m+(-b+F[1][3])/a,p);\n" } {MPLTEXT 1 0 42 "while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sy slibGF'6%-I#miGF$6%Q\"SF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I #moGF$60Q#:=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretch yGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%%form GQ&infixF'/%'lspaceGQ/thickmathspaceF'/%'rspaceGFO/%(minsizeGQ\"1F'/%( maxsizeGQ)infinityF'-I(mactionGF$6$-I(mfencedGF$6%-I'mtableGF$6&-I$mtr GF$6#-I$mtdGF$6#-F#6$-F,6%Q-~0~..~20000~F'F/F2-F,6%Q&ArrayF'F/F2-F\\o6 #-F_o6#-F#6$-F,6%Q,Data~Type:~F'F/F2-F,6%Q)anythingF'F/F2-F\\o6#-F_o6# -F#6$-F,6%Q*Storage:~F'F/F2-F,6%Q,rectangularF'F/F2-F\\o6#-F_o6#-F#6$- F,6%Q(Order:~F'F/F2-F,6%Q.Fortran_orderF'F/F2/%%openGQ\"[F'/%&closeGQ \"]F'/%+actiontypeGQ-browsertableF'" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for \+ j from 2 to nops(F) do\n" }{MPLTEXT 1 0 37 " ppp:=F[j]; p:=ppp[1]; lp :=ppp[2];\n" }{MPLTEXT 1 0 31 " x:=modp(m+(-b+ppp[3])/a,p);\n" } {MPLTEXT 1 0 46 " while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:\n" } {MPLTEXT 1 0 31 " x:=modp(m+(-b-ppp[3])/a,p);\n" }{MPLTEXT 1 0 46 " \+ while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:\n" }{MPLTEXT 1 0 3 "od:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "R:=[]; TT:=floor(log[2.](a* m^2/2.)/T); " }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "for j \+ from 0 to 2*m do if S[j]>=TT then R:=[op(R),j-m] fi od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "R;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7%\"%:7\"%DE\"%CS" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "map(y- >ifactors(a*y^2+2*b*y+c),R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%7$!\" \"7*7$\"\"#\"\"$7$\"\"&\"\"\"7$\"\"(F+7$\"#>F+7$\"#TF+7$\"#ZF+7$\"#`F+ 7$\"%PmF+7$F$7)7$F'\"#7F)7$\"#BF+7$\"#PF+F2F47$\"#rF+7$F$7*F)F,F.F " 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 }