{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 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 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 "Normal" -1 256 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 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 39 "(3,5)-case Quadratic rel ations PrintOut" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Set current directory." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "currentdir(\"C://Documents and Settings/mengland/My Documents/Mapl e/DM-35\"):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Read in relations " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "read(\"Quadratic.txt\"):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nops(KNOWN_q);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"$5#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT -1 30 "Procedure to calculate weights" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 343 "you:=[7,4,2,1]:\ncalc_p_weight:=proc(term,j)\nlocal \+ tot;\nif type(term,function) then tot:=add(you[op(i,term)], i=1..nop s(term)); RETURN(tot);\nelif type(term,`*`) then tot:= add( calc_p_wei ght(op(i,term)), i=1..nops(term)); RETURN(tot);\nelif type(term,`^`) t hen tot:= op(2,term) * calc_p_weight(op(1,term)); RETURN(tot);\nelse R ETURN(0) fi:\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 36 "We print out the relations by weight" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "for i from 6 to 42 do print([[i]]): \nRELS:=select(X ->calc_p_weight(lhs(X))=i, KNOWN_q):for j from 1 to nops(RELS) do \npr int(op(select(has,KNOWN_q,op(j,RELS)))); \nod: od: " }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7#7#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)-%\" PG6%\"\"%F)F)\"\"#\"\"\",0*&F)F+)-F'6$F)F)\"\"$F+F+*(F*F+&%'lambdaG6#F )F+-F'6$F1F)F+F+*$)F3F*F+F+*&F)F+&F46#F1F+!\"\"*&F)F+-F'6$F*F1F+F=*(F) F+-F'6$F1F1F+F/F+F=*$)F6F*F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7# \"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"$\"\"%F)\"\"\" -F&6%F)F)F)F*,,*(F)F*-F&6$F(F)F*)-F&6$F)F)\"\"#F*F**&&%'lambdaG6#F)F*- F&6$F(F(F*!\"\"*&#F4F(F*&%\"QG6&F4F)F)F)F*F;*(F4F*-F&6$F4F)F*F2F*F**&F 9F*F/F*F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"$F(\"\"%\"\"\"-F&6%F)F)F)F*,4*(\"\" #F*)-F&6$F(F)F/F*-F&6$F)F)F*F**(F/F*-F&6$F(F(F*)F3F/F*F**&&%'lambdaG6# F)F*-F&6$F/F)F*!\"\"**F/F*F:F*F1F*F3F*F**&F)F*-F&6$F*F)F*F?*&F/F*-F&6$ F/F/F*F**(F/F*-F&6$F/F(F*F3F*F?*&F=F*F1F*F?*&F/F*)F6F/F*F?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)-%\"PG6%\"\"$\"\"%F*\"\"#\"\"\",**(F*F,) -F'6$F)F*F+F,-F'6$F*F*F,F,*&F*F,-F'6$F,F*F,F,*(F*F,-F'6$F+F*F,F0F,F,*$ )-F'6$F)F)F+F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7#\"\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"$F(\"\"%\"\"\"-F&6%F(F) F)F*,.**\"\"#F*-F&6$F(F(F*-F&6$F(F)F*-F&6$F)F)F*F**&F/F*)F2F(F*F**(F/F *&%'lambdaG6#F)F*)F2F/F*F**&F/F*-F&6$F*F(F*!\"\"*(F/F*-F&6$F/F(F*F2F*F @*&-F&6$F/F)F*F0F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\" \"#\"\"%F)\"\"\"-F&6%F)F)F)F*,2*(F)F*-F&6$F(F)F*)-F&6$F)F)F(F*F**&&%'l ambdaG6#F)F*-F&6$F(\"\"$F*!\"\"*(F(F*&F66#F:F*-F&6$F:F)F*F**&F(F*&F66# F(F*F;*&F(F*-F&6$F*F:F*F;*&#F(F:F**&F2F*&%\"QG6&F(F)F)F)F*F*F**&F8F*F? F*F**(F(F*F/F*-F&6$F:F:F*F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\" PG6%\"\"$F(F(\"\"\"-F&6%\"\"%F,F,F),:**\"\"'F)-F&6$F(F(F)-F&6$F(F,F)-F &6$F,F,F)F)*&\"\"#F))F2F(F)!\"\"*&&%'lambdaG6#F,F)-F&6$F7F(F)F)**F7F)F ;F)F0F)F4F)F9*(F,F)F;F))F2F7F)F9*(F7F))F;F7F)F2F)F9*(F/F)&F<6#F(F)F2F) F)*&F7F)&F<6#F7F)F)*&F7F)-F&6$F)F(F)F)*(F7F)F4F)&%\"QG6&F7F,F,F,F)F9*( \"\"(F)F>F)F2F)F)*(F7F)-F&6$F7F,F)F0F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7#\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#\"\" %F)\"\"\"-F&6%\"\"$F)F)F*,,**F)F*-F&6$F(F)F*-F&6$F-F)F*-F&6$F)F)F*F**& #F(F-F*&%\"QG6&F*F)F)F)F*!\"\"*&#F(F-F**&F2F*&F96&F(F)F)F)F*F*F**&-F&6 $F(F-F*-F&6$F-F-F*F**&F(F*)F0F(F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/*$)-%\"PG6%\"\"$F)\"\"%\"\"#\"\"\",,*(F*F,-F'6$F)F)F,)-F'6$F)F*F+F,F ,*&#F*F)F,&%\"QG6&F,F*F*F*F,!\"\"*(F*F,-F'6$F,F*F,-F'6$F*F*F,F9*&#F*F) F,*&F2F,&F76&F+F*F*F*F,F,F9*$)-F'6$F+F*F+F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"$F(F(\"\"\"-F&6%F(\"\"%F,F),2*(\"\"#F))- F&6$F(F(F/F)-F&6$F,F,F)F)*(F/F)F1F))-F&6$F(F,F/F)F)**F/F)&%'lambdaG6#F ,F)F1F)F7F)F)*&#F/F(F)&%\"QG6&F)F,F,F,F)F)*(\"\")F)-F&6$F)F,F)F3F)F)*& F>F)*&F7F)&F@6&F/F,F,F,F)F)F)*&-F&6$F/F(F)F1F)!\"\"*&F/F))-F&6$F/F,F/F )FM" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#\"\"$\"\"%\"\" \"-F&6%F*F*F*F+,4**F(F+-F&6$F(F*F+-F&6$F)F*F+-F&6$F*F*F+F+*(F(F+-F&6$F (F)F+)F4F(F+F+*&#F+F)F+*&&%'lambdaG6#F*F+&%\"QG6&F(F*F*F*F+F+!\"\"**F( F+F=F+F0F+F4F+F+*(F(F+&F>6#F)F+-F&6$F)F)F+FC*(F*F+-F&6$F+F*F+F4F+F+*(F (F+-F&6$F(F(F+F4F+FC*&#F+F)F+*&F2F+F@F+F+FC*(F(F+F7F+FHF+FC" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7#\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /*&-%\"PG6%\"\"#\"\"$\"\"%\"\"\"-F&6%F)F*F*F+,0*(F(F+-F&6$F(F*F+)-F&6$ F)F*F(F+F+**F(F+-F&6$F(F)F+-F&6$F*F*F+F3F+F+*(F(F+&%'lambdaG6#F*F+-F&6 $F+F*F+F+**F(F+F;F+F0F+F3F+F+*(F(F+-F&6$F+F)F+F8F+F+*(F(F+F>F+F3F+F+*& #F+F)F+*&-F&6$F)F)F+&%\"QG6&F(F*F*F*F+F+!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#\"\"$F)\"\"\"-F&6%\"\"%F-F-F*,B*(F(F*-F &6$F(F-F*)-F&6$F)F-F(F*!\"\"**F-F*-F&6$F(F)F*-F&6$F-F-F*F3F*F***F(F*F0 F*F9F*-F&6$F)F)F*F**(F(F*&%'lambdaG6#F-F*-F&6$F*F-F*F5*&F?F*-F&6$F(F(F *F***F(F*F?F*F7F*F9F*F5**F-F*F?F*F0F*F3F*F5*(F(F*)F?F(F*F0F*F5*(\"\"'F *&F@6#F)F*F0F*F***FLF*FMF*F3F*F9F*F**(F(F*&F@6#F(F*F9F*F5*(F(F*-F&6$F* F)F*F9F*F5*(F(F*FBF*F3F*F5*&FEF*F3F*F**&#F(F)F**&F*(\"\"'F)F9F)F3F)F)*(F2F)-F&6$F2F2F)F3F)F>*&#F2F(F)*&F0F )&%\"QG6&F2F,F,F,F)F)F>*&-F&6$F2F(F)-F&6$F2F,F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#\"\"%F)\"\"\"-F&6%\"\"$F-F)F*,6*(F(F*-F &6$F(F)F*)-F&6$F-F)F(F*F***F(F*F0F*-F&6$F)F)F*-F&6$F-F-F*F**(F(F*&%'la mbdaG6#F)F*-F&6$F*F)F*!\"\"**F(F*F;F*F0F*F3F*F**&F(F*-F&6$F*F(F*F**(F( F*-F&6$F*F-F*F6F*F@*(F(F*F>F*F3F*F**(F(F*-F&6$F(F(F*F3F*F@*&#F(F-F**&F 8F*&%\"QG6&F(F)F)F)F*F*F**&-F&6$F(F-F*F0F*F@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7#\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6% \"\"#\"\"$F)\"\"\"-F&6%F)\"\"%F-F*,<**F(F*&%'lambdaG6#F-F*-F&6$F(F-F*- F&6$F)F)F*F**&#F-F)F*&F16#F*F*F**&#F(F)F**&F0F*&F16#F(F*F*!\"\"*&#F*F) F*&%\"QG6&F(F(F)F)F*F**&-F&6$F(F(F*F5F*F@*&#F-F)F**&-F&6$F-F-F*&FD6&F* F-F-F-F*F*F@*&#F(F)F**&F3F*&FD6&F(F-F-F-F*F*F***F(F*-F&6$F(F)F*FLF*F5F *F**(F(F*FVF*)-F&6$F)F-F(F*F**(F(F*&F16#F)F*FYF*F**&FgnF*FVF*F@*&#F-F) F**&F0F*-F&6$F*F)F*F*F@*&FQF**&F>F*FZF*F*F*" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#\"\"%F)\"\"\"-F&6%\"\"$F-F-F*,@**F(F*&% 'lambdaG6#F)F*-F&6$F(F-F*-F&6$F-F)F*F**&#F)F-F*&F16#F*F*F**&F8F**&F0F* &F16#F(F*F*F**&#F(F-F*&%\"QG6&F(F(F-F-F*!\"\"*(F)F*-F&6$F*F-F*F5F*F**$ )F3F(F*FD*&#F)F-F**&-F&6$F)F)F*&FB6&F*F)F)F)F*F*FD*&#F)F-F**&-F&6$F(F) F*&FB6&F(F)F)F)F*F*FD**F)F*FTF*F5F*-F&6$F-F-F*F***F(F*F3F*FMF*FYF*F**( F(F*F3F*)F5F(F*FD*(F)F*&F16#F-F*FgnF*FD*(F(F*FinF*F3F*F**&#\"\")F-F**& F0F*FFF*F*F**&F]oF**&F=F*F5F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ *&-%\"PG6%\"\"\"\"\"%F)F(-F&6%F)F)F)F(,6*&#F)\"\"$F(&%'lambdaG6#F(F(! \"\"*&#\"\"#F/F(*&&F16#F)F(&F16#F6F(F(F(*&#F(F/F(&%\"QG6&F6F6F/F/F(F3* &-F&6$F(F/F(-F&6$F/F)F(F(*(F6F(-F&6$F(F)F(-F&6$F/F/F(F3*&F5F(*&-F&6$F) F)F(&F?6&F(F)F)F)F(F(F(*(F)F(FGF()FMF6F(F(*&&F16#F/F(-F&6$F6F/F(F(*&#F (F/F(*&F8F(FBF(F(F(*&#F)F/F(*&F:F(FDF(F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"#F(\"\"%\"\"\"-F&6%F)F)F)F*,H*(&%'lambda G6#F)F*&F06#\"\"$F*-F&6$F4F)F*F**&#F(F4F**(F/F*-F&6$F)F)F*&%\"QG6&F(F) F)F)F*F*F***F(F*F/F*-F&6$F(F)F*-F&6$F4F4F*!\"\"**F(F*F2F*FBF*F:F*F***F (F*F/F*-F&6$F(F4F*F5F*F**&#F)F4F*&F06#F*F*FD*&#F*F4F**&F/F*&F06#F(F*F* FD*&#F*F4F*&F=6&F(F(F4F4F*FD*(F(F*-F&6$F*F4F*F5F*F**(F(F*-F&6$F*F)F*FB F*FD*&F(F*)FGF(F*FD*&F8F**&F:F*&F=6&F*F)F)F)F*F*F**&#F(F4F**&F@F*F6&F*F)F)F)F*F*F**(F(F*&FD6#F-F*FKF*F**(F (F*&FD6#F*F*F;F*F7*&#F)F-F**&)FCF(F*FKF*F*F7*&#\"\")F-F**(FCF*FKF*F5F* F*F**(FXF*FMF*F;F*F**&FAF**(FCF*&FD6#F(F*F;F*F*F**&#F)F-F**(FboF*F5F*F ;F*F*F7*&#F]oF-F**&-F&6$F*F-F*-F&6$F(F)F*F*F7*&FPF**(FCF*FSF*&F>6&F(F) F)F)F*F*F**&#F(F-F**(FCF*FMF*F\\pF*F*F7*&FAF**&FXF*)FSF(F*F*F**&#F)F-F 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F,F(*&&F36#F0F()F?F,F(F(F(**F,F(-F&6$F(F)F(-F&6$F)F)F(-F&6$F,F,F(F(*&F /F(*(F2F(&F86&F,F)F)F)F(FIF(F(F(*(F=F(-F&6$F0F0F(FKF(F(*(\"\"&F(&F36# \"\"!F(-F&6$F0F)F(F(*(F2F(F=F(FenF(F(*&F=F()FenF,F(FA*(FEF(FIF(FTF(F(* &F/F(*(F2F(-F&6$F(F0F(F?F(F(F(*&F/F(*(&F36#F,F(F?F(FenF(F(F(*&F5F(&F86 &F(F,F)F)F(FA*&#F(F0F(*&FQF(-F&6$F(F,F(F(FA*&#F(\"\"'F(*&F?F(&F86&F,F, F0F0F(F(FA*&#F(F0F(*(F2F(FaoF(F?F(F(F(*(F,F(FIF()F5F,F(F(*&F2F(FXF(FA* &FbpF(*&FMF(F7F(F(F(*$)F]oF,F(F(*&-F&6$F(F(F(FTF(FA*&F/F(*&FIF(F7F(F(F (" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&-%\"PG6%\"\"\"F(\"\"%F(-F&6%F) F)F)F(,N*&&%'lambdaG6#\"\"#F(-F&6$F(\"\"$F(!\"\"*(&F/6#F4F(F2F(-F&6$F4 F)F(F(*&#F1F4F(*(&F/6#F)F(-F&6$F1F)F(&%\"QG6&F(F)F)F)F(F(F5*&#F1F4F(*& &F/6#F(F(-F&6$F1F4F(F(F(*&#F(F1F(*&F7F()FJF1F(F(F5*(F7F(-F&6$F)F)F(FBF (F(*&#F4F1F(*()F7F1F(-F&6$F4F4F(FQF(F(F5*&#F(F1F(*(F7F(FQF(&FC6&F1F4F4 F4F(F(F(*(F7F(-F&6$F(F)F(FWF(F5*&#F1F4F(*(F>F(F2F(FJF(F(F5*&#F1F4F(*(F .F(FJF(F9F(F(F5*&F@F(&FC6&F(F1F)F)F(F(*&#F(F4F(*&&FC6&F1F)F)F)F(-F&6$F 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