{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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 0 145 "A:=x^6+(x+y)^2*(x-y)*y^2+f* x^5*y+g*x^4*y^2+h*x^3*y^3+j*x^2*y^4+k*x*y^5+l*y^6+m*x^7+n*x^6*y+p*x^5* y^2+q*x^4*y^3+r*x^3*y^4+s*x^2*y^5+t*x*y^6+u*y^7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,B*$)%\"xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F (F*F.!\"\"F*)F.F/F*F**(%\"fGF*)F(\"\"&F*F.F*F**(%\"gGF*)F(\"\"%F*F2F*F **(%\"hGF*)F(\"\"$F*)F.F>F*F**(%\"jGF*)F(F/F*)F.F:F*F**(%\"kGF*F(F*)F. F6F*F**&%\"lGF*)F.F)F*F**&%\"mGF*)F(\"\"(F*F**(%\"nGF*F'F*F.F*F**(%\"p GF*F5F*F2F*F**(%\"qGF*F9F*F?F*F**(%\"rGF*F=F*FCF*F**(%\"sGF*FBF*FFF*F* *(%\"tGF*F(F*FIF*F**&%\"uGF*)F.FMF*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#,(*&%\"uG\"\"\")%#_ZG\"\"#F+F+*&%\"lGF+F-F+F+F+! \"\",&*(\"\"%F1,0F+F+%\"jGF+%\"fGF1%\"hGF1F0F+%\"gGF+%\"kGF1F.*&F$F+,0 #F+F.F1*&F.F1F6F+F1*&F.F1F7F+F+*&F.F1F8F+F+*&F.F1F0F+F1*&F.F1F9F+F1*&F .F1F:F+F+F1#\"\"$F.F+*(,0#F+F.F+*&F.F1F6F+F+*&F.F1F7F+F1*&F.F1F8F+F1*& F.F1F0F+F+*&F.F1F9F+F+*&F.F1F:F+F1F+F$F+F " 0 "" {MPLTEXT 1 0 50 "solve(-1/2-1/2*j+1/2*f-1/2*l-1/2*g+1/2*h+ 1/2*k,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.\"\"\"F$%\"jGF$%\"kG!\" \"%\"hGF'%\"lGF$%\"gGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " A1:=eval(A,f=1+j-k+l+g-h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A1G,B *$)%\"xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**( ,.F*F*%\"jGF*%\"kGF1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F(\" \"%F*F2F*F**(F7F*)F(\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F*)F .F;F*F**&F8F*)F.F)F*F**&%\"mGF*)F(\"\"(F*F**(%\"nGF*F'F*F.F*F**(%\"pGF *F:F*F2F*F**(%\"qGF*F=F*FBF*F**(%\"rGF*F@F*FEF*F**(%\"sGF*FDF*FGF*F**( %\"tGF*F(F*FIF*F**&%\"uGF*)F.FMF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&%\"xG-%'RootOfG6#,(*&%\"uG\"\"\")%#_ZG\"\"#F+F+*&%\"lGF+F-F+F+F+! \"\"*$),$F$F1#\"\"$F.F+,&F$F1*&)F$F.F+-F&6#,6*&F.F+F,F+F+*&,.F+F+*&\" \"%F+%\"kGF+F+*&\"\"&F+F0F+F1%\"gGF1*&F6F+%\"jGF+F1*&F.F+%\"hGF+F+F+F- F+F+%\"rGF+%\"tGF+%\"qGF1%\"pGF+%\"nGF1F*F1%\"mGF+%\"sGF1F+F+" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 60 "discrim(2*_Z^2+(1+4*k-5*l-g-3*j+2*h)*_Z+r+t- q+p-n-u+m-s,_Z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,fn\"\"\"F$*&\"\") F$%\"rGF$!\"\"*&F&F$%\"tGF$F(*&\"\"'F$%\"jGF$F(*&F&F$%\"uGF$F$*&\"#5F$ %\"lGF$F(*&\"\"#F$%\"gGF$F(*&F&F$%\"pGF$F(*&F&F$%\"nGF$F$*&F&F$%\"mGF$ F(*&F&F$%\"kGF$F$*&F&F$%\"sGF$F$*&F&F$%\"qGF$F$*&\"\"%F$%\"hGF$F$*(\"# ;F$FDF$F=F$F$*(\"#?F$FDF$F2F$F(*(FCF$FDF$F5F$F(*(\"#7F$FDF$F-F$F(*&FCF $)FDF4F$F$*(\"#CF$F-F$F=F$F(*(\"#IF$F-F$F2F$F$*(F,F$F-F$F5F$F$*&\"\"*F $)F-F4F$F$*&FFF$)F=F4F$F$*(\"#SF$F=F$F2F$F(*(F&F$F=F$F5F$F(*&\"#DF$)F2 F4F$F$*(F1F$F2F$F5F$F$*$)F5F4F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "solve(1-8*r-8*t-6*j+8*u-10*l-2*g-8*p+8*n-8*m+8*k+8*s +8*q+4*h+16*h*k-20*h*l-4*h*g-12*h*j+4*h^2-24*j*k+30*j*l+6*j*g+9*j^2+16 *k^2-40*k*l-8*k*g+25*l^2+10*l*g+g^2,m);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,Z%\"rG!\"\"%\"tGF%*(\"\"$\"\"\"\"\"%F%%\"jGF)F%%\"uGF)*(\"\"&F) F*F%%\"lGF)F%*&F*F%%\"gGF)F%%\"pGF%%\"nGF)%\"kGF)%\"sGF)%\"qGF)*&\"\"# F%%\"hGF)F)*(F8F)F9F)F4F)F)**F.F)F8F%F9F)F/F)F%*(F8F%F9F)F1F)F%**F(F)F 8F%F9F)F+F)F%*&F8F%F9F8F)*(F(F)F+F)F4F)F%**\"#:F)F*F%F+F)F/F)F)**F(F)F *F%F+F)F1F)F)*(\"\"*F)\"\")F%F+F8F)*&F8F))F4F8F)F)*(F.F)F4F)F/F)F%*&F4 F)F1F)F%*(\"#DF)FEF%F/F8F)**F.F)F*F%F/F)F1F)F)*&FEF%F1F8F)#F)FEF)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "A2:=eval(A1,m=-r-t-3/4*j+u- 5/4*l-1/4*g-p+n+k+s+q+1/2*h+2*h*k-5/2*h*l-1/2*h*g-3/2*h*j+1/2*h^2-3*j* k+15/4*j*l+3/4*j*g+9/8*j^2+2*k^2-5*k*l-k*g+25/8*l^2+5/4*l*g+1/8*g^2+1/ 8);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A2G,B*$)%\"xG\"\"'\"\"\"F**( ),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**(,.F*F*%\"jGF*%\"kGF1%\" hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F(\"\"%F*F2F*F**(F7F*)F(\" \"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F*)F.F;F*F**&F8F*)F.F)F*F* *&,Z%\"rGF1%\"tGF1*(FAF*F>F1F5F*F1%\"uGF**(F;F*F>F1F8F*F1*&F>F1F9F*F1% \"pGF1%\"nGF*F6F*%\"sGF*%\"qGF**&F/F1F7F*F**(F/F*F7F*F6F*F***F;F*F/F1F 7F*F8F*F1*(F/F1F7F*F9F*F1**FAF*F/F1F7F*F5F*F1*&F/F1F7F/F**(FAF*F5F*F6F *F1**\"#:F*F>F1F5F*F8F*F***FAF*F>F1F5F*F9F*F**(\"\"*F*\"\")F1F5F/F**&F /F*)F6F/F*F**(F;F*F6F*F8F*F1*&F6F*F9F*F1*(\"#DF*F\\oF1F8F/F***F;F*F>F1 F8F*F9F*F**&F\\oF1F9F/F*#F*F\\oF*F*)F(\"\"(F*F**(FSF*F'F*F.F*F**(FRF*F :F*F2F*F**(FUF*F=F*FBF*F**(FLF*F@F*FEF*F**(FTF*FDF*FGF*F**(FMF*F(F*FIF *F**&FOF*)F.FgoF*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 12 "" 1 "" {XPPMATH 20 "6#<&%\"xG,(*(\"(_r4#!\" \",`w\"\"&F(*&\"#k\"\"\"%\"rGF-F(*&\"#'*F-%\"tGF-F(*&\"#@F-%\"jGF-F-*& \"$7\"F-%\"uGF-F-*&\"#:F-%\"lGF-F-*&\"#6F-%\"gGF-F-*&\"#KF-%\"pGF-F(*& \"#;F-%\"nGF-F-*&\"#?F-%\"kGF-F(*&\"#!)F-%\"sGF-F-**\"%S5F-%\"hGF-FFF- F:F-F(**\"$g'F-FLF-F:F-F4F-F-**FHF-FLF-FFF-F=F-F(*&\"#[F-%\"qGF-F-*&\" #=F-FLF-F(**\"$S\"F-FLF-F:F-F=F-F-**\"$K%F-FLF-FFF-F4F-F(*(FBF-FLF-FFF -F-*(\"#gF-FLF-F:F-F(*(FEF-FLF-F=F-F-*(\"#7F-FLF-F4F-F-*&FhnF-)FL\"\"# F-F(*(\"#sF-F4F-FFF-F(*(\"$]\"F-F4F-F:F-F-*(FTF-F4F-F=F-F(*&\"\"*F-)F4 F[oF-F-*&FHF-)FFF[oF-F-*(\"$!GF-FFF-F:F-F(*(\"\")F-FFF-F=F-F-*&\"$D#F- )F:F[oF-F-*(\"#5F-F:F-F=F-F-*&\"\"(F-)F=F[oF-F(**\"#OF-FLF-F=F-F4F-F-* *\"%+=F-F4F-FFF-F:F-F-**\"$o\"F-F4F-FFF-F=F-F-**\"$q#F-F4F-F:F-F=F-F(* *\"$S%F-FFF-F:F-F=F-F-*(F6F-FjnF-FFF-F-*(\"$_$F-FLF-FeoF-F-*(\"$!=F-Fj nF-F:F-F(*(\"$](F-FLF-F\\pF-F-*(\"\"%F-FjnF-F=F-F(*(F[oF-FLF-FapF-F(*( FenF-FjnF-F4F-F(*(\"$E\"F-FLF-FcoF-F-*(\"$C'F-F4F-FeoF-F(*&FioF-)FL\" \"$F-F-*&\"#\")F-)F4F]rF-F(*&\"$?$F-)FFF]rF-F-*&\"$v)F-)F:F]rF-F(*$)F= F]rF-F-*(\"$'RF-FcoF-FFF-F-*(\"%v7F-F4F-F\\pF-F(*(\"$&eF-FcoF-F:F-F(*( F]rF-F4F-FapF-F(*(\"#XF-FcoF-F=F-F(*(\"%g8F-FeoF-F:F-F(*(\"$W\"F-FeoF- F=F-F(*(\"%+>F-FFF-F\\pF-F-*(FhnF-FFF-FapF-F-*(\"$D$F-F\\pF-F=F-F(*(\" #DF-F:F-FapF-F(*(F?F-FCF-FLF-F-*(F,F-FCF-FFF-F-*(FHF-FCF-F:F-F(*(FBF-F CF-F=F-F(*(FQF-FCF-F4F-F(*(F,F-F@F-FLF-F(*(\"$G\"F-F@F-FFF-F(*(\"$g\"F -F@F-F:F-F-*(F?F-F@F-F=F-F-*(F0F-F@F-F4F-F-*(F0F-FRF-FLF-F-*(\"$#>F-FR F-FFF-F-*(\"$S#F-FRF-F:F-F(*(FQF-FRF-F=F-F(*(FesF-FRF-F4F-F(*(\"$c#F-F .F-FFF-F(*(FbrF-F.F-F:F-F-*(F,F-F.F-F=F-F-*(F[uF-F.F-F4F-F-*(FdtF-F.F- FLF-F(*(FftF-FIF-FLF-F-*(FbrF-FIF-FFF-F-*(\"$+%F-FIF-F:F-F(*(FHF-FIF-F =F-F(*(F]uF-FIF-F4F-F(*(F[uF-F1F-FLF-F(*(\"$%QF-F1F-FFF-F(*(\"$![F-F1F -F:F-F-*(F0F-F1F-F=F-F-*(\"$)GF-F1F-F4F-F-*(\"$C#F-F7F-FLF-F-*(\"$[%F- F7F-FFF-F-*(\"$g&F-F7F-F:F-F(*(F6F-F7F-F=F-F(*(\"$O$F-F7F-F4F-F(F]r*&F $F-,`w*&F[oF(F.F-F(*(F]rF-FdqF(F1F-F(*(F3F-FdtF(F4F-F-*(F`pF-FioF(F7F- F-*(F9F-FdtF(F:F-F-*(F " 0 "" {MPLTEXT 1 0 922 "factor(-1/2*r-3/4 *t+21/128*j+7/8*u+15/128*l+11/128*g-1/4*p+1/8*n-5/32*k+5/8*s+3/8*q-9/6 4*h-65/8*h*k*l+1/8*h*k-15/32*h*l+5/32*h*g+3/32*h*j-3/32*h^2-9/16*j*k+7 5/64*j*l-9/64*j*g+9/128*j^2+5/8*k^2-35/16*k*l+1/16*k*g+225/128*l^2+5/6 4*l*g-7/128*g^2-5/8*h*k*g-27/8*h*k*j+35/32*h*l*g+165/32*h*l*j+9/32*h*g *j+225/16*j*k*l+21/16*j*k*g-135/64*j*l*g+55/16*k*l*g+7/8*h^2*k+11/4*h* k^2-45/32*h^2*l+375/64*h*l^2-1/32*h^2*g-1/64*h*g^2-15/32*h^2*j+63/64*h *j^2-39/8*j*k^2+99/32*j^2*k-1275/128*j*l^2-585/128*j^2*l-3/128*j*g^2-4 5/128*j^2*g+1/16*h^3-81/128*j^3-85/8*k^2*l-9/8*k^2*g+475/32*k*l^2+3/32 *k*g^2-325/128*l^2*g-25/128*l*g^2+5/2*k^3-875/128*l^3+1/128*g^3+1/4*n* h+1/2*n*k-5/8*n*l-1/8*n*g-3/8*n*j-1/2*p*h-p*k+5/4*p*l+1/4*p*g+3/4*p*j+ 3/4*q*h+3/2*q*k-15/8*q*l-3/8*q*g-9/8*q*j-2*r*k+5/2*r*l+1/2*r*g+3/2*r*j -r*h+5/4*s*h+5/2*s*k-25/8*s*l-5/8*s*g-15/8*s*j-3/2*t*h-3*t*k+15/4*t*l+ 3/4*t*g+9/4*t*j+7/4*u*h+7/2*u*k-35/8*u*l-7/8*u*g-21/8*u*j-5/128);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"$G\"!\"\",.\"\"\"F&*&\"\"#F(%\"h GF(F&*&\"\"%F(%\"kGF(F&*&\"\"&F(%\"lGF(F(%\"gGF(*&\"\"$F(%\"jGF(F(F(,V F0F(*&\"#kF(%\"rGF(F(*&\"#'*F(%\"tGF(F(*&\"\"'F(F5F(F&*&\"$7\"F(%\"uGF (F&*&\"#5F(F1F(F(*&F>F(F2F(F&*&\"#KF(%\"pGF(F(*&\"#;F(%\"nGF(F&*&\"#!) F(%\"sGF(F&*&\"#[F(%\"qGF(F&*&\"\")F(F+F(F(*(FOF(F+F(F.F(F&*(FLF(F+F(F 1F(F(*(\"#CF(F+F(F5F(F(*&F-F()F+F*F(F&*(F;F(F5F(F.F(F(*(\"$]\"F(F5F(F1 F(F&*(F>F(F5F(F2F(F&*&\"#FF()F5F*F(F&*&FLF()F.F*F(F&*(\"$S#F(F.F(F1F(F (*(FIF(F.F(F2F(F(*&\"$v\"F()F1F*F(F&*(\"#IF(F1F(F2F(F&*$)F2F*F(F(F(F( " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Case B: short factor=0; case \+ A: long factor=0 [7]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sol ve(-1-2*h-4*k+5*l+g+3*j,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,\"\" \"F$*&\"\"#F$%\"hGF$F$*&\"\"%F$%\"kGF$F$*&\"\"&F$%\"lGF$!\"\"*&\"\"$F$ %\"jGF$F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "B1:=eval(A2,g= 1+2*h+4*k-5*l-3*j);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#B1G,B*$)%\"x G\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**(,,F/F** &F/F*%\"jGF*F1*&\"\"$F*%\"kGF*F*%\"hGF**&\"\"%F*%\"lGF*F1F*)F(\"\"&F*F .F*F**(,,F*F**&F/F*F:F*F**&FF*F2F*F**(FgnF*FFF*FIF*F**(FSF*FHF*FLF*F**(FXF*F KF*FNF*F**(FTF*F(F*FPF*F**&FUF*)F.FjoF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(B1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&,& %\"xG\"\"\"%\"yGF'F',hp*()F&\"\"&F'F(F'%\"uGF'F'*(F+F'F(F'%\"tGF'!\"\" *()F&\"\"#F')F(\"\"$F'%\"lGF'F0*&)F(F,F'F6F'F0*&F-F')F(\"\"'F'F0*$F+F' F0*$)F(\"\"%F'F'*(F&F'F>F'F6F'F'*&%\"nGF')F&F;F'F0*&)F&F?F'F(F'F0*(F+F 'F(F'%\"pGF'F0*(F+F'F(F'%\"sGF'F'**F3F'FEF'%\"jGF'F(F'F'**F?F'FEF'F6F' F(F'F'*(FEF'%\"hGF'F(F'F0*(FEF')F(F3F'%\"rGF'F'*(FEF'FPF'F/F'F'*(FEF'F -F'FPF'F0*(FEF'FPF'FIF'F0*(FEF'FPF'%\"qGF'F0*()F&F5F'FPF'F6F'F'*(FXF'F PF'%\"kGF'F0*(FXF'FPF'FKF'F'*(FXF'FPF'FNF'F0*(FXF'F4F'FQF'F0*(FXF'F4F' F/F'F0*(FXF'F-F'F4F'F'*(FXF'F4F'FIF'F'*(F2F'F4F'FZF'F'*(F2F'F4F'FKF'F0 *&FCF'FQF'F'*&FCF'F/F'F'*&FCF'F-F'F0*&FCF'FGF'F'*&FCF'FIF'F0*&FCF'FVF' F0*&FPF'F2F'F0*(F+F'F(F'FVF'F'*(F2F'F>F'F/F'F'*(F2F'F-F'F>F'F0*(F2F'F> F'FIF'F0*(F&F'F>F'FZF'F0*(F&F'F8F'F/F'F0*(F&F'F-F'F8F'F'*(F+F'F(F'FQF' F0**F5F'FEF'FZF'F(F'F0F'F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "pol ynomial factors, case B complete [5]" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Back to case A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "s olve(5+64*r+96*t-6*j-112*u+10*l-6*g+32*p-16*n-80*s-48*q+8*h-48*h*k+80* h*l+24*h*j-4*h^2+96*j*k-150*j*l-6*j*g-27*j^2-80*k^2+240*k*l+16*k*g-175 *l^2-30*l*g+g^2,n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,T*&\"\"%\"\"\" %\"rGF&F&*&\"\"'F&%\"tGF&F&*(\"\"$F&\"\")!\"\"%\"jGF&F.*&\"\"(F&%\"uGF &F.*(\"\"&F&F-F.%\"lGF&F&*(F,F&F-F.%\"gGF&F.*&\"\"#F&%\"pGF&F&*&F4F&% \"sGF&F.*&F,F&%\"qGF&F.*&F9F.%\"hGF&F&*(F,F&F@F&%\"kGF&F.*(F4F&F@F&F5F &F&**F,F&F9F.F@F&F/F&F&*&F%F.F@F9F.*(F)F&F/F&FBF&F&**\"#vF&F-F.F/F&F5F &F.**F,F&F-F.F/F&F7F&F.*(\"#FF&\"#;F.F/F9F.*&F4F&)FBF9F&F.*(\"#:F&FBF& F5F&F&*&FBF&F7F&F&*(\"$v\"F&FLF.F5F9F.**FPF&F-F.F5F&F7F&F.*&FLF.F7F9F& #F4FLF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "A3:=eval(A2,n=4 *r+6*t-3/8*j-7*u+5/8*l-3/8*g+2*p-5*s-3*q+1/2*h-3*h*k+5*h*l+3/2*h*j-1/4 *h^2+6*j*k-75/8*j*l-3/8*j*g-27/16*j^2-5*k^2+15*k*l+k*g-175/16*l^2-15/8 *l*g+1/16*g^2+5/16);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A3G,B*$)%\" xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**(,.F*F* %\"jGF*%\"kGF1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F(\"\"%F*F 2F*F**(F7F*)F(\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F*)F.F;F*F **&F8F*)F.F)F*F**&,T*&FAF*%\"rGF*F**&F;F*%\"tGF*F**(\"\"*F*\"\")F1F5F* F1*&F)F*%\"uGF*F1*(F;F*FRF1F8F*F1*(F;F*FRF1F9F*F1%\"pGF*F6F**&F>F*%\"s GF*F1*&F/F*%\"qGF*F1F7F**&F7F*F6F*F1**F;F*F/F1F7F*F8F*F**(F/F1F7F*F9F* F1*&F>F1F7F/F**(FAF*F5F*F6F*F***\"#XF*FRF1F5F*F8F*F1**FAF*FRF1F5F*F9F* F**(FQF*\"#;F1F5F/F1*&FAF*)F6F/F*F1*(\"#5F*F6F*F8F*F**(\"$D\"F*F_oF1F8 F/F1**F;F*FRF1F8F*F9F*F1*(FAF*F_oF1F9F/F*#\"\"(F_oF*F*)F(FioF*F**(,T*& F>F*FMF*F**&F)F*FOF*F**(FAF*FRF1F5F*F1*&FioF*FTF*F1*(F;F*FRF1F8F*F**(F AF*FRF1F9F*F1*&F/F*FWF*F**&F;F*FYF*F1*&FAF*FenF*F1*&F/F1F7F*F**(FAF*F7 F*F6F*F1*(F;F*F7F*F8F*F***FAF*F/F1F7F*F5F*F**&F>F1F7F/F1*(F)F*F5F*F6F* F***\"#vF*FRF1F5F*F8F*F1**FAF*FRF1F5F*F9F*F1*(\"#FF*F_oF1F5F/F1*&F;F*F aoF*F1*(\"#:F*F6F*F8F*F**&F6F*F9F*F**(\"$v\"F*F_oF1F8F/F1**FcqF*FRF1F8 F*F9F*F1*&F_oF1F9F/F*#F;F_oF*F*F'F*F.F*F**(FWF*F:F*F2F*F**(FenF*F=F*FB F*F**(FMF*F@F*FEF*F**(FYF*FDF*FGF*F**(FOF*F(F*FIF*F**&FTF*)F.FioF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A3,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<&%\"xG-%'RootOfG6#,(*&%\"uG\"\"\")%#_ ZG\"\"#F+F+*&%\"lGF+F-F+F+F+!\"\",(F$F1*&)F$F.F+,.#F+\"\"%F1*&F.F1%\"h GF+F1%\"kGF1*(\"\"&F+F7F1F0F+F+*&F7F1%\"gGF+F+*(\"\"$F+F7F1%\"jGF+F+F+ F+*&)F$F@F+-F&6#,jilF+F+*&\"#CF+%\"rGF+F+*&\"#gF+%\"tGF+F+*&\"\")F+FAF +F1*&\"#%)F+F*F+F1*&F7F+F>F+F1*&F7F+%\"pGF+F+*&\"\"'F+F:F+F+**\"%W8F+F *F+F9F+F:F+F1**\"%gLF+F*F+F:F+F0F+F+**\"%+;F+%\"sGF+F:F+F0F+F+*&\"#SF+ FfnF+F1**\"%+=F+FLF+FAF+F0F+F+**\"$?\"F+%\"qGF+F0F+F>F+F1**\"$+)F+FfnF +F9F+F0F+F+**FhnF+FSF+F0F+F>F+F+**\"$?(F+F9F+F:F+F0F+F+**\"$+%F+FfnF+F 0F+F>F+F1**\"$I$F+F9F+F0F+FAF+F1**\"$S)F+F*F+F0F+F>F+F1**\"#[F+F9F+F:F 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**F]_lF%F;F%F>F%F5F%F%**F[^lF%F;F%F>F%F8F%F%**FcwF%FMF%FAF%F>F%F%**Fg^ lF%FMF%FAF%F5F%F)**F`^lF%FMF%FAF%F8F%F)**Fj^lF%FMF%FAF%F/F%F)**Fh`lF%F MF%F/F%F>F%F)**Fj_lF%FMF%F/F%F5F%F%**F_sF%FMF%F/F%F8F%F%**Fe_lF%FMF%F> F%F5F%F)**FaoF%FMF%F>F%F8F%F)**\"'!oF$F%FFF%FAF%F>F%F%**F]_lF%FFF%FAF% F8F%F)**Fe_lF%FFF%FAF%F/F%F)**F^alF%FFF%F/F%F>F%F)**\"'+WhF%FFF%F/F%F5 F%F%**Fg^lF%FFF%F/F%F8F%F%**F__lF%FFF%F>F%F8F%F)*(F`^lF%FMF%FjnF%F%*(F guF%FMF%F`qF%F%*(FcwF%FMF%FcqF%F%*(F]vF%FMF%FjqF%F%*(F]oF%FMF%F_rF%F%* (F]_lF%FFF%FjnF%F%*(Fj_lF%FFF%F`qF%F%*(F\\clF%FFF%FcqF%F%*(\"'+?^F%FFF %FjqF%F%*(FHF%FFF%F_rF%F%*(Fg^lF%F,F%FjnF%F)*(Fd[lF%F,F%F`qF%F)*(F^alF %F,F%FcqF%F)*(\"'+!o(F%F,F%FjqF%F)*(F+F%F,F%F_rF%F)**F^alF%F,F%FAF%F>F %F)**FaclF%F,F%FAF%F5F%F%**Fg^lF%F,F%FAF%F8F%F%**\"'!GP(F%F,F%F/F%F>F% F%**Fj_lF%F,F%F/F%F8F%F)**Fe_lF%F,F%F>F%F8F%F%**Fg_lF%F,F%F5F%F8F%F)** F\\`lF%F2F%FAF%F8F%F)**\"''4;&F%F2F%FAF%F/F%F)**\"(S-H\"F%F2F%F/F%F5F% F%**Fc`lF%F2F%F/F%F8F%F%**F^`lF%F2F%F>F%F8F%F)*(F\\`lF%F2F%FjnF%F%*(\" 'sqQF%F2F%F`qF%F%*(F@F%F2F%FcqF%F%*(\"(+_2\"F%F2F%FjqF%F%*(F1F%F2F%F_r F%F%*(F[^lF%FatF%F>F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " factor(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"#k\"\"\"),.F&!\"\" *&\"\"#F&%\"hGF&F)*&\"\"%F&%\"kGF&F)*&\"\"&F&%\"lGF&F&%\"gGF&*&\"\"$F& %\"jGF&F&F+F&,T\"#F&%\"rGF&F&*&\"$![F&%\"tGF&F&*&\"#9F&F6F&F &*&\"$s'F&%\"uGF&F)*&\"#IF&F2F&F&*&F@F&F3F&F&*&\"#KF&%\"pGF&F&*&\"#;F& F/F&F)*&\"$?$F&%\"sGF&F)*&\"#'*F&%\"qGF&F)*&FKF&F,F&F)*(F%F&F,F&F/F&F) *(\"$g\"F&F,F&F2F&F&*(FKF&F,F&F6F&F&*(\"$w\"F&F6F&F/F&F&*(\"$q$F&F6F&F 2F&F)*(F+F&F6F&F3F&F)*&\"#LF&)F6F+F&F)*&F:F&)F/F+F&F)*(\"$?(F&F/F&F2F& F&*(FKF&F/F&F3F&F&*&\"$D'F&)F2F+F&F)*(\"#]F&F2F&F3F&F)*$)F3F+F&F)F&F) " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "The shorter factor is the sa me as the one considered in case B. Here we will consider the longer \+ factor [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "solve(-17+1 92*r+480*t+14*j-672*u+30*l+14*g+32*p-16*k-320*s-96*q-16*h-64*h*k+160*h *l+16*h*j+176*j*k-370*j*l-2*j*g-33*j^2-192*k^2+720*k*l+16*k*g-625*l^2- 50*l*g-g^2,p);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,R#\"#<\"#K\"\"\"*& \"\"'F'%\"rGF'!\"\"*&\"#:F'%\"tGF'F+*(\"\"(F'\"#;F+%\"jGF'F+*&\"#@F'% \"uGF'F'*(F-F'F1F+%\"lGF'F+*(F0F'F1F+%\"gGF'F+**\"#XF'\"\"#F+%\"kGF'F7 F'F+*&F " 0 "" {MPLTEXT 1 0 190 "A4:=eval(A3,p=17/32-6* r-15*t-7/16*j+21*u-15/16*l-7/16*g-45/2*k*l+1/2*k+10*s+3*q+1/2*h+2*h*k- 5*h*l-1/2*h*j-11/2*j*k+185/16*j*l+1/16*j*g+33/32*j^2+6*k^2+1/32*g^2-1/ 2*k*g+625/32*l^2+25/16*l*g);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A4G ,B*$)%\"xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F* *(,.F*F*%\"jGF*%\"kGF1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F( \"\"%F*F2F*F**(F7F*)F(\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F* )F.F;F*F**&F8F*)F.F)F*F**&,V*&FAF*%\"rGF*F1*&\"#5F*%\"tGF*F1*(\"#DF*\" #;F1F5F*F1*&\"#:F*%\"uGF*F**(FRF*FSF1F8F*F1*(\"#F1F7F/F***F;F*F/F1F5F*F6F*F 1**\"#&*F*FSF1F5F*F8F*F***\"\"(F*FSF1F5F*F9F*F**(FUF*\"#KF1F5F/F**&FAF *)F6F/F*F***FRF*F/F1F6F*F8F*F1*(F/F1F6F*F9F*F1*(\"$v$F*FdoF1F8F/F***FU F*FSF1F8F*F9F*F**(FboF*FdoF1F9F/F*#\"#JFdoF*F*)F(FboF*F**(,R*&\"\")F*F MF*F1*&\"#CF*FPF*F1*(F;F*F>F1F5F*F1*&\"#NF*FVF*F**(F;F*F>F1F8F*F1*(F;F *F>F1F9F*F1F6F**&FUF*FfnF*F**&FAF*FgnF*F**(FAF*F/F1F7F*F*#\"#6FcpF*Fin F**(F;F*F7F*F8F*F1*(F/F1F7F*F5F*F**&F>F1F7F/F1*(F;F*F5F*F6F*F1**\"#bF* F>F1F5F*F8F*F**(F>F1F5F*F9F*F1*(FAF*FcpF1F5F/F**&FboF*FfoF*F**(\"#IF*F 6F*F8F*F1*(\"$D#F*FcpF1F8F/F***F;F*F>F1F8F*F9F*F**&FcpF1F9F/F*F*F'F*F. F*F**(,R#FYFdoF**&F)F*FMF*F1*&FUF*FPF*F1*(FboF*FSF1F5F*F1*&\"#@F*FVF*F **(FUF*FSF1F8F*F1*(FboF*FSF1F9F*F1**\"#XF*F/F1F6F*F8F*F1*&F/F1F6F*F**& FOF*FfnF*F**&FAF*FgnF*F**&F/F1F7F*F**(F/F*F7F*F6F*F**(F;F*F7F*F8F*F1*( F/F1F7F*F5F*F1**F_qF*F/F1F5F*F6F*F1**\"$&=F*FSF1F5F*F8F*F**(FSF1F5F*F9 F*F**(\"#LF*FdoF1F5F/F**&F)F*FfoF*F**&FdoF1F9F/F**(F/F1F6F*F9F*F1*(\"$ D'F*FdoF1F8F/F***FRF*FSF1F8F*F9F*F*F*F:F*F2F*F**(FgnF*F=F*FBF*F**(FMF* F@F*FEF*F**(FfnF*FDF*FGF*F**(FPF*F(F*FIF*F**&FVF*)F.FboF*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#,(*&%\"uG\"\"\")%#_ ZG\"\"#F+F+*&%\"lGF+F-F+F+F+!\"\",**(\"1'\\qti*f.XF1,j\\o\"#\\F1*&\"$c #F+%\"rGF+F1*$)%\"gG\"\"&F+F+*&\"'v=F+%\"qGF+F0F+FF+FhnF+F0F+FCF+F*F+F^pF+FVF+F+**\"'+S]F +F*F+FJF+FipF+F1**\"'+CIF+F*F+F^pF+F0F+F1**\"&g,#F+F*F+FJF+F]rF+F1**\" &![gF+F*F+F^pF+FF+FhnF+FVF+FipF+F +**F[zF+FhnF+FVF+F]rF+F+**\"&+![F+FhnF+FipF+FF+F0F +FF+Fh^lF+F+* &\"%+;F+F_pF+F1*&\"&]A\"F+FerF+F1*&\"$U\"F+FCF+F+*(\"%'p'F+F^pF+FVF+F1 *(\"%]SF+FJF+FipF+F1*(\"%5`F+F^pF+F0F+F+*(\"%'3\"F+FJF+F]rF+F+*(\"%YEF +F^pF+FF+FYF+FVF+F]rF+F1**\"%+=F+FjqF+F0F+FF+FjqF+FipF+F+*(\"&+g)F+FYF+FerF+F1*(\"$C'F+FhrF+F< F+F+*(\"$k&F+FjqF+F]rF+F1*(\"$C#F+FYF+FCF+F+*(\"%#R\"F+FhrF+FJF+F+*(\" %GEF+FjqF+F^pF+F1*(\"%W>F+FYF+Fh^lF+F+*(\"&%e>F+FJF+F_pF+F1*(\"&w8\"F+ F^pF+FdrF+F+*(\"%'H\"F+Fh^lF+FVF+F1*(\"&g-\"F+Fh^lF+F0F+F+*(\"&gD)F+F_ pF+F0F+F1*(\"%)o#F+F_pF+FF+F_ oF+F)F+FGF+F_pF+F1**\"'?vMF+FJF+F_pF+F0F+F+**\"'+*3\"F+Fjq F+FipF+FJF+F1**\"'+SdF+FYF+FVF+FerF+F1**\"&S)>F+FhrF+FVF+F0F+F1**\"'+g =F+FjqF+FVF+FipF+F+**\"&k;\"F+FYF+FVF+Fh^lF+F1**\"%%=&F+Fh^lF+FVF+FF+FYF+FdrF +FF+FYF+F0F+F^pF+FVF+F1*,\"'?BNF+FYF+FdrF+F0F+FJF+F+*,Fe`mF+FhnF+ FJF+FVF+F0F+F+*(\"%'4%F+F_oF+F_pF+F+**Fc[lF+F_oF+FYF+FipF+F+*,\"%35F+F YF+FVF+F]rF+FJF+F1*,\"%cqF+FYF+FVF+F)F1FF+Fg jmF1FYF.F1**\"$^#F+Fa]nF1FJF+FVF+F+**\"%b6F+FgjmF1FJF+F0F+F1**\"$6$F+F gjmF1FJF+F\"F+F^\\nF1F)F+FgjmF1FYF.FJF+F+**F_hnF+Fgj mF1FYF+FJF.F1**\"$6%F+Fa]nF1FJF+FVF.F+*(\"#(*F+FagnF1FYFDF1*(\"$***F+F ^\\nF1FJFDF+*(\"#DF+F_dnF1FVFDF1*(\"%DhF+F^\\nF1F0FDF1*(\"#rF+F^\\nF1F F+F_rF1FYFDFVF+FJF+F1*,\"$8&F+F a]nF1FYF.FVF+FJF.F+**FgimF+FgjmF1FJFDFF+Fa]nF1FJF.FVF.F0F+F1*,F^dnF+FagnF1FYF+F0F +F " 0 "" {MPLTEXT 1 0 7415 "factor(-1/32*r-5/32*t+471/ 8192*j+35/128*u+765/8192*l+177/8192*g-155/2048*k+15/4*s*h*k+5/64*s+1/1 28*q-163/4096*h+7/16*h^3*k^2+15/8*h^2*k^3+807/128*j^2*k^3-1647/512*j^3 *k^2-1179/512*j^2*k^2*g-249/512*j*k^2*g^2-15375/512*k^2*l^2*g-1275/512 *k^2*l*g^2-111/16*h*k^3*j-395/16*h*k^3*l-27/16*h*k^3*g+2715/64*j*k^3*l +203/64*j*k^3*g-19215/512*j^2*k^2*l-5085/256*j*k^2*g*l+1/8192*g^5+555/ 512*h*k*l-705/256*j*k*l*g+75/512*h*l*g*j-213/256*h*k*g*j+2055/256*h*k* l*j+225/256*h*k*l*g-1605/1024*h^2*l*g*j+165/256*h*l*g^2*j+3105/1024*h* l*g*j^2+6225/512*h*l^2*j*g-2655/4096*j^2*l*g^2-3915/2048*j^3*l*g-42125 /2048*j*l^3*g-11175/4096*j*l^2*g^2-165/2048*j*l*g^3+5625/512*j^2*l*g*k +2325/64*j*l^2*g*k+675/256*j*l*g^2*k+5/8*s*h^3-135/64*s*j^3-625/64*s*l ^3-5/64*s*g^3+1/16*q*h^3-27/128*q*j^3-125/128*q*l^3-1/128*q*g^3-5/4*t* h^3+135/32*t*j^3+625/32*t*l^3+5/32*t*g^3+1/2*q*k^3+15/2*r*h*k*l+3/2*r* h*k*g+9/2*r*h*k*j-15/8*r*h*l*g-45/8*r*h*l*j-9/8*r*h*g*j-525/8*u*h*k*l- 105/8*u*h*k*g-315/8*u*h*k*j+525/32*u*h*l*g+68175/1024*j^2*l^2*k+29875/ 256*j*l^3*k+3645/256*j^3*l*k+171/1024*j^2*g^2*k+1/128*j*g^3*k+81/128*j ^3*g*k+1/32*h^4*k+1485/2048*j^4*k+7375/128*k^3*l^2+47/128*k^3*g^2-4662 5/512*k^2*l^3-13/512*k^2*g^3+143125/2048*l^4*k-3/2048*g^4*k+2575/1024* h^3*l^2-5/32*h^4*l-26625/2048*h^2*l^3-1/1024*h^3*g^2+3/2048*h^2*g^3-3/ 4096*h*g^4+15/1024*h^3*j^2-135/2048*h^2*j^3+405/4096*h*j^4+47475/2048* h*j^2*l^2-43875/4096*j^2*l^2*g+2625/64*u*h*l^2-75/16*r*h*l^2+1575/16*u *j*k*l-45/4*r*j*k*l+225/8*s*j*k*l-54675/4096*j^3*l^2-373125/8192*j*l^4 -15795/8192*j^4*l-151125/4096*j^2*l^3+15/4096*j^2*g^3-27/4096*j^3*g^2+ 11/8192*j*g^4-351/8192*j^4*g-106875/8192*l^4*g-11375/4096*l^3*g^2-875/ 4096*l^2*g^3-15/8192*l*g^4+113125/4096*l^4*h+35/2*u*k^3-2*r*k^3+2*k^5+ 16425/256*h*k^2*l^2-195/16*h^2*k^2*l-9/4*r*j*k*g+45/16*r*j*l*g-15/4*r* k*l*g+315/16*u*j*k*g-1575/64*u*j*l*g+525/16*u*k*l*g+45/8*s*j*k*g-225/3 2*s*j*l*g+75/8*s*k*l*g+9/16*q*j*k*g-45/64*q*j*l*g+15/16*q*k*l*g-45/4*t *j*k*g+225/16*t*j*l*g-75/4*t*k*l*g+27/32*r*j^2*g+15/2*r*k^2*l+3/2*r*k^ 2*g+5*s*k^3+375/32*s*h*l^2-75/8*r*k*l^2-3/8*r*k*g^2+75/32*r*l^2*g+15/3 2*r*l*g^2+105/8*u*h^2*k+105/4*u*h*k^2-525/32*u*h^2*l-105/32*u*h^2*g+10 5/64*u*h*g^2-315/32*u*h^2*j+945/64*u*h*j^2-315/8*u*j*k^2+945/32*u*j^2* k-7875/128*u*j*l^2-4725/128*u*j^2*l-315/128*u*j*g^2-945/128*u*j^2*g-52 5/8*u*k^2*l-105/8*u*k^2*g+2625/32*u*k*l^2+105/32*u*k*g^2-2625/128*u*l^ 2*g-525/128*u*l*g^2+15/4*s*h^2*k+15/2*s*h*k^2-75/16*s*h^2*l-15/16*s*h^ 2*g+15/32*s*h*g^2-45/16*s*h^2*j+135/32*s*h*j^2-45/4*s*j*k^2+135/16*s*j ^2*k-1125/64*s*j*l^2-675/64*s*j^2*l-45/64*s*j*g^2-135/64*s*j^2*g-75/4* s*k^2*l-15/4*s*k^2*g+375/16*s*k*l^2+15/16*s*k*g^2-375/64*s*l^2*g-75/64 *s*l*g^2+3/8*q*h^2*k+3/4*q*h*k^2-15/32*q*h^2*l-3/32*q*h^2*g+3/64*q*h*g ^2-9/32*q*h^2*j+27/64*q*h*j^2-9/8*q*j*k^2+27/32*q*j^2*k-225/128*q*j*l^ 2-135/128*q*j^2*l-9/128*q*j*g^2-27/128*q*j^2*g-15/8*q*k^2*l-3/8*q*k^2* g+75/32*q*k*l^2+3/32*q*k*g^2-75/128*q*l^2*g-15/128*q*l*g^2-15/2*t*h^2* k-15*t*h*k^2+75/8*t*h^2*l+15/8*t*h^2*g-15/16*t*h*g^2+45/8*t*h^2*j-135/ 16*t*h*j^2+45/2*t*j*k^2-135/8*t*j^2*k+1125/32*t*j*l^2+675/32*t*j^2*l+4 5/32*t*j*g^2+135/32*t*j^2*g+75/2*t*k^2*l+15/2*t*k^2*g-375/8*t*k*l^2-15 /8*t*k*g^2+375/32*t*l^2*g+75/32*t*l*g^2+735/64*k^3*l*g-55425/512*k^2*l ^2*j+16875/512*l^3*g*k+4875/1024*l^2*g^2*k+95/512*l*g^3*k+5505/128*h*k ^2*l*j+1425/128*h*k^2*l*g+297/128*h*k^2*g*j-10725/512*h*l^2*g*k-705/51 2*h*l*g^2*k+825/256*h^2*l*g*k-12285/512*h*l*j^2*k-39975/512*h*l^2*j*k+ 3405/256*h^2*l*j*k-441/512*h*g*j^2*k-63/512*h*g^2*j*k-23/4*k^4*j-35/2* k^4*l-3/2*k^4*g+13/4*k^4*h+9/512*h^2*k*g^2-3/64*h^3*k*g+1/512*h*k*g^3+ 513/512*h^2*k*j^2-19/64*h^3*k*j-729/512*h*k*j^3-6975/2048*h^2*l^2*g-31 5/2048*h^2*l*g^2+135/512*h^3*l*g+12375/1024*h*l^3*g+3075/2048*h*l^2*g^ 2+35/1024*h*l*g^3-27225/2048*h^2*l^2*j-6975/2048*h^2*l*j^2+615/512*h^3 *l*j+135/32*h*l*j^3+5625/128*h*l^3*j+15/2048*h^2*g^2*j-27/2048*h^2*g*j ^2-1/512*h^3*g*j-9/2048*h*g^2*j^2+27/512*h*g*j^3-3/512*h*g^3*j+57/256* h*k^2*g^2-9/16*h^2*k^2*g+1305/256*h*k^2*j^2-21/8*h^2*k^2*j+75/64*q*h*l ^2+45/16*q*j*k*l-225/4*t*j*k*l-375/16*t*h*l^2-10*t*k^3+1/32*r*g^3+125/ 32*r*l^3-1/4*r*h^3+27/32*r*j^3+1575/32*u*h*l*j+315/32*u*h*g*j-75/4*s*h *k*l-15/4*s*h*k*g-45/4*s*h*k*j+75/16*s*h*l*g+225/16*s*h*l*j+45/16*s*h* g*j-15/8*q*h*k*l-3/8*q*h*k*g-9/8*q*h*k*j+15/32*q*h*l*g+45/32*q*h*l*j+9 /32*q*h*g*j+75/2*t*h*k*l+15/2*t*h*k*g+45/2*t*h*k*j-75/8*t*h*l*g-225/8* t*h*l*j-45/8*t*h*g*j-49/8192-3/2*r*h^2*k-3*r*h*k^2+15/8*r*h^2*l+3/8*r* h^2*g-3/16*r*h*g^2+9/8*r*h^2*j-27/16*r*h*j^2+9/2*r*j*k^2-27/8*r*j^2*k+ 225/32*r*j*l^2+135/32*r*j^2*l+9/32*r*j*g^2+35/16*u*h^3-945/128*u*j^3-4 375/128*u*l^3-35/128*u*g^3+11625/512*h^2*k*l^2-35875/512*h*k*l^3-155/6 4*h^3*k*l-181/512*h*k+215/512*h*l+27/256*h*g+279/1024*h*j-195/2048*h^2 +251/512*j*k-1155/2048*j*l-311/2048*j*g-789/4096*j^2-155/512*k^2+85/12 8*k*l+51/256*k*g-1375/4096*l^2-495/2048*l*g-119/4096*g^2+303/512*h*k*g +669/512*h*k*j-675/1024*h*l*g-315/256*h*l*j-237/512*h*g*j-195/256*j*k* l-51/64*j*k*g+1695/2048*j*l*g-435/512*k*l*g-255/512*h^2*k-183/256*h*k^ 2+1065/2048*h^2*l-225/2048*h*l^2+333/2048*h^2*g-189/2048*h*g^2+819/204 8*h^2*j-1125/2048*h*j^2+411/512*j*k^2-837/1024*j^2*k-2025/4096*j*l^2+2 655/4096*j^2*l+543/4096*j*g^2+1323/4096*j^2*g-97/1024*h^3+999/4096*j^3 -135/512*k^2*l+237/512*k^2*g+1875/1024*k*l^2-177/1024*k*g^2+1125/4096* l^2*g+825/4096*l*g^2-25/128*k^3-6125/4096*l^3+71/4096*g^3-3075/256*h*l *g*j*k+93/256*h^2*g*j*k-435/256*h^2*k*l-1095/128*h*k^2*l+8925/512*h*k* l^2+93/256*h^2*k*g+33/128*h*k^2*g-11/64*h^3*k+17/16*h*k^3+15/512*h^3*l +4875/2048*h^2*l^2-5375/512*h*l^3+39/512*h^3*g-141/2048*h^2*g^2+7/256* h*g^3+87/512*h^3*j-657/2048*h^2*j^2+243/1024*h*j^3-153/64*j*k^3+711/51 2*j^2*k^2-81/512*j^3*k+37875/2048*j*l^3-123/512*h*k*g^2+129/256*h^2*k* j-111/128*h*k^2*j-135/512*h*k*j^2-225/1024*h^2*l*g-225/128*h*l^2*g+105 /512*h*l*g^2+405/1024*h^2*l*j-9675/1024*h*l^2*j-765/512*h*l*j^2-327/10 24*h^2*g*j+201/1024*h*g^2*j+27/64*h*g*j^2+4245/256*j*k^2*l-16275/512*j *k*l^2-135/16*j^2*k*l+9/256*j*k^2*g+153/512*j*k*g^2+99/256*j^2*k*g+772 5/2048*j*l^2*g-375/2048*j*l*g^2+675/2048*j^2*l*g+855/256*k^2*l*g-1875/ 256*k*l^2*g-1/32*h^4-405/8192*j^4+36675/4096*j^2*l^2+2565/2048*j^3*l-8 1/2048*j*g^3-549/4096*j^2*g^2-351/2048*j^3*g-645/64*k^3*l+13875/512*k^ 2*l^2-21/64*k^3*g-69/512*k^2*g^2-3875/128*k*l^3+13/256*k*g^3+9375/2048 *l^3*g+1125/4096*l^2*g^2-105/2048*l*g^3+5/4*k^4+99375/8192*l^4-33/8192 *g^4-405/8192*j^5-171875/8192*l^5+3/64*q*h+3/32*q*k-15/128*q*l-3/128*q *g-9/128*q*j-3/8*r*k+15/32*r*l+3/32*r*g+9/32*r*j-3/16*r*h+15/32*s*h+15 /16*s*k-75/64*s*l-15/64*s*g-45/64*s*j-15/16*t*h-15/8*t*k+75/32*t*l+15/ 32*t*g+45/32*t*j+105/64*u*h+105/32*u*k-525/128*u*l-105/128*u*g-315/128 *u*j+3/8*q*h*k+3/32*q*h^2+27/128*q*j^2+3/8*q*k^2+75/128*q*l^2+3/128*q* g^2-15/32*q*h*l-3/32*q*h*g-9/32*q*h*j-9/16*q*j*k+45/64*q*j*l+9/64*q*j* g-15/16*q*k*l-3/16*q*k*g+15/64*q*l*g-3/2*r*h*k+15/8*r*h*l+3/8*r*h*g+9/ 8*r*h*j+9/4*r*j*k-45/16*r*j*l-9/16*r*j*g+15/4*r*k*l+3/4*r*k*g-15/16*r* l*g-75/16*s*h*l-15/16*s*h*g-45/16*s*h*j-45/8*s*j*k+225/32*s*j*l+45/32* s*j*g-3/8*r*h^2-27/32*r*j^2-3/2*r*k^2-75/32*r*l^2-3/32*r*g^2+15/16*s*h ^2+135/64*s*j^2+15/4*s*k^2+375/64*s*l^2+15/64*s*g^2-75/8*s*k*l-15/8*s* k*g+75/32*s*l*g-15/2*t*h*k+75/8*t*h*l+15/8*t*h*g+45/8*t*h*j+45/4*t*j*k -225/16*t*j*l-45/16*t*j*g+75/4*t*k*l+15/4*t*k*g-75/16*t*l*g+105/8*u*h* k-525/32*u*h*l-105/32*u*h*g-315/32*u*h*j-315/16*u*j*k+1575/64*u*j*l+31 5/64*u*j*g-525/16*u*k*l-105/16*u*k*g+525/64*u*l*g-15/8*t*h^2-135/32*t* j^2-15/2*t*k^2-375/32*t*l^2-15/32*t*g^2+105/32*u*h^2+945/128*u*j^2+105 /8*u*k^2+2625/128*u*l^2+105/128*u*g^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"%#>)!\"\",.\"\"\"F&*&\"\"#F(%\"hGF(F&*&\"\"%F(%\"kGF(F&*& \"\"&F(%\"lGF(F(%\"gGF(*&\"\"$F(%\"jGF(F(F4,N*&\"#:F()F5F*F(F&*&\"#IF( F5F(F&*(F*F(F5F(F2F(F(*(\"$g\"F(F5F(F.F(F(*(\"$5&F(F5F(F1F(F&\"#\\F(*& F;F(F1F(F&*&F;F(F2F(F&*&\"#KF(F.F(F(*&FEF(F+F(F(*(FEF(F+F(F.F(F&*(F>F( F+F(F1F(F(*&\"$c#F()F.F*F(F&*(\"%!G\"F(F.F(F1F(F(*&\"%v8F()F1F*F(F&*(F ;F(F1F(F2F(F&*$)F2F*F(F(*&FJF(%\"rGF(F(*&FMF(%\"tGF(F(*&\"%SAF(%\"uGF( F&*&\"$S'F(%\"sGF(F&*&\"#kF(%\"qGF(F&F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Again, the shorter factor is the same as in case B. We w ill consider the longer factor [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "solve(-15*j^2-510*j*l+160*j*k-30*j+2*j*g+49-30*l-30* g+32*k+32*h-32*h*k+160*h*l-256*k^2+1280*k*l-1375*l^2-30*l*g+g^2+256*r+ 1280*t-2240*u-640*s-64*q,q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,L*(\" #:\"\"\"\"#k!\"\"%\"jG\"\"#F(*(F%F&\"#KF(F)F&F(*(F,F(F)F&%\"gGF&F&**\" \"&F&F*F(F)F&%\"kGF&F&**\"$b#F&F,F(F)F&%\"lGF&F(#\"#\\F'F&*(F%F&F,F(F4 F&F(*(F%F&F,F(F.F&F(*&F*F(F1F&F&*&F*F(%\"hGF&F&*(F*F(F;F&F1F&F(**F0F&F *F(F;F&F4F&F&*&\"\"%F&)F1F*F&F(*(\"#?F&F1F&F4F&F&*(\"%v8F&F'F(F4F*F(** F%F&F,F(F4F&F.F&F(*&F'F(F.F*F&*&F?F&%\"rGF&F&*&FBF&%\"tGF&F&*&\"#NF&% \"uGF&F(*&\"#5F&%\"sGF&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "A5:=eval(A4,q=-15/64*j^2-255/32*j*l+5/2*j*k-15/32*j+1/32*j*g+49/6 4-15/32*l-15/32*g+1/2*k+1/2*h-1/2*h*k+5/2*h*l-4*k^2+20*k*l-1375/64*l^2 -15/32*l*g+1/64*g^2+4*r+20*t-35*u-10*s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A5G,B*$)%\"xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\" \"F*)F.F/F*F**(,.F*F*%\"jGF*%\"kGF1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F. F*F**(F9F*)F(\"\"%F*F2F*F**(F7F*)F(\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F *F**(F6F*F(F*)F.F;F*F**&F8F*)F.F)F*F**&,P%\"rGF**&\"#5F*%\"tGF*F**(\"# lF*\"#KF1F5F*F1*&\"#?F*%\"uGF*F1*(FQF*FRF1F8F*F1*(\"#\\F*FRF1F9F*F1*&F /F*F6F*F**&F>F*%\"sGF*F1*&F/F*F7F*F**(F/F1F7F*F6F*F**(F/F1F7F*F9F*F1*( F/F1F7F*F5F*F1*&F>F1F7F/F***FQF*FRF1F5F*F8F*F1**\"#:F*FRF1F5F*F9F*F**( F]oF*\"#kF1F5F/F**$)F6F/F*F1**F]oF*F/F1F6F*F8F*F**(F/F1F6F*F9F*F1*(\"$ D'F*F_oF1F8F/F1**F]oF*FRF1F8F*F9F*F**(F]oF*F_oF1F9F/F*#\"$6\"F_oF*F*)F (\"\"(F*F**(,P*&F>F*FLF*F**&\"#OF*FOF*F**(\"#&)F*FRF1F5F*F1*&\"#qF*FUF *F1*(FbpF*FRF1F8F*F1*(FbpF*FRF1F9F*F1*(F;F*F/F1F6F*F**&F]oF*FenF*F1*&F AF*F7F*F*#\"$N#F_oF**(F/F1F7F*F6F*F1**F;F*F/F1F7F*F8F*F**(F/F1F7F*F5F* F**&F>F1F7F/F1**F;F*F/F1F5F*F6F*F***\"$D$F*FRF1F5F*F8F*F1**F;F*FRF1F5F *F9F*F1*(\"#@F*F_oF1F5F/F1*&F;F*FaoF*F1*(\"#IF*F6F*F8F*F**(\"%DBF*F_oF 1F8F/F1**F;F*FRF1F8F*F9F*F1*(\"#6F*F_oF1F9F/F*F*F'F*F.F*F**(,P*&F)F*FL F*F**&\"#XF*FOF*F**(\"#fF*FRF1F5F*F1*&\"#%)F*FUF*F1*(\"#vF*FRF1F8F*F1* 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We will consider the longer facto r [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "solve(-j^2-386*j *l+62*j-2*j*g+64*j*k-129+62*l+62*g-64*k-64*h+64*h*l-192*k^2+1408*k*l-1 985*l^2-2*l*g-g^2+128*r+1920*t-4480*u-640*s,r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,H*&\"$G\"!\"\"%\"jG\"\"#\"\"\"**\"$$>F)\"#kF&F'F)%\"lG F)F)*(F(F&F'F)%\"kGF)F&*(F,F&F'F)%\"gGF)F)*(\"#JF)F,F&F'F)F&#\"$H\"F%F )*(F3F)F,F&F-F)F&*(F3F)F,F&F1F)F&*&F(F&F/F)F)*&F(F&%\"hGF)F)*(F(F&F:F) F-F)F&*(\"\"$F)F(F&F/F(F)*(\"#6F)F/F)F-F)F&*(\"%&)>F)F%F&F-F(F)*(F,F&F -F)F1F)F)*&F%F&F1F(F)*&\"#:F)%\"tGF)F&*&\"#NF)%\"uGF)F)*&\"\"&F)%\"sGF )F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "A6:=eval(A5,r=1/128 *j^2+193/64*j*l-31/64*j+1/64*j*g-1/2*j*k+129/128-31/64*l-31/64*g+1/2*k +1/2*h-1/2*h*l+3/2*k^2-11*k*l+1985/128*l^2+1/64*l*g+1/128*g^2-15*t+35* u+5*s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A6G,B*$)%\"xG\"\"'\"\"\" F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**(,.F*F*%\"jGF*%\"kGF 1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F(\"\"%F*F2F*F**(F7F*)F (\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F*)F.F;F*F**&F8F*)F.F)F *F**&,R*&F;F*%\"tGF*F1*(\"$h\"F*\"#kF1F5F*F1*&\"#:F*%\"uGF*F**(FOF*FPF 1F8F*F1*(\"$H\"F*FPF1F9F*F1*(F;F*F/F1F6F*F*%\"sGF**(F;F*F/F1F7F*F**(F/ F1F7F*F6F*F**(F/F1F7F*F8F*F1*(F/F1F7F*F9F*F1*(F/F1F7F*F5F*F1*&F>F1F7F/ F**(F/F1F5F*F6F*F1**\"#jF*FPF1F5F*F8F*F***\"#JF*FPF1F5F*F9F*F**(F]oF* \"$G\"F1F5F/F**&F/F1F6F/F***\"\"(F*F/F1F6F*F8F*F1*(F/F1F6F*F9F*F1*(\"$ N(F*F_oF1F8F/F***F]oF*FPF1F8F*F9F*F**(F]oF*F_oF1F9F/F*#\"$^$F_oF*F*)F( FboF*F**(,N*&\"#CF*FMF*F1*(\"$Z\"F*\"#KF1F5F*F1*&\"#qF*FSF*F**(F`pF*Fa pF1F8F*F1*(F`pF*FapF1F9F*F1*(\"\"*F*F/F1F6F*F**&F;F*FXF*F**&F;F*F7F*F* #\"$$\\FPF**(F/F1F7F*F6F*F1*(F/F1F7F*F8F*F**(F/F1F7F*F5F*F**&F>F1F7F/F 1*(F/F1F5F*F6F*F***\"#hF*FapF1F5F*F8F*F***FAF*FapF1F5F*F9F*F1*(\"#>F*F PF1F5F/F1*$)F6F/F*F**(\"#9F*F6F*F8F*F1*(\"%X;F*FPF1F8F/F***FAF*FapF1F8 F*F9F*F1*(\"#8F*FPF1F9F/F*F*F'F*F.F*F**(,N*&\"#XF*FMF*F1*(FeqF*F>F1F5F *F1*&\"$E\"F*FSF*F**(\"#@F*F>F1F8F*F1*(FeqF*F>F1F9F*F1*&F;F*F6F*F**&\" #5F*FXF*F**&F;F*F7F*F**(F/F1F7F*F6F*F**(F/F1F7F*F8F*F1*(F/F1F7F*F5F*F1 *&F5F*F6F*F1**\"#BF*F>F1F5F*F8F*F**(F>F1F5F*F9F*F**(FAF*\"\")F1F5F/F** &FAF*FgqF*F***\"#dF*F/F1F6F*F8F*F1*(F/F1F6F*F9F*F1*(\"$&QF*FesF1F8F/F* *(F>F1F8F*F9F*F**&FesF1F9F/F*#\"#rFesF*F*F:F*F2F*F**(,J*&\"#SF*FMF*F1* (\"#xF*FapF1F5F*F1*&\"$0\"F*FSF*F**(FetF*FapF1F8F*F1*(FetF*FapF1F9F*F1 *(F;F*F/F1F6F*F**&F[sF*FXF*F**(F;F*F/F1F7F*F**(F/F1F7F*F6F*F1*(F/F1F7F *F8F*F**(F/F1F5F*F6F*F***\"$J\"F*FapF1F5F*F8F*F***FAF*FapF1F5F*F9F*F** (F^rF*FPF1F5F/F1*&F/F*FgqF*F**(F^pF*F6F*F8F*F1*(\"%&f#F*FPF1F8F/F***F^ rF*FapF1F8F*F9F*F1*(FAF*FPF1F9F/F*#\"$2$FPF*F*F=F*FBF*F**(,H*&F_oF1F5F /F***\"$$>F*FPF1F5F*F8F*F**(F/F1F5F*F6F*F1*(FPF1F5F*F9F*F**(F]oF*FPF1F 5F*F1#FVF_oF**(F]oF*FPF1F8F*F1*(F]oF*FPF1F9F*F1*&F/F1F6F*F**&F/F1F7F*F **(F/F1F7F*F8F*F1*(FAF*F/F1F6F/F**(\"#6F*F6F*F8F*F1*(\"%&)>F*F_oF1F8F/ F**(FPF1F8F*F9F*F**&F_oF1F9F/F**&FRF*FMF*F1*&\"#NF*FSF*F**&F;F*FXF*F*F *F@F*FEF*F**(FXF*FDF*FGF*F**(FMF*F(F*FIF*F**&FSF*)F.FboF*F*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A6,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<&%\"xG,,*(\">o^(>x'zo@8d739'R!\"\",d[ w\"$@$F(*,\"'gHb\"\"\"%\"tGF-%\"hGF-)%\"gG\"\"#F-%\"jGF-F-*,\"(!))e;F- F.F-F/F-F1F-)F3F2F-F-*,\")+%=@#F-F.F-F3F-)%\"kGF2F-%\"lGF-F(*,\")+![w# F-F.F-F3F-F:F-)F;F2F-F-*.\"(+c'eF-F/F-F;F-F6F-F1F-F:F-F(*&\"$h*F-)F1\" \"&F-F-*,\"(+g@*F-F.F-F:F-F>F-F1F-F-*,\"(+K%=F-F.F-F:F-F;F-F0F-F-**\"( ?\"\\HF-F.F-)F/F2F-F9F-F(*&\"'v=#*F-)F;FDF-F(**\"(+)G7F-F.F-)F/\"\"$F- F;F-F-**\"(+!3YF-F.F-FKF-F>F-F(**\"(++o(F-F.F-F/F-)F;FRF-F-*(\"&!Q_F-F ;F-)F1FRF-F(*&\"%O:F-F.F-F(*&\"%T\\F-F3F-F-*&\"%w`F-%\"uGF-F-*&\"%^\") F-F;F-F-*&\"%JF-F0F-F:F-F-*,\"(g0P# F-F3F-)F:FRF-F;F-F1F-F-*,\"'+_iF-F6F-F>F-F1F-F:F-F-*,\"'?:DF-F/F-FZF-F 3F-F:F-F(*,\"(!)[^\"F-F/F-F1F-FeoF-F:F-F(**\")+!o.\"F-F.F-F6F-F>F-F(** \")+?V=F-F.F-F9F-F>F-F(**\"'!GP(F-F.F-F9F-F0F-F(**\"(+?:\"F-F.F-F>F-F0 F-F(**\"'SI)*F-F.F-FQF-F:F-F(**\"'?ZTF-F.F-F6F-F0F-F(*&\"%[lF-F:F-F(** \"'g,')F-F[oF-F/F-F:F-F-*,\"'?RvF-FQF-F1F-F3F-F:F-F(*,\"'!oV*F-F/F-F0F -F6F-F:F-F(**\"(?bj'F-F.F-F6F-F9F-F(**\")++O:F-F.F-FWF-F:F-F-**\"(++%Q F-F.F-FWF-F1F-F(**\"'!)G7F-F.F-FZF-F:F-F-**\"&g@*F-F.F-FZF-F3F-F(**\"( gxJ$F-F.F-FeoF-F:F-F-**\"'g`LF-)F:\"\"%F-F;F-F1F-F(**\"(+/:#F-F[oF-F:F -F;F-F(*,\")+))e;F-F.F-F6F-F:F-F;F-F-*,\"(!oBWF-F.F-F3F-F9F-F1F-F(*,\" (?f5\"F-F.F-F3F-F:F-F0F-F-*,FbrF-F.F-F6F-F:F-F1F-F-*,\"(?^g\"F-FKF-F1F -F6F-F:F-F-*,\"'g&e'F-FKF-F0F-F3F-F:F-F-**\"'+C5F-%\"sGF-F:F-F;F-F(*( \"(+C-'F-FerF-F>F-F-*(\"'gP@F-FerF-F0F-F(*.\"(+%)>#F-F/F-F>F-F3F-F1F-F :F-F(*,\"(S)RBF-F/F-F\\pF-F1F-F3F-F(**\"'gdCF-F.F-FQF-F1F-F-**\"&S9'F- F.F-F/F-FZF-F-**FhpF-F.F-FQF-F3F-F-**F5F-F.F-FKF-F6F-F(**F5F-F.F-F/F-F eoF-F-**\"'?V=F-F.F-FKF-F0F-F(*&\"$c#F-FfsF-F-**\"'+3YF-F.F-F3F-F;F-F( **\"&+7&F-FfsF-F/F-F;F-F(**\"'+%e)F-F/F-F:F-F;F-F-**\"&+c#F-FfsF-F;F-F 1F-F-*,F\\sF-F.F-FKF-F:F-F3F-F-*,\"(gt%))F-F.F-F/F-F9F-F3F-F-*,FhqF-F. 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l^2+257425/32768*j^2*k*l-9805/4096*j*k^2*g+21805/32768*j*k*g^2+59705/3 2768*j^2*k*g-453275/131072*j*l^2*g-107975/131072*j*l*g^2-294385/131072 *j^2*l*g-15465/4096*k^2*l*g+144625/32768*k*l^2*g+35145/32768*k*l*g^2-2 245/32768*h^4-164115/524288*j^4-1207925/262144*j^2*l^2-264945/131072*j ^3*l-7985/131072*j*g^3-66125/262144*j^2*g^2-60405/131072*j^3*g+555/128 *k^3*l-60425/8192*k^2*l^2+535/512*k^3*g-3585/8192*k^2*g^2+173875/32768 *k*l^3+2635/32768*k*g^3-217375/131072*l^3*g-168025/262144*l^2*g^2-1309 5/131072*l*g^3-1885/2048*k^4-696875/524288*l^4-2875/524288*g^4+129303/ 524288*j^5-921875/524288*l^5-655/1024*k^4*l*g+5/1024*s*h+5/512*s*k-25/ 2048*s*l-5/2048*s*g-15/2048*s*j-15/512*t*h-15/256*t*k+75/1024*t*l+15/1 024*t*g+45/1024*t*j+105/1024*u*h+105/512*u*k-525/2048*u*l-105/2048*u*g -315/2048*u*j-25/256*s*h*l-5/256*s*h*g-15/256*s*h*j-15/128*s*j*k+75/51 2*s*j*l+15/512*s*j*g+5/256*s*h^2+45/1024*s*j^2+5/64*s*k^2+125/1024*s*l ^2+5/1024*s*g^2+7875/32*u*h*k^2*l^2-25/128*s*k*l-5/128*s*k*g+25/512*s* l*g-15/32*t*h*k+75/128*t*h*l+15/128*t*h*g+45/128*t*h*j+45/64*t*j*k-225 /256*t*j*l-45/256*t*j*g+75/64*t*k*l+15/64*t*k*g-75/256*t*l*g+105/64*u* h*k-525/256*u*h*l-105/256*u*h*g-315/256*u*h*j-315/128*u*j*k+1575/512*u *j*l+315/512*u*j*g-525/128*u*k*l-105/128*u*k*g+525/512*u*l*g-15/128*t* h^2-135/512*t*j^2-15/32*t*k^2-375/512*t*l^2-15/512*t*g^2+105/256*u*h^2 +945/1024*u*j^2+105/64*u*k^2+2625/1024*u*l^2+105/1024*u*g^2-14745/8192 *h*k*g^2*j^2-11835/4096*h*k*g*j^3-1965/4096*h*k*g^3*j-30015/4096*h*k*l *j^3+183375/4096*h*k*l^3*j+43875/4096*h*k*l^3*g-15375/8192*h*k*l^2*g^2 -2885/4096*h*k*l*g^3-26775/32768*h^2*l^2*g^2-68025/32768*h^2*l^2*j^2-7 64375/65536*h*l^3*j^2-934375/131072*h*l^4*g-15375/65536*h*l^3*g^2);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"')GC&!\"\",.\"\"\"F&*&\"\"#F(% \"hGF(F&*&\"\"%F(%\"kGF(F&*&\"\"&F(%\"lGF(F(%\"gGF(*&\"\"$F(%\"jGF(F(F 0,D*$)F5F*F(F(*&\"$E\"F(F5F(F&*(F*F(F5F(F2F(F(*(F:F(F5F(F1F(F&\"$@$F(* &F:F(F1F(F&*&F:F(F2F(F&*&\"$G\"F(F.F(F(*&FAF(F+F(F(*&\"#kF()F.F*F(F&*( \"$'*)F(F.F(F1F(F(*&\"%b=F()F1F*F(F&*(F*F(F1F(F2F(F(*$)F2F*F(F(*&\"%O: F(%\"tGF(F(*&\"%w`F(%\"uGF(F&*&\"$c#F(%\"sGF(F&F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "The shorter factor is the same as in case B. W e will consider the longer factor [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "solve(j^2-126*j*l-126*j+2*j*g+321-126*l-126*g+128*k+ 128*h-64*k^2+896*k*l-1855*l^2+2*l*g+g^2+1536*t-5376*u-256*s,s);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,B*&\"$c#!\"\"%\"jG\"\"#\"\"\"*(\"#jF) \"$G\"F&F'F)F&*(F,F&F'F)%\"gGF)F)**F+F)F,F&F'F)%\"lGF)F&#\"$@$F%F)*(F+ F)F,F&F0F)F&*(F+F)F,F&F.F)F&*&F(F&%\"kGF)F)*&F(F&%\"hGF)F)*&\"\"%F&F6F (F&**\"\"(F)F(F&F6F)F0F)F)*(\"%b=F)F%F&F0F(F&*(F,F&F0F)F.F)F)*&F%F&F.F (F)*&\"\"'F)%\"tGF)F)*&\"#@F)%\"uGF)F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A7:=eval(A6,s=%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%#A7G,B*$)%\"xG\"\"'\"\"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F. 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SYE&Q=_F&FJF&F`pF&F-F&F+F&F&*,FgtF&FJF&F*F&FF&F`oF& F+F&F&**\"/+[cBY7PF&F>F&FQF&FBF&F&**F`eqF&Fe_lF&FQF&F(F&F&**\"0+SQ3')> @\"F&FgqF&F`oF&FBF&F1**F9F&F6F&FGF&F+F&F&**\",S)z\"eV&F&F`pF&FGF&FBF&F &*&\"(w&[5F&)F+FdeuF&F&*&\"/++++Oz;F&)F0FdeuF&F&*,FcfpF&FJF&FgqF&F0F&F CF&F&*,\"/+?b2'R:&F&FJF&FgqF&FQF&F+F&F&*,F]flF&FJF&F0F&FjyF&F(F&F&*,\" -+W4XUkF&FJF&F0F&F*F&FBF&F1*,FgglF&FJF&F0F&FjyF&F-F&F&*,\".+gt71h\"F&F JF&FQF&F*F&F(F&F&*,\"/++W4XUkF&FJF&FGF&F`oF&F+F&F1*,\".g$f$HrF*F&FJF&F 'F&FF& FJF&FGF&FQF&FCF&F1*,\"/!GH0xO/\"F&FJF&F(F&F`pF&F-F&F1*,FdirF&FJF&FBF&F DF&F-F&F&*,\"/++!ojI0)F&FJF&F(F&FcyF&F-F&F1**\"/+?jT>JBF&F'F&F`oF&F " 0 "" {MPLTEXT 1 0 10 "factor(%); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"(w&[5\"\"\"),.F&!\"\"*&\"\"# F&%\"hGF&F)*&\"\"%F&%\"kGF&F)*&\"\"&F&%\"lGF&F&%\"gGF&*&\"\"$F&%\"jGF& F&\"\"'F&,@*$)F6F+F&F)*(F+F&F6F&F3F&F)*&\"$a#F&F6F&F&*(F+F&F6F&F2F&F) \"$p(F)*&F=F&F2F&F&*&F=F&F3F&F&*&\"$c#F&F/F&F)*&FCF&F,F&F)*(FCF&F/F&F2 F&F&*&\"%D5F&)F2F+F&F)*(F+F&F2F&F3F&F)*$)F3F+F&F)*&\"$7&F&%\"tGF&F&*& \"%%e$F&%\"uGF&F)F&F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "The shor ter factor is the same as in case B. We will consider the longer fact or [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "solve(-j^2-2*j* g-2*j*l+254*j-769+254*l+254*g-256*k-256*h+256*k*l-1025*l^2-2*l*g-g^2+5 12*t-3584*u,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,>*&\"$7&!\"\"%\"jG \"\"#\"\"\"*(\"$c#F&F'F)%\"gGF)F)*(\"$F\"F)F+F&F'F)F&*(F+F&F'F)%\"lGF) F)#\"$p(F%F)*(F.F)F+F&F0F)F&*(F.F)F+F&F,F)F&*&F(F&%\"kGF)F)*&F(F&%\"hG F)F)*(F(F&F6F)F0F)F&*(\"%D5F)F%F&F0F(F)*(F+F&F0F)F,F)F)*&F%F&F,F(F)*& \"\"(F)%\"uGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A8:=eva l(A7,t=%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A8G,B*$)%\"xG\"\"'\" \"\"F**(),&F(F*%\"yGF*\"\"#F*,&F(F*F.!\"\"F*)F.F/F*F**(,.F*F*%\"jGF*% \"kGF1%\"hGF1%\"lGF*%\"gGF*F*)F(\"\"&F*F.F*F**(F9F*)F(\"\"%F*F2F*F**(F 7F*)F(\"\"$F*)F.FAF*F**(F5F*)F(F/F*)F.F>F*F**(F6F*F(F*)F.F;F*F**&F8F*) F.F)F*F**&,N*(\"$(*)F*\"$c#F1F5F*F1%\"uGF**(FMF*FNF1F8F*F1*(\"$p(F*FNF 1F9F*F1*(\"\"(F*F/F1F6F*F**(FTF*F/F1F7F*F*#\"%:G\"$7&F**(F/F1F7F*F6F*F **(F/F1F7F*F8F*F1*(F/F1F7F*F9F*F1*(F/F1F7F*F5F*F1*&F>F1F7F/F**(F/F1F5F *F6F*F1**\"$F\"F*FNF1F5F*F8F*F***FjnF*FNF1F5F*F9F*F**(FjnF*FXF1F5F/F** &F>F1F6F/F**(F/F1F6F*F8F*F1*(F/F1F6F*F9F*F1*(\"$b#F*FXF1F8F/F***FjnF*F NF1F8F*F9F*F**(FjnF*FXF1F9F/F*F*)F(FTF*F**(,J*(\"$@$F*\"#KF1F5F*F1*&FT F*FOF*F**(FhoF*FioF1F8F*F1*(FhoF*FioF1F9F*F1*&\"#5F*F6F*F**(\"#@F*F/F1 F7F*F*#\"%r9\"#kF**(F/F1F7F*F6F*F1*(F/F1F7F*F8F*F**(F/F1F7F*F5F*F**&F> F1F7F/F1*(F/F1F5F*F6F*F***\"#F1F6F/F1*(F/F1F6F*F8F*F**(\"#&*F*FcpF1F8F/F**(FioF1F8F *F9F*F1*(\"#:F*FcpF1F9F/F*F*F'F*F.F*F**(,J*(\"%\"Q%F*FNF1F5F*F1*&F`pF* FOF*F**(\"%4XF*FNF1F8F*F1*(FgqF*FNF1F9F*F1*(\"#NF*F/F1F6F*F**(F]rF*F/F 1F7F*F*#\"&*\\AFXF**(F/F1F7F*F6F*F**(F/F1F7F*F8F*F1*(F/F1F7F*F5F*F1*&F 5F*F6F*F1**\"$F#F*FNF1F5F*F8F*F***\"#**F*FNF1F5F*F9F*F**(FfrF*FXF1F5F/ F**&F/F1F6F/F**&F6F*F8F*F1*(F/F1F6F*F9F*F1*(\"%:HF*FXF1F8F/F***FhrF*FN F1F8F*F9F*F**(FhrF*FXF1F9F/F*F*F:F*F2F*F**(,F*(\"#pF*F>F1F5F*F1*&F]rF* FOF*F**(FdsF*F>F1F8F*F1*(FdsF*F>F1F9F*F1*(F]rF*F/F1F6F*F**(F]rF*F/F1F7 F*F*#\"$z$\"\")F**(F/F1F7F*F6F*F1*(F/F1F7F*F8F*F**(F/F1F5F*F6F*F***FAF *F>F1F5F*F8F*F1*(F>F1F5F*F9F*F**&F\\tF1F5F/F1*&F/F1F6F/F1F[sF**(\"#lF* F\\tF1F8F/F**(F>F1F8F*F9F*F1*&F\\tF1F9F/F*F*F=F*FBF*F**(,D*(\"%fEF*FNF 1F5F*F1*&F]rF*FOF*F**(F[uF*FNF1F8F*F1*(F[uF*FNF1F9F*F1*(F`pF*F/F1F6F*F **(F`pF*F/F1F7F*F*#\"&h_\"FXF**(F/F1F7F*F8F*F1*(F/F1F5F*F6F*F1**\"$d\" F*FNF1F5F*F8F*F***\"#HF*FNF1F5F*F9F*F**(FhuF*FXF1F5F/F**&F>F1F6F/F*F[s F1*(\"%lZF*FXF1F8F/F***FhuF*FNF1F8F*F9F*F**(FhuF*FXF1F9F/F*F*F@F*FEF*F **(,@*(\"$6\"F*FioF1F5F*F1*&F`pF*FOF*F**(FbvF*FioF1F8F*F1*(FbvF*FioF1F 9F*F1*(FTF*F/F1F6F*F**(FTF*F/F1F7F*F***FcqF*FioF1F5F*F8F*F1*(FioF1F5F* F9F*F**&FcpF1F5F/F**&F>F1F6F/F1*(F/F1F6F*F8F*F**(\"$0$F*FcpF1F8F/F**(F ioF1F8F*F9F*F**&FcpF1F9F/F*#\"$d'FcpF*F*FDF*FGF*F**(,>*&FXF1F5F/F**(FN F1F5F*F9F*F**(FjnF*FNF1F5F*F1*(FNF1F5F*F8F*F*#FRFXF**(FjnF*FNF1F8F*F1* (FjnF*FNF1F9F*F1*&F/F1F6F*F**&F/F1F7F*F**(F/F1F6F*F8F*F1*(\"%D5F*FXF1F 8F/F**(FNF1F8F*F9F*F**&FXF1F9F/F**&FTF*FOF*F*F*F(F*FIF*F**&FOF*)F.FTF* F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A8,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<&%\"xG-%'RootOfG6#,(*&%\"uG\"\"\")%#_ ZG\"\"#F+F+*&%\"lGF+F-F+F+F+!\"\",.*(\"OCmu#QO^\\\\%pfGe5))ffq#pZsU\"F 1,fc`l\"%$z\"F1*,\")gx*\\$F+)%\"hG\"\"$F+)%\"gGF;F+%\"jGF+%\"kGF+F1*, \")+GLVF+F9F+FF+F0F+F+*,\")![)ycF+F9F+F\"\"&F+F:F+F?F+F0F+F1*,\"*7x%G9F+FFF+F:F+F?F+F=F+F1*,\"+?ZTGHF+)F>F .F+)F?\"\"%F+F:F+F0F+F+*,\"*+sY(>F+)F:F.F+F?F+)F=F.F+)F>F;F+F+*,\")?B$ )**F+FQF+)F?F.F+FF+F1*.\"++_&HB#F+F:F+F0F+FLF+F=F+F?F+F1*&\"&Qb&F +)F=FGF+F+*&\"*]iqF\"F+)F0FGF+F+*(\"(_4a\"F+F0F+FF+F +*&\"%C5F+F*F+F+*&\"&lK'F+F0F+F+*&\"&hI\"F+F=F+F+*&\")ukf5F+FFF+F+**\" *!3q'='F+FSF+FMF+F:F+F+**\"*+q'3^F+)F>FNF+)F0F;F+F=F+F1**\")O(G]&F+)F: FGF+FVF+F>F+F+**\")?X,LF+FioF+FF+FjoF+F=F+F?F+F +*,\"*+WXk*F+F>F+)F0F.F+FRF+F?F+F+*,\"+!onh\">F+F>F+)F?F;F+F0F+F=F+F+* ,\"++k9+FF+FLF+FdpF+F=F+F?F+F+*,\")![!=dF+F:F+FF+F?F+F1*,\"*SMx_% F+F:F+F=F+FSF+F?F+F1*&\"&;2&F+F?F+F1**\"'kSMF+F*F+F:F+F?F+F+*,\"*+393# F+F9F+F=F+F>F+F?F+F1*,\"*?F%=CF+F:F+FRF+FLF+F?F+F1**\"*?>/L'F+FMF+F0F+ F=F+F1**\"'g,')F+F*F+F?F+F0F+F1*,\"*gF+F?F+F+*(\"++s=V9F+FMF+FdpF+F1*(\")!)[zoF+FMF+FRF+F1*. \"+++#\\m$F+F:F+FdpF+F>F+F=F+F?F+F1*,\"*?bF\"zF+F:F+FgpF+F=F+F>F+F1*& \"(3')Q)F+)F?\"\")F+F1*.\"+g`x,DF+F>F+FMF+F=F+F:F+F0F+F+**\")!oxe\"F+F :F+F?F+F0F+F+**\")37'>\"F+F:F+F0F+F>F+F1**\"'S]@F+F*F+F0F+F=F+F+**\"(C EJ$F+F:F+F?F+F=F+F+*(\")7T*y%F+FFF+F:F+F+*,\"*+;3R\"F+F0F+FF+F?F+ F+*,\")?R:%*F+F0F+FF+F?F+F1*(\"*](G*)QF+F>F+FetF+F+**\"'!3I%F +F*F+F:F+F0F+F1*(\")+DW7F+FF+F+**\"*?v-B\"F+F^tF+F0F+F>F+F1**\"++gUM 9F+FQF+FjoF+F>F+F1**\"*?**ei$F+F9F+F0F+FLF+F+**\"*?V)*=\"F+FSF+FRF+F?F +F+**\"*+GHL'F+F9F+FVF+F0F+F+**\"(+/Z(F+F\\uF+F>F+F?F+F+**\"++w42DF+FS F+FdpF+F?F+F+**\"++SC,TF+FLF+FjoF+F?F+F+**\")+3CUF+FF+F? 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