{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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart: with(algcur ves):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 264 "The puiseux program can give unnecessarily large answers. Reading the following code into Map le before using the puiseux command will help to prevent one (but not \+ all) of the causes of these large answers, namely it will help to prev ent some unnecessary expanding." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2225 "`algcurves/lift_exp` := proc(v, f, x, y)\nlocal i, ii, r, re s, v7, vv7, v3, ext, a, j, n, np, ram, j3;\n if v[5] = 1 then retur n \{v\} end if;\n v3 := degree(v[3], x);\n res := \{\};\n r : = v[1] + y*x^v[2];\n vv7 := v[7]*v3 + v[2] - 1;\n vv7 := vv7 + v [5];\n ii := `algcurves/truncate_subs`(subs(x = v[3], f), x, y, r, \+ vv7 + 1,\n v[4]);\n if ii = 0 then error \"degree estimate w as wrong\" end if;\n v7 := (ldegree(ii, x) - v[2])/v3;\n r := `a lgcurves/v_ext_m`(\n `algcurves/g_factors`(tcoeff(ii, x), y, v[ 4]), y);\n for i in r do res := res union `algcurves/lift_exp`([\n \+ v[1] + x^v[2]*i[1], v[2] + 1, v[3], [op(i[3]), op(v[4])], i[2], \n v[6]*i[4], v7, [op(v[8]), [op(1 .. 4, v)]]], f, x, y)\n e nd do;\n if add(i[5]*i[6]*degree(i[3], x)/(v[6]*v3), i = res) <>\n \+ degree(tcoeff(ii, x), y) then error \"found wrong number of expansi ons\"\n end if;\n if v[5] = degree(tcoeff(ii, x), y) then\n \+ if ldegree(ii, x) <> vv7 then error \"degree estimate was wrong\"\n end if;\n return res\n end if;\n ii := collect(ii , y);\n ii := add(`algcurves/normal_tcoeff`(coeff(ii, y, i), x)*y^i ,\n i = 0 .. degree(ii, y));\n np := `algcurves/Newtonpolygo n`(ii, x, y);\n if nops(np) = 2 and np[1][3] = 0 then\n erro r \"found wrong number of expansions\"\n end if;\n for j in np d o\n if 2 < nops(j) and 0 < j[3] and j[3] < 1 then\n \+ r := `algcurves/g_factors`(j[4], x, v[4]);\n r := `algcurve s/v_ext_m`(r, x);\n for i in r do\n j3 := j[ 3] - v[2];\n ext := [op(i[3]), op(v[4])];\n \+ n := mods(1/numer(j3), denom(j3));\n ram := i[1]^n* x^denom(j3);\n a := v[2]*denom(j3) - numer(j[3]);\n \+ res := res union `algcurves/lift_exp`([collect(\n \+ subs(x = ram, v[1])\n + x^a*i[1]^((1 - \+ n*numer(j3))/denom(j3)), x, normal),\n a + 1, norma l(subs(x = ram, v[3])), ext, i[2],\n v[6]*i[4],\n \+ (j[2] - j[1]*j[3] - a/degree(ram, x))/degree(v[3], x ),\n [op(v[8]), [op(1 .. 4, v)]]], f, x, y)\n \+ end do\n end if\n end do;\n res\nend proc:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "A:=y^2*(y-x)-x^5+2*x^3*y+a*x ^4*y+b*x^2*y^2+c*x^3*y^2+d*x*y^3+e*x^2*y^3+f*y^4+g*x*y^4+h*y^5;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,8*&)%\"yG\"\"#\"\"\",&F(F*%\"xG !\"\"F*F**$)F,\"\"&F*F-*(F)F*)F,\"\"$F*F(F*F**(%\"aGF*)F,\"\"%F*F(F*F* *(%\"bGF*)F,F)F*F'F*F**(%\"cGF*F2F*F'F*F**(%\"dGF*F,F*)F(F3F*F**(%\"eG F*F:F*F?F*F**&%\"fGF*)F(F7F*F**(%\"gGF*F,F*FDF*F**&%\"hGF*)F(F0F*F*" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polynomial [1]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,(*&%\"hG\"\"\")%#_ ZG\"\"#F+F+*&%\"fGF+F-F+F+F+F+,&*$)F$F.F+F+*&)*&F$F+,(%\"aGF+%\"bGF+F+ F+!\"\"#\"\"&F.F+)F7\"\"$F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 " numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A1:=eval (A,b=-a-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,8*&)%\"yG\"\"#\"\"\",&F(F*%\"xG!\"\"F*F**$)F,\" \"&F*F-*(F)F*)F,\"\"$F*F(F*F**(%\"aGF*)F,\"\"%F*F(F*F**(,&F5F-F*F-F*)F ,F)F*F'F*F**(%\"cGF*F2F*F'F*F**(%\"dGF*F,F*)F(F3F*F**(%\"eGF*F:F*F?F*F **&%\"fGF*)F(F7F*F**(%\"gGF*F,F*FDF*F**&%\"hGF*)F(F0F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,(*&%\"hG\"\"\")%#_ZG\"\"#F+F +*&%\"fGF+F-F+F+F+F+,&*$)F$F.F+F+*&)F$\"\"$F+-F&6#,**$F,F+F+*&,&F+!\" \"%\"aGF+F+F-F+F+%\"dGF=%\"cGF=F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dis crim(_Z^2+(-1+a)*_Z-d-c,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&\" \"%\"\"\"%\"dGF&F&*&F%F&%\"cGF&F&F&F&*&\"\"#F&%\"aGF&!\"\"*$)F,F+F&F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&#\"\"\"\"\"%F&*$)%\"aG\"\"#F&F&!\"\"%\"c GF,#F&F'F,*&#F&F+F&F*F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A2:=eval(A1,d=%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G,8*&)% \"yG\"\"#\"\"\",&F(F*%\"xG!\"\"F*F**$)F,\"\"&F*F-*(F)F*)F,\"\"$F*F(F*F **(%\"aGF*)F,\"\"%F*F(F*F**(,&F5F-F*F-F*)F,F)F*F'F*F**(%\"cGF*F2F*F'F* F**(,**&#F*F7F**$)F5F)F*F*F-F " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=0,y,0);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#<%,(*(\"%'4%!\"\",2\"\"\"F)%\"aGF'*$) F*\"\"#F)F'*$)F*\"\"$F)F)*&\"\"%F)%\"cGF)F'*(F2F)F3F)F*F)F)*&\"\")F)% \"eGF)F)*&F6F)%\"fGF)F)F2*&%\"xGF),2#F)F6F)*&F6F'F*F)F'*&F6F'F*F-F'*&F 6F'F*F0F)*&F-F'F3F)F'*(F-F'F3F)F*F)F)F7F)F9F)F'#\"\"(F-F)*,\"%C5F'F(F0 ,&F)F'F*F)F)F;F0F " 0 "" {MPLTEXT 1 0 53 "solv e(1/8-1/8*a-1/8*a^2+1/8*a^3-1/2*c+1/2*c*a+e+f,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0#\"\"\"\"\")!\"\"*&#F%F&F%%\"aGF%F%*&F)F%*$)F*\"\"#F% F%F%*&#F%F&F%*$)F*\"\"$F%F%F'*&#F%F.F%%\"cGF%F%*&#F%F.F%*&F6F%F*F%F%F' %\"eGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "A3:=eval(A2,f=-1 /8+1/8*a+1/8*a^2-1/8*a^3+1/2*c-1/2*c*a-e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A3G,8*&)%\"yG\"\"#\"\"\",&F(F*%\"xG!\"\"F*F**$)F,\" \"&F*F-*(F)F*)F,\"\"$F*F(F*F**(%\"aGF*)F,\"\"%F*F(F*F**(,&F5F-F*F-F*)F ,F)F*F'F*F**(%\"cGF*F2F*F'F*F**(,**&#F*F7F**$)F5F)F*F*F-F " 0 "" {MPLTEXT 1 0 20 "puiseux(A3,x=0,y,0);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#<%%\"xG,(*$)F$\"\"#\"\"\"F)*&)F$\"\"$F),&#F)F(F) *&F(!\"\"%\"aGF)F0F)F)*&)F$\"\"%F)-%'RootOfG6#,<*&\"#;F))%#_ZGF(F)F)*& ,*\"#?F0*&F:F)%\"cGF)F)*&\"#CF)F1F)F)*&F4F))F1F(F)F0F)F " 0 "" {MPLTEXT 1 0 103 "discrim(16*_Z^2+(-20+16*c+24*a-4*a^2)*_Z-8*c-a^4+12*a^2-8*c*a^2-8 *e*a+8*e-14*a-16*g-2*a^3+5+16*c*a,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,:*&\"$G\"\"\"\"%\"cGF&!\"\"\"#!)F&*(\"$%QF&F'F&)%\"aG\"\"#F&F&* (\"$7&F&%\"eGF&F-F&F&*&F0F&F1F&F(*&\"#kF&F-F&F(*&\"%C5F&%\"gGF&F&*&F4F &)F-\"\"$F&F(*(\"$c#F&F'F&F-F&F(*&F)F&)F-\"\"%F&F&*&\"#KF&F,F&F(*&F " 0 "" {MPLTEXT 1 0 11 "solve(%,e);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"#K!\"\",6*&\"\")\"\"\"%\"cGF*F& \"\"&F**(\"#CF*F+F*)%\"aG\"\"#F*F**&\"\"%F*)F0\"\"$F*F&*(\"#;F*F+F*F0F *F&*&F3F*F0F*F&*&\"#kF*%\"gGF*F**&F7F*)F+F1F*F**&F,F*)F0F3F*F**&F1F*F/ F*F&F*,&F*F&F0F*F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A4: =eval(A3,e=%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A4G,8*&)%\"yG\"\" #\"\"\",&F(F*%\"xG!\"\"F*F**$)F,\"\"&F*F-*(F)F*)F,\"\"$F*F(F*F**(%\"aG F*)F,\"\"%F*F(F*F**(,&F5F-F*F-F*)F,F)F*F'F*F**(%\"cGF*F2F*F'F*F**(,**& #F*F7F**$)F5F)F*F*F-F " 0 "" {MPLTEXT 1 0 20 "pui seux(A4,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG 6#,**&,&*&\"#K\"\"\"%\"hGF-!\"\"*(F,F-F.F-%\"aGF-F-F-)%#_ZG\"\"#F-F-*& ,6\"\"*F-*&\"#7F-F1F-F/*&F4F-)F1F4F-F/*&\"\"%F-)F1\"\"$F-F-*$)F1F=F-F- *&\"#CF-%\"cGF-F/*(\"#;F-FDF-F1F-F-*(\"\")F-FDF-F;F-F-*&\"#kF-%\"gGF-F -*&FFF-)FDF4F-F-F-F3F-F-F,F/*&F,F-F1F-F-,***\".wxi6&*4\"F/,N*&F9F-FDF- F-*&\"$c#F-F.F-F-*(\"#cF-FDF-F;F-F/*&\"#IF-F1F-F/*&\"$#>F-FKF-F/*(FUF- F.F-F1F-F/*(\"$G\"F-FKF-F1F-F-*(FFF-FDF-F>F-F-*(F,F-FMF-F1F-F-*&F4F-)F 1\"\"&F-F-F7F-*$)F1\"\"'F-F-*&FJF-)FDF?F-F-*(F9F-FAF-FDF-F-*(\"#[F-FMF -F;F-F-*(FJF-FKF-F;F-F-*(FUF-FKF-FDF-F-*&F=F-F>F-F/*(FFF-FDF-F1F-F-*&F 7F-FAF-F/*&\"#JF-F;F-F-*&\"#!)F-FMF-F/F]o,&F-F/F1F-!\"&,$**FUF-F$F-FRF /F_pF-F/#F7F4F/*(FHF/,**&F`oF-F1F-F-*$F;F-F/*&F=F-FDF-F-F]oF/F-F$F=F/* (F4F/F_pF-F$F?F/*$)F$F4F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "nu merator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "solve(12* c+256*h-56*c*a^2-30*a-192*g-256*h*a+128*g*a+16*c*a^3+32*c^2*a+2*a^5+9+ a^6+64*c^3+12*a^4*c+48*c^2*a^2+64*g*a^2+256*g*c-4*a^3+16*c*a-9*a^4+31* a^2-80*c^2,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"#k!\"\",F*&\"# 7\"\"\"%\"cGF*F**&\"$c#F*%\"hGF*F**(\"#cF*F+F*)%\"aG\"\"#F*F&*&\"#IF*F 2F*F&*(F-F*F.F*F2F*F&*(\"#;F*F+F*)F2\"\"$F*F**(\"#KF*)F+F3F*F2F*F**&F3 F*)F2\"\"&F*F*\"\"*F**$)F2\"\"'F*F**&F%F*)F+F:F*F**(F)F*)F2\"\"%F*F+F* F**(\"#[F*F=F*F1F*F**&FIF*F9F*F&*(F8F*F+F*F2F*F**&FAF*FHF*F&*&\"#JF*F1 F*F**&\"#!)F*F=F*F&F*,*F:F&*&F3F*F2F*F**$F1F*F**&FIF*F+F*F*F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A5:=eval(A4,g=%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A5G,8*&)%\"yG\"\"#\"\"\",&F(F*%\"xG!\"\"F *F**$)F,\"\"&F*F-*(F)F*)F,\"\"$F*F(F*F**(%\"aGF*)F,\"\"%F*F(F*F**(,&F5 F-F*F-F*)F,F)F*F'F*F**(%\"cGF*F2F*F'F*F**(,**&#F*F7F**$)F5F)F*F*F-F " 0 "" {MPLTEXT 1 0 11 " factor(A5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$**\"#k!\"\",2*(\"\"% \"\"\"%\"yGF*%\"xGF*F&*(F)F*%\"cGF*)F+\"\"#F*F**(F0F*F/F*%\"aGF*F**&F/ F*)F2F0F*F**&\"\")F*)F,F0F*F&**F)F*F,F*F+F*F2F*F**&F6F*F+F*F**&\"\"$F* F/F*F&F*,V*(F;F*F,F*F/F*F&*&\"#CF*)F,F;F*F**&F?F*F/F*F**(\"#7F*F+F*F7F *F&**F6F*F/F*F,F*F2F*F**(\"#KF*F.F*F/F*F&*(\"#;F*F/F*F2F*F&**\"\"'F*F/ F*F,F*F4F*F&*,F6F*F.F*F/F*F,F*F4F*F**,FHF*F.F*F+F*F7F*F2F*F**(F6F*F/F* F4F*F&**F)F*F+F*F7F*F2F*F&*(F/F*F,F*)F2F)F*F***F)F*F+F*F7F*)F2F;F*F*** F6F*F+F*F,F*F4F*F***FCF*F+F*F7F*F4F*F**(F6F*F@F*F4F*F&**FHF*F,F*F/F*)F .F0F*F***FFF*F.F*F+F*F,F*F***FHF*F.F*F+F*F7F*F**(F%F*%\"hGF*)F+F;F*F&* (F?F*F+F*F,F*F&**FHF*F,F*F+F*F2F*F***F6F*F/F*F,F*F.F*F&*(FFF*F.F*F@F*F &*(FHF*F@F*F2F*F&F*,*F;F&*&F0F*F2F*F**$F4F*F**&F)F*F.F*F*F&F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "polynomial factors [5]" }}}}{MARK "32 0 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }