{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 0 149 "A:=y^2*(x-y)-2*x^3*y+x^5+0* x^6+0*x^4*y+1*x^2*y^2+d*x^5*y+e*x^3*y^2+f*x*y^3+g*x^4*y^2+h*x^2*y^3+j* y^4+k*x^3*y^3+l*x*y^4+m*x^2*y^4+n*y^5+p*x*y^5+q*y^6;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F *)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F**(%\" eGF*F/F*F'F*F**(%\"fGF*F,F*)F(F0F*F**(%\"gGF*)F,\"\"%F*F'F*F**(%\"hGF* F5F*F " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,**&%\"qG\"\"\")%#_ ZG\"\"$F+F+*&%\"nGF+)F-\"\"#F+F+F+!\"\"*&%\"jGF+F-F+F+,&*$)F$F2F+F+*&) F$F.F+-F&6#,,F-F3%\"fGF+%\"dGF+*$F1F+F+%\"eGF+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "expand((1)-4*(f+d+e));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"\"F$*&\"\"%F$%\"eGF$!\"\"*&F&F$%\"fGF$F(*&F&F$%\"dGF$F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A1:=eval(A,f=1/4*(1-4*e-4* d));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A1G,B*&)%\"yG\"\"#\"\"\",&% \"xGF*F(!\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**( %\"dGF*F2F*F(F*F**(%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F *F**(%\"gGF*)F,F=F*F'F*F**(%\"hGF*F5F*F>F*F**&%\"jGF*)F(F=F*F**(%\"kGF *F/F*F>F*F**(%\"lGF*F,F*FFF*F**(%\"mGF*F5F*FFF*F**&%\"nGF*)F(F3F*F**(% \"pGF*F,F*FOF*F**&%\"qGF*)F(\"\"'F*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 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,**&%\"qG\"\"\")%#_ZG\"\"$F+F+*&%\"nGF+)F-\"\"#F +F+F+!\"\"*&%\"jGF+F-F+F+,(*(\"%'4%F3,.F+F+*&\"\"%F+%\"eGF+F+*&\"\")F+ %\"gGF+F3*&F>F+%\"dGF+F+*&F>F+F5F+F3*&F>F+%\"hGF+F3F;*&F$F+,.#F+F>F+*& F2F3F " 0 "" {MPLTEXT 1 0 31 "A2:=eval(A1,j=1/8+1/ 2*e-g+d-h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A2G,B*&)%\"yG\"\"#\" \"\",&%\"xGF*F(!\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F )F*F**(%\"dGF*F2F*F(F*F**(%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F *)F(F0F*F**(%\"gGF*)F,F=F*F'F*F**(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F -F9F*F*F@F-F7F*FCF-F*)F(F=F*F**(%\"kGF*F/F*F>F*F**(%\"lGF*F,F*FIF*F**( %\"mGF*F5F*FIF*F**&%\"nGF*)F(F3F*F**(%\"pGF*F,F*FRF*F**&%\"qGF*)F(\"\" 'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3 ]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=0,y,0);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%% \"xG,(*$)F$\"\"#\"\"\"F)*&F(!\"\"F$\"\"$F)*&)F$\"\"%F)-%'RootOfG6#,4*& \"#;F))%#_ZGF(F)F)*&,(*&F5F)%\"eGF)F+*&\"#KF)%\"dGF)F+\"#?F+F)F7F)F)*& \"\")F)F;F)F)*&F5F)%\"gGF)F+\"\"&F)*&F?F)F>F)F)*&FAF)%\"hGF)F+*&F5F)% \"kGF)F)*&F5F)%\"lGF)F)F)F)-F16#,*FAF+*(FAF)%\"qGF))F7F,F)F)*(FAF)%\"n GF)F6F)F)*&,,F)F)*&FAF)FCF)F+*&FAF)F>F)F)*&FAF)FGF)F+*&F/F)F;F)F)F)F7F )F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "expand((-16*e-32*d-20)^2-4*16*(8*e- 16*g+5+20*d-8*h+16*k+16*l));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*&\" $c#\"\"\")%\"eG\"\"#F&F&*(\"%C5F&F(F&%\"dGF&F&*&\"$G\"F&F(F&F&*&F+F&)F ,F)F&F&\"#!)F&*&F+F&%\"gGF&F&*&\"$7&F&%\"hGF&F&*&F+F&%\"kGF&!\"\"*&F+F &%\"lGF&F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "A3:=eval(A2,l =1/1024*(256*e^2+1024*e*d+128*e+1024*d^2+80+1024*g+512*h-1024*k));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A3G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F( !\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F 2F*F(F*F**(%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F*F**(%\" gGF*)F,F=F*F'F*F**(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F-F9F*F*F@F-F7F* FCF-F*)F(F=F*F**(%\"kGF*F/F*F>F*F**(,2*&F=F-F9F)F**&F9F*F7F*F**&FGF-F9 F*F**$)F7F)F*F*#F3\"#kF*F@F**&F)F-FCF*F*FKF-F*F,F*FIF*F**(%\"mGF*F5F*F IF*F**&%\"nGF*)F(F3F*F**(%\"pGF*F,F*FZF*F**&%\"qGF*)F(\"\"'F*F*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "puiseux(A3,x=0,y,0,T);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG%\"TG/%\"yGF'7$/F&,$*(\"#K! \"\",<\"\"$\"\"\"*&\"\"%F2%\"eGF2F2*&\"#;F2%\"gGF2F2*&F.F2%\"nGF2F/*&F .F2%\"mGF2F/*&F7F2%\"kGF2F2*&\"#7F2%\"hGF2F2*(F7F2F5F2%\"dGF2F/*&F.F2) FC\"\"#F2F/*(F.F2F8F2F5F2F2*(\"#kF2F8F2FCF2F2*(F7F2FAF2F5F2F2*(F.F2FAF 2FCF2F2F2F'FFF2/F),**(\")KWbLF/F0\"\"&F'\"\"*F2**\"(3')Q)F/F0F4,(*&\" \")F2FCF2F2FPF2*&F4F2F5F2F2F2F'FVF2*(\"&Ob'F/F0F1F'\"\"'F2*(\"%C5F/F0F FF'F4F27$F%/F)-%'RootOfG6#,*FVF/*(FVF2%\"qGF2)%#_ZGF1F2F2*(FVF2F:F2)F` oFFF2F2*&,,F2F2*&FVF2F8F2F/*&FVF2FCF2F2*&FVF2FAF2F/*&F4F2F5F2F2F2F`oF2 F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [8]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "A4:=eval(A3,k=-1/16*(3+4*e+16*g-32* n-32*m+12*h-16*e*d-32*d^2+32*g*e+64*g*d+16*h*e+32*h*d));" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%#A4G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F** (F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F** (%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F*F**(%\"gGF*)F,F=F *F'F*F**(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F-F9F*F*F@F-F7F*FCF-F*)F(F =F*F**(,:#F0\"#;F-*&F=F-F9F*F-F@F-*&F)F*%\"nGF*F**&F)F*%\"mGF*F**(F0F* F=F-FCF*F-*&F9F*F7F*F**&F)F*)F7F)F*F**(F)F*F@F*F9F*F-*(F=F*F@F*F7F*F-* &FCF*F9F*F-*(F)F*FCF*F7F*F-F*F/F*F>F*F**(,:*&F=F-F9F)F**(F0F*FGF-F9F*F **$FVF*F-#\"#<\"#kF**&F)F*F@F*F**(F3F*F=F-FCF*F**&F)F*FPF*F-*&F)F*FRF* F-*(F)F*F@F*F9F*F**(F=F*F@F*F7F*F*FYF**(F)F*FCF*F7F*F*F*F,F*FIF*F**(FR F*F5F*FIF*F**&FPF*)F(F3F*F**(%\"pGF*F,F*FfoF*F**&%\"qGF*)F(\"\"'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A4,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,*\"\")!\"\"*(F)\" \"\"%\"qGF,)%#_ZG\"\"$F,F,*(F)F,%\"nGF,)F/\"\"#F,F,*&,,F,F,*&F)F,%\"gG F,F**&F)F,%\"dGF,F,*&F)F,%\"hGF,F**&\"\"%F,%\"eGF,F,F,F/F,F,,**$)F$F4F ,F,*&F4F*F$F0F,*&)F$F>F,,(#\"\"&F)F,*&F4F*F?F,F,F:F,F,F,*&)F$FHF,-F&6# ,hn\"$P#F,*(\"#kF,F:F,)F?F4F,F**&\"$/&F,F?F,F,*(\"$c#F,F?F,)F:F4F,F**& \"$[%F,F8F,F,*&FVF,%\"pGF,F,*&\"$'zF,F:F,F,*&FQF,F2F,F**&\"$#>F,%\"mGF ,F**(\"$7&F,F " 0 "" {MPLTEXT 1 0 278 "discrim(237-64*d*e^2+504*e- 256*e*d^2+448*g+256*p+796*d-64*n-192*m+512*h*d^2-256*m*e-512*m*d-256*n *e-512*n*d+1024*g*d^2+512*h*d*e+256*g*e^2+128*h*e^2+1024*g*e*d+200*h+2 56*_Z^2+272*e^2+800*e*d+512*d^2+(-512*e-512-512*g-768*d-256*h)*_Z+704* g*e+1408*g*d+320*h*e+640*h*d-256*d^3,_Z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,jn\"&c%>\"\"\"*(\"&Ob'F%%\"dGF%)%\"eG\"\"#F%F%*&\"%#>) F%F*F%F%*(\"'W@EF%F*F%)F(F+F%F%*&F'F%%\"gGF%F%*&F/F%%\"pGF%!\"\"*&\"&s 'GF%F(F%F5*&F'F%%\"nGF%F%*&\"'3m>F%%\"mGF%F%*(\"')GC&F%%\"hGF%F0F%F5*( F/F%FF%FF%F9F%F(F%F%*(\"(w&[ 5F%F2F%F0F%F5**F>F%F?F%F(F%F*F%F5*(F/F%F2F%F)F%F5*(\"'s58F%F?F%F)F%F5* *FEF%F2F%F*F%F(F%F5*&\"&Wt&F%F?F%F%*&F/F%)F2F+F%F%*(F/F%F2F%F?F%F%*&F' F%)F?F+F%F%*&\"&%Q;F%F)F%F5*(\"&oF$F%F*F%F(F%F5*&F'F%F0F%F%*(F;F%F2F%F *F%F5*(\"'g`lF%F2F%F(F%F5*(F'F%F?F%F*F%F5*(F/F%F?F%F(F%F5*&F/F%)F(\"\" $F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 345 "A5:=eval(A4,p=1/2 62144*(19456+65536*d*e^2+8192*e+262144*e*d^2+65536*g-28672*d+65536*n+1 96608*m-524288*h*d^2+262144*m*e+524288*m*d+262144*n*e+524288*n*d-10485 76*g*d^2-524288*h*d*e-262144*g*e^2-131072*h*e^2-1048576*g*e*d+57344*h+ 262144*g^2+262144*g*h+65536*h^2-16384*e^2-32768*e*d+65536*d^2-196608*g *e-655360*g*d-65536*h*e-262144*h*d+262144*d^3));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A5G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F*)F ,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F**(%\"eGF *F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F*F**(%\"gGF*)F,F=F*F'F*F* *(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F-F9F*F*F@F-F7F*FCF-F*)F(F=F*F**( ,:#F0\"#;F-*&F=F-F9F*F-F@F-*&F)F*%\"nGF*F**&F)F*%\"mGF*F**(F0F*F=F-FCF *F-*&F9F*F7F*F**&F)F*)F7F)F*F**(F)F*F@F*F9F*F-*(F=F*F@F*F7F*F-*&FCF*F9 F*F-*(F)F*FCF*F7F*F-F*F/F*F>F*F**(,:*&F=F-F9F)F**(F0F*FGF-F9F*F**$FVF* F-#\"#<\"#kF**&F)F*F@F*F**(F3F*F=F-FCF*F**&F)F*FPF*F-*&F)F*FRF*F-*(F)F *F@F*F9F*F**(F=F*F@F*F7F*F*FYF**(F)F*FCF*F7F*F*F*F,F*FIF*F**(FRF*F5F*F IF*F**&FPF*)F(F3F*F**(,hn*(F=F-F7F*F9F)F**&\"#KF-F9F*F**&F9F*FVF*F**&F =F-F@F*F**(\"\"(F*F\\oF-F7F*F-*&F=F-FPF*F**(F0F*F=F-FRF*F**(F)F*FCF*FV F*F-*&FRF*F9F*F**(F)F*FRF*F7F*F**&FPF*F9F*F**(F)F*FPF*F7F*F**(F=F*F@F* FVF*F-**F)F*FCF*F7F*F9F*F-*&F@F*)F9F)F*F-*(F)F-FCF*F9F)F-**F=F*F@F*F9F *F7F*F-*(F_pF*F[pF-FCF*F**$)F@F)F*F**&F@F*FCF*F**&F=F-FCF)F*#\"#>\"$c# F**&FMF-F9F)F-*(FGF-F9F*F7F*F-*&F=F-F7F)F***F0F*F=F-F@F*F9F*F-**F3F*F) F-F@F*F7F*F-*(F=F-FCF*F9F*F-*&FCF*F7F*F-*$)F7F0F*F*F*F,F*FfoF*F**&%\"q GF*)F(\"\"'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate pol ynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "puiseux(A5,x =0,y,0,T);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG,$*(\"$7&!\"\" ,^o\"#jF**&\"$/\"\"\"\"%\"eGF/F**&\"$O\"F/%\"gGF/F**&\"#'*F/%\"dGF/F** &\"$G\"F/%\"nGF/F**&\"$?$F/%\"mGF/F**(F)F/%\"hGF/)F6\"\"#F/F**(\"$c#F/ FF/F6F/F0F/F***\"%C5F /F>F/F0F/F3F/F/*(F8F/F3F/)F0F@F/F/*&F)F/%\"qGF/F/*&\"$W\"F/F>F/F**&FBF /)F3F@F/F/*(F8F/F3F/F>F/F/*(FGF/FF/F**(FBF/)F>F@F /F0F/F/*(FGF/F9F/F3F/F**(F)F/F9F/F>F/F**(FGF/FOF/F0F/F/*(F)F/FTF/F6F/F /*(\"%[?F/FOF/F6F/F/**FZF/F>F/F6F/F3F/F/*&\"#[F/FIF/F**(F8F/F0F/F6F/F* *&F8F/F?F/F**(F8F/F3F/F0F/F/*(FBF/F3F/F6F/F/*(\"#kF/F>F/F0F/F**(F]oF/F >F/F6F/F*F/%\"TGF@F*/%\"yG,,*(\"2%)>[4&)R9!=F*F+\"\"'F_o\"#6F/**\"/kw< W(o.(F*F+\"\"&,,F@F/*&F@F/F0F/F/*&\"\"$F/F6F/F/*&F@F/F3F/F/F>F/F/F_o\" #5F***\"-))Q\"ev\\&F*F+\"\"%,(*&\"\")F/F6F/F/FioF/*&FbpF/F0F/F/F/F_oFe pF/*(\"*caVo#F*F+F]pF_oFeoF**(\"'W@EF*F+F@F_oFbpF/7$/F&F_o/FaoF_o7$F\\ q/Fao-%'RootOfG6#,*FepF**(FepF/FKF/)%#_ZGF]pF/F/*(FepF/F9F/)FfqF@F/F/* &,,F/F/*&FepF/F3F/F**&FepF/F6F/F/*&FepF/F>F/F**&FbpF/F0F/F/F/FfqF/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [8]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "A6:=eval(A5,q=-1/512*(-63-104*e-13 6*g-96*d-128*n-320*m-512*h*d^2-256*m*e+512*n*d-512*g*d^2-256*h*d*e+102 4*h*e*g+128*g*e^2-144*h+256*g^2+128*g*h-1024*m*g-512*m*h+256*h^2*e-102 4*n*g-512*n*h+1024*g^2*e+512*h^2*d+2048*g^2*d+2048*h*d*g-48*e^2-128*e* d-128*d^2+128*g*e+256*g*d-64*h*e-64*h*d));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A6G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F*)F ,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F**(%\"eGF *F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F*F**(%\"gGF*)F,F=F*F'F*F* *(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F-F9F*F*F@F-F7F*FCF-F*)F(F=F*F**( ,:#F0\"#;F-*&F=F-F9F*F-F@F-*&F)F*%\"nGF*F**&F)F*%\"mGF*F**(F0F*F=F-FCF *F-*&F9F*F7F*F**&F)F*)F7F)F*F**(F)F*F@F*F9F*F-*(F=F*F@F*F7F*F-*&FCF*F9 F*F-*(F)F*FCF*F7F*F-F*F/F*F>F*F**(,:*&F=F-F9F)F**(F0F*FGF-F9F*F**$FVF* F-#\"#<\"#kF**&F)F*F@F*F**(F3F*F=F-FCF*F**&F)F*FPF*F-*&F)F*FRF*F-*(F)F *F@F*F9F*F**(F=F*F@F*F7F*F*FYF**(F)F*FCF*F7F*F*F*F,F*FIF*F**(FRF*F5F*F IF*F**&FPF*)F(F3F*F**(,hn*(F=F-F7F*F9F)F**&\"#KF-F9F*F**&F9F*FVF*F**&F =F-F@F*F**(\"\"(F*F\\oF-F7F*F-*&F=F-FPF*F**(F0F*F=F-FRF*F**(F)F*FCF*FV F*F-*&FRF*F9F*F**(F)F*FRF*F7F*F**&FPF*F9F*F**(F)F*FPF*F7F*F**(F=F*F@F* FVF*F-**F)F*FCF*F7F*F9F*F-*&F@F*)F9F)F*F-*(F)F-FCF*F9F)F-**F=F*F@F*F9F *F7F*F-*(F_pF*F[pF-FCF*F**$)F@F)F*F**&F@F*FCF*F**&F=F-FCF)F*#\"#>\"$c# F**&FMF-F9F)F-*(FGF-F9F*F7F*F-*&F=F-F7F)F***F0F*F=F-F@F*F9F*F-**F3F*F) F-F@F*F7F*F-*(F=F-FCF*F9F*F-*&FCF*F7F*F-*$)F7F0F*F*F*F,F*FfoF*F**&,\\o *(\"#8F*F\\oF-F9F*F**(F[oF*F\\oF-F@F*F**(F0F*FMF-F7F*F**&F=F-FPF*F**(F 3F*FGF-FRF*F**&FCF*FVF*F**(F)F-FRF*F9F*F**&FPF*F7F*F-*&F@F*FVF*F***F)F -FCF*F7F*F9F*F***F)F*FCF*F9F*F@F*F-*(F=F-F@F*F9F)F-*(\"\"*F*F[pF-FCF*F **&F)F-F@F)F-*(F=F-F@F*FCF*F-#\"#j\"$7&F**(F)F*FRF*F@F*F**&FRF*FCF*F** (F)F-FCF)F9F*F-*(F)F*FPF*F@F*F**&FPF*FCF*F**(F)F*F_qF*F9F*F-*&)FCF)F*F 7F*F-*(F=F*F_qF*F7F*F-**F=F*FCF*F7F*F@F*F-*(F0F*F[pF-F9F)F**(F=F-F9F*F 7F*F**&F=F-F7F)F**(F=F-F@F*F9F*F-*(F)F-F@F*F7F*F-*(FGF-FCF*F9F*F**(FGF -FCF*F7F*F*F*)F(\"\"'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reev aluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pu iseux(A6,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOf G6#,*\"$7&\"\"\"*&,\\o\"#j!\"\"*&\"$/\"F*%\"eGF*F.*&\"$O\"F*%\"gGF*F.* &\"#'*F*%\"dGF*F.*&\"$G\"F*%\"nGF*F.*&\"$?$F*%\"mGF*F.*(F)F*%\"hGF*)F7 \"\"#F*F.*(\"$c#F*F=F*F1F*F.*(F)F*F:F*F7F*F**(F)F*F4F*F@F*F.**FCF*F?F* F7F*F1F*F.**\"%C5F*F?F*F1F*F4F*F**(F9F*F4F*)F1FAF*F**&\"$W\"F*F?F*F.*& FCF*)F4FAF*F**(F9F*F4F*F?F*F**(FHF*F=F*F4F*F.*(F)F*F=F*F?F*F.*(FCF*)F? FAF*F1F*F**(FHF*F:F*F4F*F.*(F)F*F:F*F?F*F.*(FHF*FNF*F1F*F**(F)F*FSF*F7 F*F**(\"%[?F*FNF*F7F*F***FYF*F?F*F7F*F4F*F**&\"#[F*FJF*F.*(F9F*F1F*F7F *F.*&F9F*F@F*F.*(F9F*F4F*F1F*F**(FCF*F4F*F7F*F**(\"#kF*F?F*F1F*F.*(F\\ oF*F?F*F7F*F.F*)%#_ZG\"\"$F*F**(F)F*F:F*)F_oFAF*F.*&,,*&F)F*F?F*F**&F) F*F7F*F.F\\oF.*&FCF*F1F*F.*&F)F*F4F*F*F*F_oF*F*,,*$)F$FAF*F**&FAF.F$F` oF**&)F$\"\"%F*,(#\"\"&\"\")F**&FAF.F1F*F*F7F*F*F**&)F$FbpF*,,F*F*F1F* *(F`oF*FAF.F7F*F*F4F**&FAF.F?F*F*F*F**&)F$\"\"'F*-F&6#,hr\"%RfF**(\"&' HBF*F7F*FJF*F**&\"&7Y\"F*F1F*F**(\"&s9%F*F1F*F@F*F**&\"&CI\"F*F4F*F**& \"&/6#F*F7F*F**&\"%7pF*F:F*F**&\"%siF*F=F*F**(\"%'4%F*F?F*F@F*F.*(\"%# >)F*F=F*F1F*F**(\"&)G7F*F=F*F7F*F**(\"%/()F*F:F*F1F*F**(FdrF*F:F*F7F*F **(\"&S-\"F*F4F*F@F*F.**\"%WhF*F?F*F7F*F1F*F.**FirF*F?F*F1F*F4F*F.**F[ sF*F?F*FJF*F7F*F.*(\"%3YF*F4F*FJF*F.*(\"%/BF*F?F*FJF*F.**\"&7L\"F*F4F* F1F*F7F*F.*&\"%cqF*F?F*F**(F`rF*F7F*)F1F`oF*F***FdrF*F?F*F1F*F@F*F.*&F YF*FboF*F**&\"%+kF*FNF*F**(\"%cmF*F4F*F?F*F**&\"%G\"%orF.*(FYF*F?F*F1F*F**(FbrF*F4F*F7F*F**( F`rF*F4F*F1F*F**(FbrF*F1F*F7F*F.*(F`rF*F?F*F7F*F**&FbrF*F4F*F.*&FdrF*F 7F*F.*&F_sF*F?F*F.*&FfrF*F1F*F.*&F`rF*F=F*F.*&FYF*FJF*F.*&FbrF*F@F*F.* &F`rF*F:F*F.F*F_oF*F**&F`vF*FcuF*F**&\"%)G%F*FgsF*F*F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 758 "discrim(5939+23296*d*e^2+14612*e+41472*e*d^2+13024 *g+21104*d+6912*n+6272*m-4096*h*d^2+8192*m*e+12288*m*d+8704*n*e+12288* n*d-10240*g*d^2-6144*h*d*e-10240*h*e*g-6144*h*e^2*d-4608*g*e^2-2304*h* e^2-13312*g*e*d+7056*h+4096*d*e^3-12288*h*e*d^2+2048*_Z^2+6400*g^2+665 6*g*h+1728*h^2+2048*m*e^2+8192*m*d^2-1024*h*e^3+8192*m*g+4096*m*h-2816 *h^2*e+10240*n*g+5120*n*h-9216*g^2*e-5120*h^2*d-16384*g^2*d-18432*h*d* g+12288*d^2*e^2+16384*e*d^3+8192*d^4+512*e^4+12464*e^2+39808*e*d+32128 *d^2-12288*g*e^2*d-24576*g*e*d^2+8192*m*e*d+8192*n*e*d+2048*n*e^2+8192 *n*d^2-2048*g*e^3-8192*h*d^3-16384*g*d^3+9344*g*e+10752*g*d+5184*h*e+6 272*h*d+(-7168+2048*h*e+8192*g*d+4096*g*e-8192*e*d+4096*h*d-8192*g-122 88*d-4608*h-8704*e-4096*m-2048*e^2-8192*d^2-4096*n)*_Z+24576*d^3+4288* e^3,_Z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,fq*(\"(_r4#\"\"\"%\"dGF&) %\"eG\"\"#F&F&*&\"(S!z]F&F)F&F&*(\"(/V>%F&F)F&)F'F*F&F&*&\")/zu5F&%\"g GF&F&*&\"(+oF$F&F'F&F&*&F%F&%\"nGF&F&*&\"(K+M(F&%\"mGF&F&*(\"(3')Q)F&% \"hGF&F/F&F&*(F.F&F9F&F)F&F&*(\");sx;F&F2F&F/F&F&**F.F&F " 0 "" {MPLTEXT 1 0 11 "solve(%,n); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6$,4*&\"\")!\"\"%\"hG\"\"\"F(*(\"\"# F&F'F(%\"eGF(F(*&F*F&%\"gGF(F(*&F-F(F+F(F(#F(\"#;F&%\"mGF&*&F'F(%\"dGF (F(*(F*F(F-F(F3F(F(*&\"#kF&,fn\"$]'F&*(\"$7&F(F3F()F+F*F(F&*&\"%S7F(F+ F(F&*(\"%C5F(F+F()F3F*F(F&*&\"%!)GF(F-F(F&*&\"$+)F(F3F(F&*&\"%!G\"F(F1 F(F&*(\"%[?F(F'F(F@F(F&*(F?F(F1F(F+F(F&*(\"%'4%F(F-F(F@F(F&**F?F(F'F(F 3F(F+F(F&*(F:F(F'F(F;F(F&*&\"%!3#F(F'F(F&*&\"%gDF()F-F*F(F&*(\"%3YF(F- F(F'F(F&*&\"%k;F()F'F*F(F&*(FKF(F1F(F-F(F&*(FHF(F1F(F'F(F&*(F:F(FWF(F+ F(F&*(FHF(FRF(F+F(F(*(\"%#>)F(FRF(F3F(F(**FKF(F'F(F3F(F-F(F(*&\"$O(F(F ;F(F&*(FFF(F+F(F3F(F&*&FFF(F@F(F&*(\"%/BF(F-F(F+F(F&*(F^oF(F'F(F+F(F&* (FFF(F'F(F3F(F&*&\"$G\"F()F+\"\"$F(F&#F(F*F(,4*&F%F&F'F(F(*(F*F&F'F(F+ F(F(*&F*F&F-F(F(F.F(#F(F0F&F1F&F2F(*(F*F(F-F(F3F(F(*&F6F&F7FeoF&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 323 "factor(1/8*h+1/2*h*e+1/2*g+ g*e-1/16-m+h*d+2*g*d+1/64*(-650-512*d*e^2-1240*e-1024*e*d^2-2880*g-800 *d-1280*m-2048*h*d^2-1024*m*e-4096*g*d^2-1024*h*d*e-512*h*e^2-2080*h-2 560*g^2-4608*g*h-1664*h^2-4096*m*g-2048*m*h-512*h^2*e+2048*g^2*e+8192* g^2*d+4096*h*d*g-736*e^2-1280*e*d-1280*d^2-2304*g*e-2304*h*e-1280*h*d- 128*e^3)^(1/2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4*&\"\")!\"\"%\"h G\"\"\"F(*(\"\"#F&F'F(%\"eGF(F(*&F*F&%\"gGF(F(*&F-F(F+F(F(#F(\"#;F&%\" mGF&*&F'F(%\"dGF(F(*(F*F(F-F(F3F(F(*&\"#kF&,$*(F*F(,*\"\"&F(*&\"\"%F(F +F(F(*&F0F(F-F(F(*&F%F(F'F(F(F(,:*&F0F()F+F*F(F(*(\"#KF(F'F(F+F(F(*&\" #sF(F+F(F(*(F6F(F+F(F3F(F(*(F6F(F-F(F+F(F&\"#lF(*&\"$G\"F()F3F*F(F(*&F JF(F1F(F(*&\"$/\"F(F'F(F(*&\"#!)F(F3F(F(*&FPF(F-F(F(*(\"$c#F(F-F(F3F(F &F(F&#F(F*F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "Factoring the so lution for n makes it considerably simpler, so we will use the above r esult for the substitution." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A7:=eval(A6,n=%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A7G,B*&)% \"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F **&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F**(%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9 F-F7F-F*F,F*)F(F0F*F**(%\"gGF*)F,F=F*F'F*F**(%\"hGF*F5F*F>F*F**&,,#F* \"\")F**&F)F-F9F*F*F@F-F7F*FCF-F*)F(F=F*F**(,.#F3\"#;F-*&F=F-F9F*F-*&F )F-FCF*F-*&\"#KF-,$*(F)F*,*F3F**&F=F*F9F*F**&FMF*F@F*F**&FGF*FCF*F*F*, :*&FMF*)F9F)F*F**(FQF*FCF*F9F*F**&\"#sF*F9F*F**(\"#kF*F9F*F7F*F**(FinF *F@F*F9F*F-\"#lF**&\"$G\"F*)F7F)F*F**&F]oF*%\"mGF*F**&\"$/\"F*FCF*F**& \"#!)F*F7F*F**&FdoF*F@F*F**(\"$c#F*F@F*F7F*F-F*F-#F*F)F**&F9F*F7F*F**& F)F*F^oF*F*F*F/F*F>F*F**(,0*&F=F-F9F)F**(F0F*FGF-F9F*F**$F^oF*F-#\"#DF inF*F@F*FCF**&FQF-FRFhoF-F*F,F*FIF*F**(F`oF*F5F*FIF*F**&,4*&FGF-FCF*F* *(F)F-FCF*F9F*F**&F)F-F@F*F**&F@F*F9F*F*#F*FMF-F`oF-*&FCF*F7F*F**(F)F* F@F*F7F*F**&FinF-FRFhoF*F*)F(F3F*F**(,hn*(F=F-F7F*F9F)F**&FQF-F9F*F**& F9F*F^oF*F**(F0F*FGF-F@F*F**(\"\"(F*FinF-F7F*F-*&F)F-F`oF*F**(F)F*FCF* F^oF*F-*&F`oF*F9F*F**(F)F*F`oF*F7F*F**(F=F*F@F*F^oF*F-**F)F*FCF*F7F*F9 F*F-*&F@F*FZF*F-*(F)F-FCF*F9F)F-**F=F*F@F*F9F*F7F*F-*&F=F-FCF*F**$)F@F )F*F**&F@F*FCF*F**&F=F-FCF)F**&FMF-F9F)F-*(FGF-F9F*F7F*F-*&F=F-F7F)F** (F)F-F@F*F9F*F-*(F)F*F@F*F7F*F-*(FGF-FCF*F9F*F-**F0F*F=F-FCF*F7F*F-*&F goF-FRFhoF**$)F7F0F*F*#\"#:FgoF**&FepF*F9F*F**(F)F*FepF*F7F*F*F*F,F*F^ qF*F**&,hn*(\"#8F*FinF-F9F*F**(FapF*FinF-F@F*F**(F0F*FMF-F7F*F**(F0F*F GF-F`oF*F**&FCF*F^oF*F**(F)F-F`oF*F9F*F**&F@F*F^oF*F***F)F-FCF*F7F*F9F *F***F)F*FCF*F9F*F@F*F-*(F=F-F@F*F9F)F-*(F3F*FMF-FCF*F**&F)F-F@F)F-*(F =F-F@F*FCF*F-*(F)F*F`oF*F@F*F**&F`oF*FCF*F**(F)F-FCF)F9F*F-*(F)F*FbrF* F9F*F-*&)FCF)F*F7F*F-*(F=F*FbrF*F7F*F-**F=F*FCF*F7F*F@F*F-*(F0F*FQF-F9 F)F**(F=F-F9F*F7F*F**&F=F-F7F)F**(F=F-FCF*F9F*F***F0F*FGF-FCF*F7F*F**& FgoF-FRFhoF*#\"#b\"$7&F**&FepF*F7F*F-*(F)F*FepF*F@F*F**&FepF*FCF*F*F*) F(\"\"'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynom ial [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "puiseux(A7,x=0,y ,0,T);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG%\"TG/%\"yGF'7$F%/ F)-%'RootOfG6#,X\"&g\"G!\"\"*&\"&[K&\"\"\"%\"eGF4F1*&\"&K'pF4%\"gGF4F1 *&\"&Ob'F4%\"dGF4F1*&\"&/$)*F4%\"mGF4F1*(\"'s58F4F>F4F5F4F1*(\"'W@EF4F >F4F;F4F1*(FBF4F8F4)F;\"\"#F4F4*(F:F4F8F4)F5FEF4F4**FBF4F8F4F5F4F;F4F4 *&F:F4%\"hGF4F1*&,`_l\"%DcF4*(\"&3u\"F4F;F4FGF4F4*&\"&+k\"F4F5F4F4*(\" '))=5F4F5F4FDF4F4*&\"&!3oF4F8F4F4*&\"%?NF4F;F4F1*&\"&Si#F4F>F4F4*(\"'[ W5F4FJF4FDF4F4*(\"&#>sF4F>F4F5F4F4*(\"&7X'F4F>F4F;F4F4*(\"%;#*F4F8F4FD F4F1**\"&K_*F4FJF4F;F4F5F4F1**\"')oE'F4FJF4F5F4F8F4F4**\"&_\"\\F4FJF4F GF4F;F4F1*(\"&!3YF4F8F4FGF4F4*(FinF4FJF4FGF4F4**\"'+SQF4F8F4F5F4F;F4F1 *(\"'!)G7F4)FJFEF4FDF4F4*&\"&ko$F4)F>FEF4F4**FaoF4F>F4FJF4F;F4F1**\"'# *H@F4FJF4FGF4F8F4F4*&\"&+K%F4FJF4F4*(\"'G\")oF4F>F4)F8FEF4F4*(\"'_(e%F 4)F8\"\"$F4F5F4F4*(\"(?2J\"F4FgpF4F;F4F1*(\"&oF$F4FdpF4)F5FhpF4F4*(\"% #>)F4F;F4F]qF4F4**FaoF4FJF4F5F4FDF4F4**F=F4FioF4F>F4F5F4F4**\"')o9\"F4 FioF4F8F4FGF4F4**\"(kGd\"F4FJF4F>F4FdpF4F4**\"')GC&F4FJF4FgpF4F5F4F1** F:F4FJF4F5F4)F;FhpF4F1**\"(Gd9$F4FJF4FgpF4F;F4F1**\"&%Q;F4FJF4F;F4F]qF 4F1**F\\qF4FJF4FDF4FGF4F1*(\"(wx'=F4FioF4FdpF4F4*(\"'kOvF4)FJFhpF4F8F4 F4*(FcqF4FcrF4F;F4F1*&\"'#f5\"F4)FJ\"\"%F4F4*&\"';wSF4FdpF4F4**\"'KkyF 4FioF4F;F4F8F4F1*(\"')3t%F4F8F4FJF4F4*&\"'S#Q\"F4FioF4F4*(\"&wX#F4F>F4 F]qF4F4*(F:F4F\\pF4FGF4F4*(F=F4F\\pF4F5F4F4**\"(['z6F4FJF4FdpF4F5F4F4* *FcpF4FJF4F>F4F8F4F4**\"(s%pF4F8F4F4**FeqF4FioF4FdpF4F;F4F1**F@F4F8F4FcrF4F 5F4F4*(\"&!orF4F>F4FGF4F4*(FBF4F>F4FDF4F4*(F]rF4FJF4F]qF4F4*(F_qF4FioF 4F]qF4F4*(\"(!3m>F4FgpF4FJF4F4*(F@F4F>F4FcrF4F4*(F\\qF4FgrF4F5F4F4*(F \\qF4FcrF4FGF4F4*(FBF4FioF4FiqF4F1*(\"(gF4FioF4F>F4F;F4F1**\"'cu9F4FioF4F5F4F;F4F1**F:F4F>F4F GF4FJF4F4**FBF4F\\pF4F5F4F;F4F4**FcqF4F>F4FGF4F;F4F4**F:F4F>F4F]qF4F8F 4F1**FBF4F>F4F5F4FDF4F4**FevF4FdpF4FGF4F;F4F4**FgqF4FdpF4FiqF4F5F4F4** \"(#zT9F4F8F4FiqF4FJF4F1**FgqF4F8F4FiqF4F>F4F1**\"(syS$F4FdpF4FDF4FJF4 F4**FgqF4F8F4FiqF4F5F4F1**\"';KRF4FdpF4FDF4FGF4F4**\"'O.FF4FdpF4F;F4F5 F4F1*(\"'G0:F4F>F4F8F4F4*(F=F4F>F4FJF4F4*(\"';7?F4FioF4F5F4F4*(\"'_*4& F4FdpF4F5F4F4*(\"'w\"y\"F4FioF4F;F4F1*(\"'k7lF4FdpF4F;F4F1**FfwF4F>F4F 5F4FdpF4F4**\"'cqbF4F8F4FDF4FJF4F4**FcqF4F8F4F]qF4F;F4F1**F@F4FdpF4F]q F4F;F4F4**F:F4FdpF4FGF4FJF4F4**\"'CMuF4FJF4F;F4F8F4F1*(\"&#RfF4FDF4FGF 4F4*(\"&?>)F4F5F4FiqF4F4*&F=F4FatF4F4*&\"%/BF4F[uF4F4*(F_qF4FDF4F]qF4F 4*,FfwF4F>F4F5F4F8F4FJF4F4*&\"&S!>F4FGF4F4*(\"%WhF4F5F4F;F4F4*&\"&%e^F 4FDF4F4*,\"'C)*eF4F>F4F5F4F8F4F;F4F1*,F\\sF4F>F4F5F4F8F4FDF4F1*,F:F4Fi oF4F8F4F5F4F;F4F4**F\\qF4FioF4F5F4FDF4F1*&\"''*3sF4)F8FhrF4F4**FfwF4Fd pF4FDF4F5F4F4*(FevF4F\\pF4F;F4F4**F\\sF4F>F4F;F4FdpF4F1*(\"(;w+\"F4Fdp F4FDF4F4*(F@F4F>F4FiqF4F4*(FBF4F\\pF4FDF4F4*,FfwF4F>F4FGF4F8F4F;F4F1*, F:F4F>F4F5F4FJF4F;F4F4*(F\\qF4FiqF4FGF4F4*(F:F4F5F4FatF4F4**FBF4FJF4FD F4F>F4F4**\"')[>$F4F8F4FGF4F;F4F1**\"'#z<%F4F8F4F5F4FDF4F1**\"';%)=F4F >F4F5F4F;F4F4*(\"'K?F4FioF4F4*(\"'C-=F4FcrF4F5F4F4*(\"&;g)F4FioF4 FGF4F4*(F@F4FJF4FatF4F4*,FBF4F8F4FDF4FJF4F5F4F1**FgvF4FJF4F5F4F>F4F4*( \"&K%=F4F8F4F]qF4F1*(FcqF4FJF4FiqF4F1*(\"'g`lF4F8F4FiqF4F1*,\"'SQ;F4F8 F4FGF4FJF4F;F4F1**FBF4FgpF4F5F4F;F4F4*,F\\sF4F8F4FJF4F>F4F;F4F1*(\"'ko 6F4F8F4F5F4F4*(\"'/2?F4F8F4F;F4F1*(\"&+'*)F4FJF4F5F4F4*(FgnF4FJF4F;F4F 1**Fb[lF4F8F4F;F4F>F4F1*(FaxF4FdpF4FGF4F4*,FBF4FdpF4FJF4F5F4F;F4F4*(\" (w&[5F4F>F4FgpF4F4*(FgqF4FbzF4F5F4F1*(\"(_r4#F4FbzF4F;F4F1**\"'o^8F4F8 F4F5F4F>F4F4*&\"&3I%F4FiqF4F4*&\"&'\\5F4F]qF4F4**FevF4F8F4FDF4F>F4F1*, \"'#fA'F4FJF4F5F4F8F4F;F4F1**FaoF4F8F4FGF4F>F4F1F4)%#_ZGFhpF4F4*&,dsFW F4*(\"&Wt&F4F;F4FGF4F4*&\"&O2#F4F5F4F4*(F=F4F5F4FDF4F4*&\"&c%>F4F8F4F1 *&\"&_j$F4F;F4F4*&FjtF4F>F4F4*(F:F4F>F4F5F4F4*(F@F4F>F4F;F4F4*(\"'w$H# F4F8F4FDF4F1**F\\qF4FJF4F;F4F5F4F4*(F\\qF4F8F4FGF4F1*(F_qF4FJF4FGF4F4* *Fd\\lF4F8F4F5F4F;F4F1**FBF4F>F4FJF4F;F4F1**F:F4FJF4FGF4F8F4F4*&\"&o*> F4FJF4F1**FjtF4F;F4,$*&,*\"#5F4*&\"\")F4F5F4F4*&\"#KF4F8F4F4*&\"#;F4FJ F4F4F4,:*&Fd`lF4FGF4F4*(Fb`lF4FJF4F5F4F4*&\"#sF4F5F4F4*(\"#kF4F5F4F;F4 F4*(F[alF4F8F4F5F4F1\"#lF4*&\"$G\"F4FDF4F4*&F_alF4F>F4F4*&\"$/\"F4FJF4 F4*&\"#!)F4F;F4F4*&FdalF4F8F4F4*(\"$c#F4F8F4F;F4F1F4F1#F4FEF8F4F1*(\"% '4%F4FioF4F[`lFhalF4*(F_qF4FdpF4F[`lFhalF4*(FjalF4FDF4F[`lFhalF4**\"%[ ?F4F;F4F[`lFhalF5F4F4**F^blF4FJF4F[`lFhalF5F4F1**FjalF4F8F4F[`lFhalF5F 4F1**FjtF4F8F4F[`lFhalFJF4F4**F_qF4F;F4F[`lFhalFJF4F1*(\"$7&F4F;F4F[`l FhalF1*(FdblF4F5F4F[`lFhalF1*(FdblF4FJF4F[`lFhalF4*&F3F4FdpF4F1*(\"'%y =\"F4F8F4FJF4F1*&\"&S9'F4FioF4F1*&F\\qF4FcrF4F1*&F@F4FgpF4F1*(F:F4F>F4 FGF4F4*(FBF4F>F4FDF4F4*(FBF4FJF4FdpF4F1*(Fd\\lF4F8F4FioF4F1**FBF4FdpF4 F;F4F5F4F4*(F=F4F>F4F8F4F1*(F=F4F>F4FJF4F1*(FaoF4FioF4F5F4F1*(F:F4FdpF 4F5F4F4*(F\\qF4FioF4F;F4F1*(FBF4FdpF4F;F4F4**FBF4F8F4FDF4FJF4F4**FevF4 FJF4F;F4F8F4F4*&F_alF4F[`lFhalF1*&\"&'pHF4FGF4F4*(\"&3U*F4F5F4F;F4F4*& \"&GP(F4FDF4F4*(FBF4FdpF4FDF4F4**FevF4F8F4FGF4F;F4F1**FfwF4F8F4F5F4FDF 4F1**FBF4F>F4F5F4F;F4F4**F@F4FJF4F5F4F>F4F1*(F\\qF4F8F4F]qF4F1*(FBF4F8 F4FiqF4F1*(F_\\lF4F8F4F5F4F1*(FjtF4F8F4F;F4F1*(FjtF4FJF4F5F4F1*(F_qF4F JF4F;F4F4**FBF4F8F4F;F4F>F4F1*(F:F4FdpF4FGF4F4**F@F4F8F4F5F4F>F4F1*&F: F4FiqF4F4*&FjtF4F]qF4F4*,FBF4FJF4F5F4F8F4F;F4F4F4Fa^lF4F4*(FjalF4F;F4F [`lFhalF1*&,bz\"%S')F4*(\"&7*QF4F;F4FGF4F1*&\"&7l\"F4F5F4F4*(F:F4F5F4F DF4F1*&\"'3!R\"F4F8F4F4*&\"&'*G$F4F;F4F1*&\"&CQ\"F4F>F4F1*(\"''\\1\"F4 FJF4FDF4F4*(\"&c]%F4F>F4F5F4F1*(Fd\\lF4F>F4F;F4F1*(\"'+'4%F4F8F4FDF4F4 **FeflF4FJF4F;F4F5F4F4**\"')[v&F4FJF4F5F4F8F4F4**Fe^lF4FJF4FGF4F;F4F4* (Fd\\lF4F8F4FGF4F4*(\"&#*\\)F4FJF4FGF4F4**\"'ovBF4F8F4F5F4F;F4F4*(FevF 4FioF4FDF4F4*&F=F4F\\pF4F1**F:F4F>F4FJF4F;F4F1**FhoF4FJF4FGF4F8F4F4*& \"&/V(F4FJF4F4*(FfwF4F>F4FdpF4F4*(F@F4FgpF4F5F4F1*(F\\sF4FgpF4F;F4F1*( F:F4FdpF4F]qF4F1*(F_qF4F;F4F]qF4F1**F=F4FJF4F5F4FDF4F4**F^blF4F;F4F[`l FhalF8F4F1*(F^blF4FdpF4F[`lFhalF1*(\"%C5F4FDF4F[`lFhalF4**FahlF4F;F4F[ `lFhalF5F4F4**FdblF4FJF4F[`lFhalF5F4F4**FahlF4F8F4F[`lFhalF5F4F1**Fahl F4F8F4F[`lFhalFJF4F1**F^blF4F>F4F5F4F[`lFhalF4**FahlF4F8F4FGF4F[`lFhal F1**FdblF4F;F4F[`lFhalFJF4F4*(F\\qF4FcrF4F;F4F4*(\"$o(F4F;F4F[`lFhalF4 *(\"$K)F4F5F4F[`lFhalF4*(\"%)3\"F4F8F4F[`lFhalF4*(\"%gDF4F[`lFhalF>F4F 4*(\"$%QF4FGF4F[`lFhalF4*(\"%_6F4FJF4F[`lFhalF4*&\"'CiVF4FdpF4F4**F:F4 FioF4F;F4F8F4F1*(\"'ovbF4F8F4FJF4F4*&\"'))e;F4FioF4F4*(F@F4F\\pF4F5F4F 1**F:F4FJF4FdpF4F5F4F4**FfwF4FJF4F>F4F8F4F4**Fb\\lF4FJF4FdpF4F;F4F1**F jalF4FDF4F[`lFhalFJF4F4**FjalF4FDF4F[`lFhalF8F4F4**F_qF4FdpF4F[`lFhalF 5F4F1**F_qF4F8F4F[`lFhalF>F4F4**F]rF4FdpF4F[`lFhalF;F4F1**F^blF4FioF4F [`lFhalF5F4F1**FjalF4FJF4F[`lFhalF>F4F4**FjalF4FioF4F[`lFhalF;F4F1*&Ff rF4FcrF4F4*&FfwF4FgpF4F4*(FgqF4FdpF4FiqF4F1**Fd\\lF4F8F4FioF4F5F4F4*(F bsF4F>F4FGF4F1*(F:F4F>F4FDF4F1*(\"&![?F4FJF4F]qF4F4*(F`uF4FJF4FdpF4F4* (\"'s1aF4F8F4FioF4F4**F@F4FioF4F5F4F;F4F4**F:F4F>F4FGF4FJF4F4**FfwF4Fd pF4FGF4F;F4F1**FBF4F8F4FiqF4FJF4F1**F@F4FdpF4F;F4F5F4F1*(\"''*)3#F4F>F 4F8F4F4*(F[clF4F>F4FJF4F4*(FevF4FioF4F5F4F4*(\"'wF4F5F4F8F4F;F4F4 **F\\sF4FdpF4FDF4F5F4F1*(FBF4F\\pF4F;F4F1**F\\qF4F8F4F]qF4FJF4F1*(Fb\\ lF4FdpF4FDF4F4*,FBF4F>F4F5F4FJF4F;F4F4**FBF4FJF4FDF4F>F4F4**Fh[lF4F8F4 FGF4F;F4F4**\"'!oF$F4F8F4F5F4FDF4F4**F@F4F>F4F5F4F;F4F1*(F=F4F>F4FioF4 F4*(FaoF4FcrF4F5F4F4*(F:F4FioF4FGF4F4*,FfwF4F8F4FDF4FJF4F5F4F1**F:F4FJ F4F5F4F>F4F4*(\"&g4%F4F8F4F]qF4F4*(F:F4FJF4FiqF4F1*(F@F4F8F4FiqF4F1*,F evF4F8F4FGF4FJF4F;F4F1*(\"'o.DF4F8F4F5F4F4*(\"&g`\"F4F8F4F;F4F4*(\"'kG 8F4FJF4F5F4F4*(\"&%=HF4FJF4F;F4F1**FevF4F8F4F;F4F>F4F4*(F\\qF4FdpF4FGF 4F1*,F_qF4F8F4F[`lFhalFJF4F5F4F1*,F]rF4F8F4F[`lFhalFJF4F;F4F1*,F^blF4F ;F4F[`lFhalFJF4F5F4F4**\"'7\\HF4F8F4F5F4F>F4F4*&F_yF4FiqF4F1*&F^blF4F] qF4F4**F\\sF4F8F4FDF4F>F4F4*,Fa_lF4FJF4F5F4F8F4F;F4F4**FevF4F8F4FGF4F> F4F4F4)Fa^lFEF4F4*(F_qF4F8F4F[`lFhalF4*(FjalF4FJF4F[`lFhalF4*&F@F4FdpF 4F1*(F@F4F8F4FJF4F1*&F\\qF4FioF4F1*&FahlF4F[`lFhalF4*&FbsF4FGF4F1*(F:F 4F5F4F;F4F1*&F:F4FDF4F1*(F@F4F8F4F;F4F4*(F:F4FJF4F5F4F1*(F:F4FJF4F;F4F 17$/F&,$*(F^blF1,dp\"$v%F4*(FcilF4F;F4FGF4F4*&\"$g*F4F5F4F4*(FdblF4F5F 4FDF4F4*&\"%+CF4F8F4F4*&\"$+'F4F;F4F4*&\"$S'F4F>F4F4*(FahlF4FJF4FDF4F4 *(FdblF4F>F4F5F4F4*(F^blF4F8F4FDF4F4**FahlF4FJF4F;F4F5F4F4**\"%O:F4FJF 4F5F4F8F4F4*(FdblF4F8F4FGF4F4*(\"$w&F4FJF4FGF4F4**FahlF4F8F4F5F4F;F4F4 *&\"%?;F4FJF4F4**F_alF4F;F4F[`lFhalF8F4F1*(Fb`lF4FDF4F[`lFhalF4**Fb`lF 4F8F4F[`lFhalF5F4F1**Fb`lF4F;F4F[`lFhalFJF4F1*(\"#7F4F5F4F[`lFhalF4*(F d`lF4F8F4F[`lFhalF4*(Fb`lF4F[`lFhalF>F4F4*(\"#CF4FJF4F[`lFhalF4*&\"%;G F4FdpF4F4*(\"%![%F4F8F4FJF4F4*&FiamF4FioF4F4*&FgalF4FcrF4F4*(FahlF4FJF 4FdpF4F4*(FahlF4F8F4FioF4F4*(F^blF4F>F4F8F4F4*(FahlF4F>F4FJF4F4*(F[ilF 4FioF4F5F4F4*(FdblF4FioF4F;F4F4*(F^blF4FdpF4F;F4F1*&\"#:F4F[`lFhalF4*& \"$C'F4FGF4F4*(F\\amF4F5F4F;F4F4*&FcamF4FDF4F4*(FailF4F8F4F5F4F4*(\"%! G\"F4F8F4F;F4F4*(\"%;?F4FJF4F5F4F4*(F_dmF4FJF4F;F4F4*&F_alF4F]qF4F4F4F 'FEF4/F),.*(\"9s#QokG=XFd6^\"F1Fh`m\"\"(F'\"#8F4**\"7'p8_kpG[mBs%F1Fh` m\"\"',4\"$3\"F4*&\"$#>F4F;F4F4*&\"$O\"F4F5F4F4*&\"$g\"F4F8F4F4*&FdalF 4FJF4F4*&Fb`lF4FGF4F4*&F_alF4FDF4F4*(F_alF4F5F4F;F4F4*$F[`lFhalF4F4F'F ebmF4**\"2Oz#z.%fd?(F1Fh`m\"\"&,,FEF4*&FEF4F5F4F4*&FhpF4F;F4F4*&FEF4F8 F4F4FJF4F4F'F^`lF4**\"0G`N)[P29F1Fh`mFhr,(*&F``lF4F;F4F4F\\fmF4*&FhrF4 F5F4F4F4F'F``lF4*(\",%=p)zr\"F1Fh`mFhpF'F\\emF4*(\"(/V>%F1Fh`mFEF'FhrF 4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [8]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1309 "factor(475+384*d*e^2+960*e+512*e* d^2+2400*g+600*d+640*m+1024*h*d^2+512*m*e+2048*g*d^2+1024*h*d*e+1536*h *e*g+512*g*e^2+576*h*e^2+1024*g*e*d+1620*h-128*d*(-(10+8*e+32*g+16*h)* (16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+80*d+80*g-256 *g*d))^(1/2)*g+32*d^2*(-(10+8*e+32*g+16*h)*(16*e^2+32*h*e+72*e+64*e*d- 64*g*e+65+128*d^2+128*m+104*h+80*d+80*g-256*g*d))^(1/2)-32*g*(-(10+8*e +32*g+16*h)*(16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+8 0*d+80*g-256*g*d))^(1/2)*e-32*d*(-(10+8*e+32*g+16*h)*(16*e^2+32*h*e+72 *e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+80*d+80*g-256*g*d))^(1/2)*h+12 *e*(-(10+8*e+32*g+16*h)*(16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+1 28*m+104*h+80*d+80*g-256*g*d))^(1/2)+16*g*(-(10+8*e+32*g+16*h)*(16*e^2 +32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+80*d+80*g-256*g*d))^ (1/2)+32*(-(10+8*e+32*g+16*h)*(16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128 *d^2+128*m+104*h+80*d+80*g-256*g*d))^(1/2)*m+24*h*(-(10+8*e+32*g+16*h) *(16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+80*d+80*g-25 6*g*d))^(1/2)+2816*g^2+4480*g*h+1536*h^2+256*h^3+1024*h*g^2+1024*g*h^2 +2048*m*g+1024*m*h+768*h^2*e+512*h^2*d-2048*g^2*d+15*(-(10+8*e+32*g+16 *h)*(16*e^2+32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+128*m+104*h+80*d+80*g -256*g*d))^(1/2)+624*e^2+960*e*d+640*d^2+2560*g*e+1280*g*d+2016*h*e+12 80*h*d+128*e^3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,dp\"$v%\"\"\"*(\" $%QF%%\"dGF%)%\"eG\"\"#F%F%*&\"$g*F%F*F%F%*(\"$7&F%F*F%)F(F+F%F%*&\"%+ CF%%\"gGF%F%*&\"$+'F%F(F%F%*&\"$S'F%%\"mGF%F%*(\"%C5F%%\"hGF%F0F%F%*(F /F%F8F%F*F%F%*(\"%[?F%F3F%F0F%F%**F:F%F;F%F(F%F*F%F%**\"%O:F%F;F%F*F%F 3F%F%*(F/F%F3F%F)F%F%*(\"$w&F%F;F%F)F%F%**F:F%F3F%F*F%F(F%F%*&\"%?;F%F ;F%F%*&\"%;GF%)F3F+F%F%*(\"%![%F%F3F%F;F%F%*&FAF%)F;F+F%F%*&\"$c#F%)F; \"\"$F%F%*(F:F%F;F%FJF%F%*(F:F%F3F%FNF%F%*(F>F%F8F%F3F%F%*(F:F%F8F%F;F %F%*(\"$o(F%FNF%F*F%F%*(F/F%FNF%F(F%F%*(F>F%FJF%F(F%!\"\"*&\"$C'F%F)F% F%*(F-F%F*F%F(F%F%*&F7F%F0F%F%*(\"%gDF%F3F%F*F%F%*(\"%!G\"F%F3F%F(F%F% *(\"%;?F%F;F%F*F%F%*(F]oF%F;F%F(F%F%*&\"#:F%,$*(F+F%,*\"\"&F%*&\"\"%F% F*F%F%*&\"#;F%F3F%F%*&\"\")F%F;F%F%F%,:*&FjoF%F)F%F%*(\"#KF%F;F%F*F%F% *&\"#sF%F*F%F%*(\"#kF%F*F%F(F%F%*(FdpF%F3F%F*F%Fen\"#lF%*&\"$G\"F%F0F% F%*&FhpF%F8F%F%*&\"$/\"F%F;F%F%*&\"#!)F%F(F%F%*&F]qF%F3F%F%*(FPF%F3F%F (F%FenF%Fen#F%F+F%*&FhpF%)F*FRF%F%*(\"#CF%F;F%FcoF`qF%*(F`pF%FcoF`qF8F %F%*(FjoF%F3F%FcoF`qF%*(\"#7F%F*F%FcoF`qF%*(F`pF%F0F%FcoF`qF%**FhpF%F( F%FcoF`qF3F%Fen**F`pF%F(F%FcoF`qF;F%Fen**F`pF%F3F%FcoF`qF*F%Fen" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 412 "We factor to simplify the radical term. Then, we set the radical equal to zero and reevaluate the polyn omial to eliminate the radical term. In so doing, we simplify the poly nomial, making it easier for Maple to compute the next Puiseux. In the above, there are two factors under the radical, so we have two cases \+ to consider. In case B we consider the shorter factor, and in case C w e consider the longer factor." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "B:=eval(A7,e=-1/4*(5+16*g+8*h));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"BG,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F*)F,\"\"$F*F (F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F2F*F(F*F**(,(#F3\"\"%F-*&F ;F*%\"gGF*F-*&F)F*%\"hGF*F-F*F/F*F'F*F**(,*#F0F)F**&F;F*F=F*F**&F)F*F? F*F*F7F-F*F,F*)F(F0F*F**(F=F*)F,F;F*F'F*F**(F?F*F5F*FEF*F**&,*#F*F)F-* &F0F*F=F*F-*&F)F*F?F*F-F7F*F*)F(F;F*F**(,(F=F**&F9F*F7F*F**&F)F*)F7F)F *F*F*F/F*FEF*F**(,,*&F;F-F9F)F*#F3\"#kF-*&F)F-F=F*F-*&F;F-F?F*F**$FSF* F-F*F,F*FNF*F**(%\"mGF*F5F*FNF*F**&,2*&\"\")F-F?F*F**(F)F-F?F*F9F*F**& F)F-F=F*F**&F=F*F9F*F*#F*\"#;F-FgnF-*&F?F*F7F*F**(F)F*F=F*F7F*F*F*)F(F 3F*F**(,Z#F3\"$c#F**&F;F-F=F*F**(\"\"(F*FXF-F7F*F-*&F)F-FgnF*F**(F)F*F ?F*FSF*F-*(F)F*FgnF*F7F*F**(F;F*F=F*FSF*F-*(F0F*F`oF-F?F*F**$)F=F)F*F* *&F=F*F?F*F**&F;F-F?F)F**&F;F-F7F)F**(F)F*F=F*F7F*F-**F0F*F;F-F?F*F7F* F-*$)F7F0F*F**(F)F*FinF*F7F*F**&FinF*F9F*F**(F)F-F?F*F9F)F-*&FgnF*F9F* F**&F=F*)F9F)F*F-*&F9F*FSF*F**(F;F-F7F*F9F)F**&F`oF-F9F)F-*(F[oF-F?F*F 9F*F-*(F[oF-F9F*F7F*F-*(F)F-F=F*F9F*F-**F;F*F=F*F9F*F7F*F-**F)F*F?F*F7 F*F9F*F-F*F,F*FcoF*F**&,Z#\"#v\"$7&F-*(\"#FF*FXF-F=F*F-*(F0F*F`oF-F7F* F**(F0F*F[oF-FgnF*F**&F?F*FSF*F**&F=F*FSF*F**(F0F*\"#KF-F?F*F-*&F)F-F= F)F-*(F;F-F=F*F?F*F-*(F)F*FgnF*F=F*F**&FgnF*F?F*F**&)F?F)F*F7F*F-*(F;F *FapF*F7F*F-**F;F*F?F*F7F*F=F*F-*&F;F-F7F)F***F0F*F[oF-F?F*F7F*F**&Fin F*F7F*F-*(F)F-F?F)F9F*F-*&FinF*F?F*F**(F)F*FinF*F=F*F**(F)F*FapF*F9F*F -*(F)F-FgnF*F9F*F**(F;F-F=F*F9F)F-*(F0F*FcrF-F9F)F**(F;F-F?F*F9F*F**(F ;F-F9F*F7F*F***F)F-F?F*F7F*F9F*F***F)F*F?F*F9F*F=F*F-F*)F(\"\"'F*F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"#;!\"\",0*&\"\"%\"\"\")%\"xG\"\"#F*F**(F-F*F ,F*%\"yGF*F**$)F/F-F*F&*(\"\")F*F1F*%\"gGF*F&*&F)F*F/F*F&*(F)F*%\"dGF* F1F*F**(F)F*F1F*%\"hGF*F&F*,P**F)F*)F,\"\"$F*F7F*F/F*F**&F)F*F " 0 "" {MPLTEXT 1 0 91 "C:=eval(A7,m=-1/128*(16*e^2+ 32*h*e+72*e+64*e*d-64*g*e+65+128*d^2+104*h+80*d+80*g-256*g*d));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"CG,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F( !\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(%\"dGF*F 2F*F(F*F**(%\"eGF*F/F*F'F*F**(,(#F*\"\"%F*F9F-F7F-F*F,F*)F(F0F*F**(%\" gGF*)F,F=F*F'F*F**(%\"hGF*F5F*F>F*F**&,,#F*\"\")F**&F)F-F9F*F*F@F-F7F* FCF-F*)F(F=F*F**(,,#F3\"#;F-*&#F*F=F*F9F*F-*&#F*F)F*FCF*F-*&F9F*F7F*F* *&F)F*)F7F)F*F*F*F/F*F>F*F**(,.*&F=F-F9F)F**(F0F*FGF-F9F*F**$FTF*F-#\" #D\"#kF*F@F*FCF*F*F,F*FIF*F**(,8*&FGF-F9F)F-*(F=F-FCF*F9F*F-*(\"\"*F*F MF-F9F*F-*(F)F-F9F*F7F*F-*(F)F-F@F*F9F*F*#\"#l\"$G\"F-FYF-*(\"#8F*FMF- FCF*F-*(F3F*FGF-F7F*F-*(F3F*FGF-F@F*F-*(F)F*F@F*F7F*F*F*F5F*FIF*F**&,8 *(\"#:F*FMF-FCF*F***F0F*F=F-FCF*F9F*F**(F\\oF*FGF-F@F*F**(F)F-F@F*F9F* F*#\"#dFaoF**&FGF-F9F)F**(F\\oF*FMF-F9F*F**(F)F-F9F*F7F*F*FYF**(F3F*FG F-F7F*F**&FCF*F7F*F*F*)F(F3F*F**(,Z*(F=F-F7F*F9F)F**&F=F-F9F*F-*&F9F*F TF*F**&FMF-F@F*F**(\"#FF*FfnF-F7F*F-*(F)F*FCF*FTF*F-*(F=F*F@F*FTF*F-** F)F*FCF*F7F*F9F*F-*&F@F*)F9F)F*F-*(F)F-FCF*F9F)F-**F=F*F@F*F9F*F7F*F-* (F3F*\"#KF-FCF*F-*$)F@F)F*F**&F@F*FCF*F**&F=F-FCF)F**&FGF-F9F)F-**F0F* FGF-F9F*F7F*F-*&F=F-F7F)F-*&FhnF*F9F*F**(F)F*FhnF*F7F*F**&FhoF*F9F*F** (F)F*FhoF*F7F*F*#FenFaoF-*(F=F-F@F*F9F*F-*&F@F*F7F*F-*(F=F-FCF*F9F*F-* *F0F*F=F-FCF*F7F*F-*$)F7F0F*F*F*F,F*FepF*F**&,hn*&FaoF-F9F*F-*(F3F*Ffq F-F@F*F**(F0F*FfnF-F7F*F-*&FCF*FTF*F**&F@F*FTF*F***F)F-FCF*F7F*F9F*F** *F)F*FCF*F9F*F@F*F-*(F=F-F@F*F9F)F-*&FaoF-FCF*F**&F)F-F@F)F-*(F=F-F@F* FCF*F-*(F)F-FCF)F9F*F-*(F)F*FhqF*F9F*F-*&)FCF)F*F7F*F-*(F=F*FhqF*F7F*F -**F=F*FCF*F7F*F@F*F-*(F0F*FfnF-F9F)F**(FMF-F9F*F7F*F**&FGF-F7F)F-*(F) F-FhnF*F9F*F**(F)F*FhoF*F@F*F**&FhoF*FCF*F**(F)F*FhnF*F@F*F**&FhnF*FCF *F**&FhoF*F7F*F-**F0F*FMF-F@F*F9F*F***F0F*F=F-F@F*F7F*F***F3F*FfqF-FCF *F9F*F***F0F*FGF-FCF*F7F*F*#\"#&)\"%C5F-F*)F(\"\"'F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "reevaluate the polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "puiseux(C,x=0,y,0,T);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#<%7$/%\"xG%\"TG/%\"yGF'7$/F&,$*(\"%C5!\"\",fn\"# v\"\"\"*(\"#kF2%\"dGF2)%\"eG\"\"#F2F2*&\"$q\"F2F7F2F2*&\"$![F2%\"gGF2F 2*&\"$+\"F2F5F2F2**\"$c#F2%\"hGF2F5F2F7F2F2**\"$o(F2FBF2F7F2F=F2F2*(FA F2F=F2F6F2F2*(\"$g\"F2FBF2F6F2F2**\"$7&F2F=F2F7F2F5F2F2*&\"$!HF2FBF2F2 *&FDF2)F=F8F2F2*(\"%)3\"F2F=F2FBF2F2*&\"$_$F2)FBF8F2F2*&\"$G\"F2)FB\" \"$F2F2*(FIF2FBF2FMF2F2*(FIF2F=F2FRF2F2*(FAF2FRF2F7F2F2*(FIF2FMF2F7F2F 2*(FAF2FRF2F5F2F2*(F.F2FMF2F5F2F2**F.F2FBF2F5F2F=F2F2*&FTF2F6F2F2*(FGF 2F7F2F5F2F2*(\"$/(F2F=F2F7F2F2*(\"$S'F2F=F2F5F2F2*(\"$K%F2FBF2F7F2F2*( \"$?$F2FBF2F5F2F2*&\"#KF2)F7FVF2F2F2F'F8F2/F),.*(\"7CMI6ur?;f!=\"F/F0 \"\"(F'\"#8F2**\"5;;b4P2WnW=F/F0\"\"',2*&\"#?F2FBF2F2\"#FF2*&\"#MF2F7F 2F2*&\"\")F2F6F2F2*&\"#SF2F=F2F2*&\"#[F2F5F2F2*(FcoF2F7F2F5F2F2*&FcoF2 )F5F8F2F2F2F'\"#7F2**\"1[_o8)*z^AF/F0\"\"&,,F8F2*&F8F2F7F2F2*&FVF2F5F2 F2*&F8F2F=F2F2FBF2F2F'\"#5F2**\".3A-$4'z)F/F0\"\"%,(*&FepF2F5F2F2F`qF2 *&FhqF2F7F2F2F2F'FepF2*(\"+[O[Z@F/F0FVF'F]pF2*(\"(w&[5F/F0F8F'FhqF27$F %/F)-%'RootOfG6#,*F.F2*&,P*&F.F2)F5FVF2F2\"#&)F2*(FTF2FBF2F6F2F2*&FTF2 FRF2F/*&\"$o#F2F7F2F2*&FcoF2F=F2F/*&\"$/&F2F5F2F2*&\"#cF2FBF2F2*&FIF2F MF2F/*&\"$S#F2F6F2F2*&FDF2F\\qF2F2*(F.F2F=F2F\\qF2F/*(FIF2F=F2FBF2F/*( \"$K)F2F7F2F5F2F2*(\"$%QF2F=F2F5F2F2*(FAF2FBF2F7F2F2*(\"$w&F2FBF2F5F2F 2**FIF2F=F2F7F2F5F2F/*(F]tF2F5F2F6F2F2*(F.F2F7F2F\\qF2F2*(FTF2F=F2F7F2 F2*&F4F2FdoF2F2**FAF2FBF2F5F2F7F2F2F2)%#_ZGFVF2F2*&,8*&F`tF2F7F2F/*&\" %_6F2F=F2F/*&\"$g*F2FBF2F/*&F]oF2F5F2F/*&F.F2F\\qF2F/*(FDF2FBF2F7F2F/* (FIF2F7F2F5F2F/*(FIF2F=F2F7F2F/*&FTF2F6F2F/\"$c%F/*(F.F2FBF2F5F2F/F2)F htF8F2F2*&,,*&FIF2F7F2F/*&F.F2FBF2F2*&F.F2F=F2F2*&F.F2F5F2F/FTF/F2FhtF 2F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [8]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 254 "factor(75+64*d*e^2+170*e+48 0*g+100*d+256*h*d*e+768*h*e*g+256*g*e^2+160*h*e^2+512*g*e*d+290*h+768* g^2+1088*g*h+352*h^2+128*h^3+512*h*g^2+512*g*h^2+256*h^2*e+512*g^2*e+2 56*h^2*d+1024*g^2*d+1024*h*d*g+128*e^2+160*e*d+704*g*e+640*g*d+432*h*e +320*h*d+32*e^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),*\"\"&\"\"\"* &\"\"%F'%\"eGF'F'*&\"#;F'%\"gGF'F'*&\"\")F'%\"hGF'F'\"\"#F',**&F1F'F*F 'F'*&F1F'F0F'F'\"\"$F'*&F)F'%\"dGF'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "C1:=eval(C,d=-1/4*(2*e+2*h+3));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#C1G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F**(F)F*)F ,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(,(*&F)F-%\"eGF*F-*&F)F-% \"hGF*F-#F0\"\"%F-F*F2F*F(F*F**(F9F*F/F*F'F*F**(,(F*F**&F)F-F9F*F-*&F) F-F;F*F*F*F,F*)F(F0F*F**(%\"gGF*)F,F=F*F'F*F**(F;F*F5F*FCF*F**&,(#F3\" \")F-FEF-*(F0F*F)F-F;F*F-F*)F(F=F*F**(,,#F3\"#;F-*&F=F-F9F*F-*&F)F-F;F *F-*&F9F*F7F*F**&F)F*)F7F)F*F*F*F/F*FCF*F**(,.*&F=F-F9F)F**(F0F*FKF-F9 F*F**$FVF*F-#\"#D\"#kF*FEF*F;F*F*F,F*FMF*F**(,6*&FKF-F9F)F-*(F=F-F;F*F 9F*F-*&F=F-F9F*F-*(F)F-F9F*F7F*F-*(F)F-FEF*F9F*F*#F3\"$G\"F-FenF-*&F)F -F;F*F-*(F3F*FKF-FEF*F-*(F)F*FEF*F7F*F*F*F5F*FMF*F**&,6*(F3F*FKF-F;F*F ***F0F*F=F-F;F*F9F*F**(\"\"*F*FKF-FEF*F**(F)F-FEF*F9F*F*#F0FaoF-*&FKF- F9F)F**&F=F-F9F*F**(F)F-F9F*F7F*F*FenF**&F;F*F7F*F*F*)F(F3F*F**(,X*(F3 F*FaoF-F9F*F-*&FQF-FEF*F**&FEF*)F9F)F*F-*(F)F-F;F*F9F)F-*(\"\"(F*FaoF- F;F*F**$)FEF)F*F**&FEF*F;F*F**&F=F-F;F)F***F)F*F;F*F7F*F9F*F-**F=F*FEF *F9F*F7F*F-*$)F7F0F*F*#\"#J\"$c#F**&F=F-F7F)F-*&FKF-F9F)F-*(F=F-FEF*F9 F*F-*(F=F-F;F*F9F*F-**F0F*FKF-F9F*F7F*F-*&FEF*F7F*F-**F0F*F=F-F;F*F7F* F-*(F=F-F7F*F9F)F**&F9F*FVF*F**(F)F*F;F*FVF*F-*(F=F*FEF*FVF*F-*&FjnF*F 9F*F**(F)F*FjnF*F7F*F**&FfoF*F9F*F**(F)F*FfoF*F7F*F*F*F,F*FapF*F**&,fn *&FhnF-F9F*F**(F3F*\"#KF-FEF*F***F)F*F;F*F9F*FEF*F-*(F=F-FEF*F9F)F-*&F irF-F;F*F**&F)F-FEF)F-*(F=F-FEF*F;F*F-*(F)F-F;F)F9F*F-*(F)F*F\\qF*F9F* F-**F)F-F;F*F7F*F9F*F***F=F*F;F*F7F*FEF*F-*&FKF-F7F)F-*(F0F*FhnF-F9F)F ***F0F*FQF-FEF*F9F*F***F3F*FirF-F;F*F9F*F**(FQF-F9F*F7F*F***F0F*F=F-FE F*F7F*F***F0F*FKF-F;F*F7F*F**&F;F*FVF*F**&FEF*FVF*F**(F)F-FjnF*F9F*F** &FfoF*F7F*F-*&)F;F)F*F7F*F-*(F=F*F\\qF*F7F*F-*(F)F*FfoF*FEF*F**&FfoF*F ;F*F**(F)F*FjnF*FEF*F**&FjnF*F;F*F*#\"#\\\"%C5F-F*)F(\"\"'F*F*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [2]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(C1,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG,.*$)F$\"\"#\"\"\"F)*&F(!\"\"F$ \"\"$F)*&)F$\"\"%F),&*&F(F+%\"hGF)F+#F)\"\")F+F)F)*&)F$\"\"&F),*#F)F4F +*&F/F+%\"eGF)F)%\"gGF)*&F/F+F2F)F+F)F)*&)F$\"\"'F),,#\"\"*\"#;F)*&#F) F(F)*$)F2F(F)F)F)*&#F7F4F)F;F)F)*&#F7F(F)F&F)F2F)FfoF)F+*(\"&7D $F)F " 0 "" {MPLTEXT 1 0 390 "discrim(5114+6735*e+24560*g-22272* h*e*g+1792*g*e^2-2320*h*e^2-2560*h*e^2*g+17865*h+4096*_Z^2+15360*h^2*g ^2-5120*h^3*g+28544*g^2+22432*g*h+17300*h^2-5120*h*g^2*e+2880*h^3-2048 *g^3+5120*g*h^2*e-320*h*e^3-51968*h*g^2-32512*g*h^2+(-16640*h-2048*g*e +3072*h*e-23040*g+16384*g*h-6400*e-512*e^2-2048*h^2-9376)*_Z-6560*h^2* e+2816*g^2*e+2600*e^2-1280*h^3*e+320*h^2*e^2+17536*g*e+7540*h*e+240*e^ 3,_Z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,\\o*&\"(glm*\"\"\"%\"eGF&F& *&\")S]lHF&%\"gGF&F&**\")G*)y\")F&%\"hGF&F'F&F*F&F&*(\")KsW?F&F*F&)F' \"\"#F&F&*(\")S'Gd\"F&F-F&F0F&F&**\")7He7F&F-F&F0F&F*F&F&*&\")?JL>F&F- F&F&\"(+;7%F&*(\");sx;F&)F-F1F&)F*F1F&F&*(F:F&)F-\"\"$F&F*F&F&*&\"(/V> %F&)F-\"\"%F&F&*&\")/nF&F&*&\")KWbLF&)F*F?F&F&**\")Ce;D F&F*F&F;F&F'F&F&*(\"(_r4#F&F-F&)F'F?F&F&*(\")#**ok*F&F-F&FF&F'F&F&*(\"(c9H'F&F;F&F0F&F&*(FSF&F *F&FTF&F&*(\")si+YF&F*F&F'F&F&*(FIF&F-F&F'F&F&*(FAF&F " 0 "" {MPLTEXT 1 0 10 "factor(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"%C5\"\"\",0*&\"#;F&)%\"eG\"\"#F& F&*&\"$?\"F&F+F&F&*(\"#kF&%\"hGF&F+F&F&\"$h\"F&*&\"$G\"F&%\"gGF&F&*&F0 F&)F1F,F&F&*&\"$S#F&F1F&F&F&),*\"\"&F&*&\"\"%F&F+F&F&*&F)F&F5F&F&*&\" \")F&F1F&F&F,F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "C2:=ev al(C1,g=-1/128*(16*e^2+120*e+64*h*e+161+64*h^2+240*h));" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%#C2G,B*&)%\"yG\"\"#\"\"\",&%\"xGF*F(!\"\"F*F** (F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(,(*&F)F-%\"eGF*F-* &F)F-%\"hGF*F-#F0\"\"%F-F*F2F*F(F*F**(F9F*F/F*F'F*F**(,(F*F**&F)F-F9F* F-*&F)F-F;F*F*F*F,F*)F(F0F*F**(,.*&#F*\"\")F**$)F9F)F*F*F-*&#\"#:\"#;F *F9F*F-*&#F*F)F**&F;F*F9F*F*F-#\"$h\"\"$G\"F-*&#F*F)F**$)F;F)F*F*F-*&# FMFHF*F;F*F-F*)F,F=F*F'F*F**(F;F*F5F*FCF*F**&,.#\"#\")FTF**&#F*FHF*FIF *F**&#FMFNF*F9F*F**&#F*F)F*FQF*F**&F`oF*FWF*F**&#F0FHF*F;F*F*F*)F(F=F* F**(,,#F3FNF-*&F=F-F9F*F-*&F)F-F;F*F-*&F9F*F7F*F**&F)F*)F7F)F*F*F*F/F* FCF*F**(,0*&FHF-F9F)F**(\"\"*F*FNF-F9F*F-*$F\\pF*F-#\"$6\"FTF-*(F)F-F; F*F9F*F-*&F)F-F;F)F-*(\"\"(F*FHF-F;F*F-F*F,F*FdoF*F**(,6*(F0F*\"#kF-F9 F)F-*(FNF-F;F*F9F*F**(\"#VF*FTF-F9F*F**(F)F-F9F*F7F*F-*(F)F-FEF*F9F*F* #\"$l(\"%C5F*FbpF-*(F_qF*F\\qF-F;F*F**(F3F*FNF-F;F)F**(F)F*FEF*F7F*F*F *F5F*FdoF*F**&,6*(\"#&*F*F\\qF-F;F*F-**F0F*FNF-F;F*F9F*F**&F\\qF-F9F)F -*(\"$.\"F*FTF-F9F*F-#\"%t9FdqF-*(FapF*FNF-F;F)F-*(F)F-FEF*F9F*F**(F)F -F9F*F7F*F*FbpF**&F;F*F7F*F*F*)F(F3F*F**(,V*(\"#DF*\"$c#F-F9F*F-*(F)F- F;F*F9F)F-*&FNF-F;F*F-*(FhpF*\"#KF-F;F)F**$)FEF)F*F***F=F*FEF*F9F*F7F* F-*(F=F-FEF*F9F*F-**F)F*F;F*F7F*F9F*F-*$)F7F0F*F**&F=F-F7F)F-*(\"# " 0 "" {MPLTEXT 1 0 22 "puiseux(C2,x=0,y,0,T);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG%\"TG/%\"yGF'7$/F&,$*(\")KWb L!\"\",do*&\");>o=\"\"\"%\"eGF3F3*(\"*+%)*\\6F3%\"hGF3)F4\"\"#F3F3*&\" )KQOPF3F7F3F3\"($o9`F3*&\"*S#Q88F3)F7\"\"%F3F3*&\"*k'4S5F3)F7F9F3F3*& \"*+7L`\"F3)F7\"\"$F3F3*(\")?\"pc'F3F7F3)F4FGF3F3*(\")![_C)F3FCF3FJF3F 3*(\"*g\\!\\;F3F?F3F4F3F3*(FNF3FFF3F8F3F3*(\"*+o**H#F3FCF3F4F3F3*(\")? Jh?F3F7F3)F4F@F3F3*(\"(S]<*F3F?F3FJF3F3*&\"(_r4#F3)F7\"\"(F3F3*&\"(S'3 #)F3FTF3F3*&\");C+EF3F8F3F3*&\"(781#F3)F4\"\"&F3F3*(\"*![wEEF3FFF3F4F3 F3*(\"*gt+(>F3FCF3F8F3F3*(FBF3F7F3F4F3F3*(\")[+,6F3)F7F\\oF3F8F3F3*(\" (K+M(F3)F7\"\"'F3F4F3F3*(\"'w$H#F3F7F3)F4FhoF3F3*(\"(ciP\"F3FCF3F[oF3F 3*(\"(?ve%F3FFF3FTF3F3*&\")%)>'f'F3FdoF3F3*&\")+k;>F3FJF3F3*&\"'CEGF3F [pF3F3*&\")Oz3=F3FgoF3F3*&\"&%Q;F3)F4FZF3F3*(\")3QEaF3FdoF3F4F3F3*(\") g(Hy'F3F?F3F8F3F3*(\"()[\"R$F3F7F3F[oF3F3*(\")S)>_%F3FFF3FJF3F3*(\")Su &p\"F3FCF3FTF3F3F3F'F9F3/F),0*(\"hnw8INGz#y$*H?ADgi6M#4i>av-**eU/Qpg\" F/F0\"\")F'\"#:F3**\"Yk#R0v>QI*f^xy>wt4U$\\$p)oT:Yrz!)*F/F0FZ,6\"%,\\F 3*&\"%WWF3F4F3F3*&\"%s5F3F8F3F3*&\"#kF3FJF3F3*&\"%)[\"F3F7F3F3*(\"$o(F 3F7F3F4F3F3*(\"$c#F3F7F3F8F3F/*&\"%7`F3FCF3F/*(\"%#z\"F3FCF3F4F3F/*&\" %[?F3FFF3F/F3F'\"#9F/**\"QWd8$)R\"\\vq!z\"37#4bHdsK$4aPl$F/F0Fho,.\"$h 'F3*&\"$S%F3F4F3F3*&\"#!)F3F8F3F3*&\"$!))F3F7F3F3*(\"$?$F3F7F3F4F3F3*& \"$#>F3FCF3F3F3F'\"#7F/**\"I'H$Q\"H3*=P*RT:a,N2(y^WaF/F0F\\o,.\"$x\"F3 *&\"#))F3F4F3F3*&\"#;F3F8F3F3*&\"$s#F3F7F3F3*(FdrF3F7F3F4F3F3*&FdrF3FC F3F3F3F'\"#5F/**\"A3IkDO(>@Ne#=![?T,\"F/F0F@,&*&F@F3F7F3F3F3F3F3F'FiqF /*(\"8O\">MK9fsjybvF/F0FGF'FhoF3*(\"1CE%o!***e7\"F/F0F9F'F@F37$F%/F)-% 'RootOfG6#,*\"&oF$F/*&,<*&\"%'4%F3FFF3F/\"$n(F/*(\"%_VF3F7F3F8F3F3*(\" %C5F3F7F3FJF3F3*&\"%_\"*F3FCF3F/*&\"%oRF3F4F3F3*&\"%;kF3F7F3F/*&\"%)3& F3F8F3F3*(\"$7&F3FCF3F4F3F3*(\"%3IF3F7F3F4F3F3*&FjrF3FTF3F3*&F`sF3FJF3 F3*(FevF3FCF3F8F3F3F3)%#_ZGFGF3F3*&,4*(\"%#>)F3FCF3F4F3F/*&\"&Cm#F3FCF 3F/*&\"&S'[F3F7F3F/*&\"&se\"F3F8F3F/*(F\\vF3F7F3F4F3F/*&F`sF3FJF3F/\"& /(GF/*&\"&)oMF3F4F3F/*(FjwF3F7F3F8F3F/F3)FfwF9F3F3*&,.*&FipF3FCF3F3*& \"&)G7F3F7F3F3*(FipF3F7F3F4F3F3*&\"&?2$F3F4F3F3\"&O2#F3*&F`vF3F8F3F3F3 FfwF3F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [8]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 522 "factor(18681916*e+114998400 *h*e^2+37363832*h+5314683+131338240*h^4+104009664*h^2+153331200*h^3+65 669120*h*e^3+82452480*h^2*e^3+164904960*h^4*e+164904960*h^3*e^2+229996 800*h^2*e+20613120*h*e^4+9175040*h^4*e^3+2097152*h^7+8208640*e^4+26002 416*e^2+2061312*e^5+262676480*h^3*e+197007360*h^2*e^2+104009664*h*e+11 010048*h^5*e^2+7340032*h^6*e+229376*h*e^6+1376256*h^2*e^5+4587520*h^3* e^4+65961984*h^5+19166400*e^3+282624*e^6+18087936*h^6+16384*e^7+542638 08*h^5*e+67829760*h^4*e^2+3391488*h*e^5+45219840*h^3*e^3+16957440*h^2* e^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&\"\"%\"\"\"%\"eGF'F'*& \"\")F'%\"hGF'F'\"\"$F'F'),(*&F&F'F(F'F'*&F*F'F+F'F'\"#6F'\"\"'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "C3:=eval(C2,e=-1/4*(8*h+3)); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#C3G,B*&)%\"yG\"\"#\"\"\",&%\"xG F*F(!\"\"F*F**(F)F*)F,\"\"$F*F(F*F-*$)F,\"\"&F*F**&F'F*)F,F)F*F**(,&*& F)F-%\"hGF*F*#F0\"\")F-F*F2F*F(F*F**(,&*&F)F*F9F*F-#F0\"\"%F-F*F/F*F'F *F**(,&#\"#6F;F**(F0F*F)F-F9F*F*F*F,F*)F(F0F*F**(,**&F;F-F=F)F-#\"#r\" $G\"F-*(F)F-F9F*F=F*F-*&F)F-F9F)F-F*)F,F@F*F'F*F**(F9F*F5F*FFF*F**&,,# \"\"*FLF-*&F;F-F=F)F**(F0F*F)F-F9F*F-*(F)F-F9F*F=F*F**&F)F-F9F)F*F*)F( F@F*F**(,(#F*F;F-*&F=F*F7F*F**&F)F*)F7F)F*F*F*F/F*FFF*F**(,.*&F;F-F=F) F**&F@F-F9F*F*#\"#dFLF-*$FinF*F-*(F)F-F9F*F=F*F-*&F)F-F9F)F-F*F,F*FYF* F**(,2*(F0F*\"#kF-F=F)F-*(\"#;F-F9F*F=F*F*#\"$2&\"%C5F**(F)F-F=F*F7F*F -*(F)F-FHF*F=F*F*F`oF-*(F3F*FhoF-F9F)F**(F)F*FHF*F7F*F*F*F5F*FYF*F**&, 4*&F;F-F9F*F***F0F*FhoF-F9F*F=F*F**&FfoF-F=F)F-#\"$b)F[pF-*(FTF*FhoF-F 9F)F-*(F)F-FHF*F=F*F**(F)F-F=F*F7F*F*F`oF**&F9F*F7F*F*F*)F(F3F*F**(,T* (\"# " 0 "" {MPLTEXT 1 0 20 "puiseux(C3,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%%\"xG-%'RootOfG6#,*\"$c#\"\"\"*&,(*&\"#KF*)%\"hG\"\"$F*F*\"#8F**& \"#UF*F0F*F*F*)%#_ZGF1F*F**&,&*&\"$#>F*)F0\"\"#F*F*\"#%)F*F*)F6FF*F**&,*\"'O2]FE*& \"(O^.$F*F0F*FE*&\"'gdCF*F;F*FE*&\"'!oF$F*F/F*F*F*F6F*F**&\"(#z)*GF*F0 F*F**&\"(g$R=F*)F0FHF*FE*&\"(;+-*F*F;F*F**&\"(g(46F*F/F*F**&\"'+O:F*)F 0FOF*FE*&\"'+C5F*)F0FWF*F*\"' " 0 "" {MPLTEXT 1 0 144 "discrim(262144*_Z^2+(-500736-3035136*h-245760*h^2+327680*h^3)*_Z+ 2898792*h-1839360*h^4+9020016*h^2+1109760*h^3-153600*h^5+102400*h^6+24 3217,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!+'Hn\\H%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Out of variables to subsitute. Cases exha usted." }}}}{MARK "68 0 0" 47 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }