{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 0 119 "A:=y^2*(y^2+x^2)+2*l*x^4*y+ m*x^6+a*x^3*y^2+b*x^2*y^3+c*x*y^4+d*y^5+e*x^5*y+f*x^4*y^2+g*x^3*y^3+h* x^2*y^4+j*x*y^5+k*y^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,<*&)% \"yG\"\"#\"\"\",&*$F'F*F**$)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F* F**&%\"mGF*)F/\"\"'F*F**(%\"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F* *(%\"cGF*F/F*)F(F3F*F**&%\"dGF*)F(\"\"&F*F**(%\"eGF*)F/FEF*F(F*F**(%\" fGF*F2F*F'F*F**(%\"gGF*F:F*F>F*F**(%\"hGF*F.F*FAF*F**(%\"jGF*F/F*FDF*F **&%\"kGF*)F(F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puis eux(A,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%*&)%\"xG\"\"#\"\" \"-%'RootOfG6#,(%\"mGF(*(F'F(%\"lGF(%#_ZGF(F(*$)F0F'F(F(F(*&F&F(-F*6#, &F1F(F(F(F(-F*6#,(*&%\"kGF(F2F(F(*&%\"dGF(F0F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "discrim(m+2*l*_Z+_Z^2,_Z);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\"%\"mGF&!\"\"*&F%F&)%\"lG\"\"#F&F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A1:=eval(A,m=l^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,<*&)%\"yG\"\"#\"\"\",&*$F'F*F** $)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/\"\"'F*F**(% \"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*)F(F3F*F**&% \"dGF*)F(\"\"&F*F**(%\"eGF*)F/FEF*F(F*F**(%\"fGF*F2F*F'F*F**(%\"gGF*F: F*F>F*F**(%\"hGF*F.F*FAF*F**(%\"jGF*F/F*FDF*F**&%\"kGF*)F(F7F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%*&%\"xG\"\"\"-%'RootOfG6#,&*$)%#_ZG \"\"#F&F&F&F&F&,&*()%\"lG\"\"$F&),&%\"eG!\"\"*&%\"aGF&F2F&F&F3F&),$*(F %F&F2F7F5F7F7#\"\"&F.F&F7*&)F%F.F&F2F&F7-F(6#,(*&%\"kGF&F,F&F&*&%\"dGF &F-F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A2:=eval(A1, e=a*l);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G,<*&)%\"yG\"\"#\"\"\" ,&*$F'F*F**$)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/ \"\"'F*F**(%\"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*) F(F3F*F**&%\"dGF*)F(\"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(%\"fGF*F2F*F'F*F **(%\"gGF*F:F*F>F*F**(%\"hGF*F.F*FAF*F**(%\"jGF*F/F*FDF*F**&%\"kGF*)F( F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=0,y, 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%*&%\"xG\"\"\"-%'RootOfG6#,&*$ )%#_ZG\"\"#F&F&F&F&F&,&*&)F%F.F&%\"lGF&!\"\"*&)F%\"\"$F&-F(6#,,*(%\"aG F&F2F&F-F&F3F+F&*&%\"fGF&)F2F.F&F&*&%\"bGF&)F2F6F&F3*$)F2\"\"%F&F&F&F& -F(6#,(*&%\"kGF&F,F&F&*&%\"dGF&F-F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "discrim(-a*l*_Z+_Z^2+f*l^2-b*l^3+l^4,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**(\"\"%\"\"\"%\"fGF&)%\"lG\"\"#F&!\"\"*(F% F&%\"bGF&)F)\"\"$F&F&*&F%F&)F)F%F&F+*&)%\"aGF*F&F(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%\"lG\"\"#\"\"\",**&\"\"%F(%\"fGF(F(*(F+F(F&F(%\"b GF(!\"\"*&F+F(F%F(F(*$)%\"aGF'F(F/F(F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A3:=eval(A2,f=-1/4*(-4*l*b+4*l^2-a^2));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#A3G,<*&)%\"yG\"\"#\"\"\",&*$F'F*F**$)%\"xGF)F *F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/\"\"'F*F**(%\"aGF*)F/ \"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*)F(F3F*F**&%\"dGF*)F( \"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(,(*&F1F*F=F*F**$F5F*!\"\"*&#F*F3F**$ )F9F)F*F*F*F*F2F*F'F*F**(%\"gGF*F:F*F>F*F**(%\"hGF*F.F*FAF*F**(%\"jGF* F/F*FDF*F**&%\"kGF*)F(F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A3,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%,(*,\" \"#!\"\"%\"lG\"#7,**&%\"bG\"\"\"%\"aGF-F'*&F&F-%\"gGF-F-*(F&F-F.F-F(F- F-*(F&F-%\"cGF-F(F-F'\"\"%F&#F-F&*(%\"xGF-F(!\"$F*F'#\"\"(F&F-**F&F'F7 \"\"$F.F-F(F-F-*&)F7F&F-F(F-F'*&F7F--%'RootOfG6#,&*$)%#_ZGF&F-F-F-F-F- -FA6#,(*&%\"kGF-FEF-F-*&%\"dGF-FFF-F-F-F-" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 39 "A4:=eval(A3,g=-1/2*(-b*a+2*a*l-2*c*l));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A4G,<*&)%\"yG\"\"#\"\"\",&*$F'F*F**$)%\"x GF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/\"\"'F*F**(%\"aGF* )F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*)F(F3F*F**&%\"dGF*) F(\"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(,(*&F1F*F=F*F**$F5F*!\"\"*&#F*F3F* *$)F9F)F*F*F*F*F2F*F'F*F**(,(*(F)FLF=F*F9F*F**&F9F*F1F*FL*&F@F*F1F*F*F *F:F*F>F*F**(%\"hGF*F.F*FAF*F**(%\"jGF*F/F*FDF*F**&%\"kGF*)F(F7F*F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A4,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%*&%\"xG\"\"\"-%'RootOfG6#,&*$)%#_ZG \"\"#F&F&F&F&F&,(*&)F%F.F&%\"lGF&!\"\"**F.F3F%\"\"$%\"aGF&F2F&F&*&)F% \"\"%F&-F(6#,2*&\"#;F&F,F&F&*&,(*&\"#KF&)F2F5F&F3*(F>F&%\"bGF&)F2F.F&F &*(\"\")F&)F6F.F&F2F&F&F&F-F&F&**FHF&%\"cGF&)F2F9F&F6F&F3*(F9F&FLF&FIF &F3*&)F6F9F&FFF&F&**F9F&FCF&FEF&FIF&F&*(F>F&%\"hGF&FLF&F&*(F>F&%\"dGF& )F2\"\"&F&F3F&F&-F(6#,(*&%\"kGF&F,F&F&*&FTF&F-F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "discrim(16*_Z^2+(-32*l^3+16*b*l^2+ 8*a^2*l)*_Z-8*c*l^4*a-4*l^4*a^2+a^4*l^2+4*l^3*b*a^2+16*h*l^4-16*d*l^5, _Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*(\"$c#\"\"\")%\"lG\"\"%F&)% \"aG\"\"#F&!\"\"*(\"%C5F&%\"dGF&)F(\"\"&F&F&**\"$7&F&%\"cGF&F'F&F+F&F& *(F/F&%\"hGF&F'F&F-*(F%F&)%\"bGF,F&F'F&F&*(F/F&F:F&F1F&F-*&F/F&)F(\"\" 'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"$c#\"\"\")%\"lG\"\"%F&,0*&F)F&)F (\"\"#F&!\"\"*(F)F&F(F&%\"dGF&F.*(F)F&F(F&%\"bGF&F&*$)%\"aGF-F&F&*(F-F &F5F&%\"cGF&F.*&F)F&%\"hGF&F&*$)F2F-F&F.F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "A5:=eval(A4,h=-1/4*(-4*l^2-4*l*d+4*l*b+a^2-2*a*c -b^2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A5G,<*&)%\"yG\"\"#\"\"\" ,&*$F'F*F**$)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/ \"\"'F*F**(%\"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*) F(F3F*F**&%\"dGF*)F(\"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(,(*&F1F*F=F*F**$ F5F*!\"\"*&#F*F3F**$)F9F)F*F*F*F*F2F*F'F*F**(,(*(F)FLF=F*F9F*F**&F9F*F 1F*FL*&F@F*F1F*F*F*F:F*F>F*F**(,.FKF**&F1F*FCF*F*FJFL*&F3FLF9F)FL*(F)F LF9F*F@F*F**&F3FLF=F)F*F*F.F*FAF*F**(%\"jGF*F/F*FDF*F**&%\"kGF*)F(F7F* F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A5,x=0,y,0); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%*&%\"xG\"\"\"-%'RootOfG6#,&*$)%# _ZG\"\"#F&F&F&F&F&,***\"#K!\"\"%\"lG\"#D,.*&%\"cGF&%\"bGF&F&*(F.F&%\"a GF&F3F&F&*&F.F&%\"jGF&F2*&F8F&F:F&F2*&%\"dGF&F:F&F&*(F.F&F7F&F3F&F2\" \"&,$**F.F&F%F&F3!\"&F5F2F2#\"\"*F.F2**\"\"%F2F3F&,(*&FHF&)F3F.F&F&*$) F:F.F&F2*(F.F&F3F&F8F&F2F&F%FHF&**F.F2F%\"\"$F:F&F3F&F&*&)F%F.F&F3F&F2 -F(6#,(*&%\"kGF&F,F&F&*&F?F&F-F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "A6:=eval(A5,j=1/2*(c*b+2*a*l-b*a+d*a-2*c*l));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A6G,<*&)%\"yG\"\"#\"\"\",&*$F'F*F** $)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/\"\"'F*F**(% \"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF*F/F*)F(F3F*F**&% \"dGF*)F(\"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(,(*&F1F*F=F*F**$F5F*!\"\"*& #F*F3F**$)F9F)F*F*F*F*F2F*F'F*F**(,(*(F)FLF=F*F9F*F**&F9F*F1F*FL*&F@F* F1F*F*F*F:F*F>F*F**(,.FKF**&F1F*FCF*F*FJFL*&F3FLF9F)FL*(F)FLF9F*F@F*F* *&F3FLF=F)F*F*F.F*FAF*F**(,,*(F)FLF@F*F=F*F*FTF**(F)FLF=F*F9F*FL*(F)FL FCF*F9F*F*FUFLF*F/F*FDF*F**&%\"kGF*)F(F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A6,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%*&%\"xG\"\"\"-%'RootOfG6#,&*$)%#_ZG\"\"#F&F&F&F&F&,** &)F%F.F&%\"lGF&!\"\"**F.F3F%\"\"$%\"aGF&F2F&F&*&)F%\"\"%F&,(*$)F2F5F&F &*&#F&F9F&*&)F6F.F&F2F&F&F3*&#F&F.F&*&%\"bGF&)F2F.F&F&F3F&F&*&)F%\"\"& F&-F(6#,D*&\"#kF&F,F&F&*&,**(\"#;F&)F6F5F&F2F&F3*(\"$c#F&FF&F@F&F^oF&FDF&F3*(FMF&)F2\"\" (F&%\"dGF&F&*&)F6\"\"'F&FEF&F&*&FMF&)F2FgnF&F&*(FMF&%\"kGF&)F2FioF&F&* (FQF&F^pF&F[oF&F&**F`oF&F^pF&FfoF&FDF&F3**FXF&FVF&F^pF&F6F&F3*(FMF&Fdo F&FDF&F3*(\"$S#F&F^pF&F@F&F&F&F&-F(6#,(*&F]pF&F,F&F&*&FfoF&F-F&F&F&F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "discrim(64*_Z^2+(-16*a ^3*l+256*l^3*a-64*c*l^3-96*l^2*b*a)*_Z+12*l^3*b*a^4+8*c*l^4*a^3+36*b^2 *l^4*a^2+48*c*l^5*a*b-32*a^4*l^4-192*a^2*l^5*b+64*l^7*d+a^6*l^2+64*l^8 +64*k*l^6+16*l^6*b^2-32*l^6*d*b-96*c*l^6*a-64*l^7*b+240*l^6*a^2,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*(\"%'4%\"\"\")%\"cG\"\"#F&)%\"lG \"\"'F&F&*(\"&%Q;F&%\"kGF&F*F&!\"\"*(F%F&F*F&)%\"bGF)F&F0*&F.F&)F+\"\" )F&F0**\"%#>)F&F(F&F*F&%\"aGF&F0**F8F&F*F&%\"dGF&F3F&F&*(F%F&F*F&)F9F) F&F&*(F.F&)F+\"\"(F&F3F&F&*(F.F&F?F&F;F&F0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*( \"%'4%\"\"\")%\"lG\"\"'F&,4*$)%\"cG\"\"#F&!\"\"*&\"\"%F&%\"kGF&F&*$)% \"bGF.F&F&*&F1F&)F(F.F&F&*(F.F&%\"aGF&F-F&F&*(F.F&%\"dGF&F5F&F/*$)F9F. F&F/*(F1F&F(F&F5F&F/*(F1F&F(F&F;F&F&F&F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "A7:=eval(A6,k=-1/4*(-c^2+b^2+4*l^2+2*a*c-2*d*b-a^2-4* l*b+4*l*d));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A7G,<*&)%\"yG\"\"# \"\"\",&*$F'F*F**$)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F) F*)F/\"\"'F*F**(%\"aGF*)F/\"\"$F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(%\"cGF* F/F*)F(F3F*F**&%\"dGF*)F(\"\"&F*F***F9F*F1F*)F/FEF*F(F*F**(,(*&F1F*F=F *F**$F5F*!\"\"*&#F*F3F**$)F9F)F*F*F*F*F2F*F'F*F**(,(*(F)FLF=F*F9F*F**& F9F*F1F*FL*&F@F*F1F*F*F*F:F*F>F*F**(,.FKF**&F1F*FCF*F*FJFL*&F3FLF9F)FL *(F)FLF9F*F@F*F**&F3FLF=F)F*F*F.F*FAF*F**(,,*(F)FLF@F*F=F*F*FTF**(F)FL F=F*F9F*FL*(F)FLFCF*F9F*F*FUFLF*F/F*FDF*F**&,2*&F3FLF@F)F**&F3FLF=F)FL FKFL*(F)FLF9F*F@F*FL*(F)FLFCF*F=F*F**&F3FLF9F)F*FJF*FXFLF*)F(F7F*F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A7,x=0,y,0);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(\"\"%!\"\"*&,2*$)%\"cG \"\"#\"\"\"F)*$)%\"bGF/F0F0*&F(F0)%\"lGF/F0F0*(F/F0%\"aGF0F.F0F0*(F/F0 %\"dGF0F3F0F)*$)F8F/F0F)*(F(F0F6F0F3F0F)*(F(F0F6F0F:F0F0F0)%#_ZGF/F0F0 *(F(F0F:F0F@F0F),,*,F/F)F6\"#U,.*&F3F0F8F0F)*&F.F0F3F0F0*&F:F0F8F0F0*& F:F0F.F0F)*(F/F0F8F0F6F0F0*(F/F0F.F0F6F0F)\"\"'F/#F0F/*(%\"xGF0F6!\"(F EF)#\"#6F/F0**\"\")F)F6F0,**(\"#;F0F8F0F5F0F0*$)F8\"\"$F0F)*(F(F0F5F0F .F0F)**FLF0F3F0F8F0F6F0F)F0FO\"\"&F)**F(F)F6F0,(*&F(F0F5F0F0F;F)*(F/F0 F6F0F3F0F)F0FOF(F0**F/F)FOFZF8F0F6F0F0*&)FOF/F0F6F0F)*&FOF0-F%6#,&*$F? F0F0F0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "factor(-b*a+c *b+d*a-d*c+2*a*l-2*c*l);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"aG \"\"\"%\"cG!\"\"F&,(%\"bGF(%\"dGF&*&\"\"#F&%\"lGF&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A8:=eval(A7,a=c);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A8G,<*&)%\"yG\"\"#\"\"\",&*$F'F*F**$)%\"xGF)F*F*F *F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F*)F/\"\"'F*F**(%\"cGF*)F/\"\"$ F*F'F*F**(%\"bGF*F.F*)F(F;F*F**(F9F*F/F*)F(F3F*F**&%\"dGF*)F(\"\"&F*F* **F9F*F1F*)F/FDF*F(F*F**(,(*&F1F*F=F*F**$F5F*!\"\"*&#F*F3F**$)F9F)F*F* F*F*F2F*F'F*F**,F)FKF9F*F=F*F/F;F(F;F**(,,FJF**&F1F*FBF*F*FIFK*&F3FKF9 F)F**&F3FKF=F)F*F*F.F*F@F*F**,F)FKFBF*F9F*F/F*F(FDF**&,,*&#F*F3F**$)F= F)F*F*FKFJFK*&#F*F)F**&FBF*F=F*F*F*FIF*FSFKF*)F(F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(A8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"%!\"\",,*&\"\"#\"\"\"%\"yGF*F**(F)F*)%\"xGF)F*% \"lGF*F**(%\"cGF*F.F*F+F*F**&)F+F)F*%\"bGF*F**(F)F*F3F*F/F*F&F*,4*(F)F *F/F*)F.F%F*F**(F)F*F/F*)F+F%F*F**(F1F*F+F*)F.\"\"$F*F**(F-F*F3F*F4F*F **(F)F*F+F*F-F*F**(F1F*)F+F=F*F.F*F**&F:F*F4F*F&*(F)F*F:F*%\"dGF*F**&F )F*FAF*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A9:=eval(A 7,b=d+2*l);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A9G,<*&)%\"yG\"\"#\" \"\",&*$F'F*F**$)%\"xGF)F*F*F*F***F)F*%\"lGF*)F/\"\"%F*F(F*F**&)F1F)F* )F/\"\"'F*F**(%\"aGF*)F/\"\"$F*F'F*F**(,&%\"dGF**&F)F*F1F*F*F*F.F*)F(F ;F*F**(%\"cGF*F/F*)F(F3F*F**&F>F*)F(\"\"&F*F***F9F*F1F*)F/FFF*F(F*F**( ,(*&F1F*F=F*F**$F5F*!\"\"*&F3FMF9F)F*F*F2F*F'F*F**(,(*(F)FMF=F*F9F*F** &F9F*F1F*FM*&FBF*F1F*F*F*F:F*F@F*F**(,.FLF**&F1F*F>F*F*FKFM*&F3FMF9F)F M*(F)FMF9F*FBF*F**&F3FMF=F)F*F*F.F*FCF*F**(,,*(F)FMFBF*F=F*F*FRF**(F)F MF=F*F9F*FM*(F)FMF>F*F9F*F*FSFMF*F/F*FEF*F**&,2*&F3FMFBF)F**&F3FMF=F)F MFLFM*(F)FMF9F*FBF*FM*(F)FMF>F*F=F*F**&F3FMF9F)F*FKF*FVFMF*)F(F7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(A9);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#,R*$)%\"yG\"\"%\"\"\"F(*&)F&\"\"#F()%\"xGF+F(F(* *F+F(%\"lGF()F-F'F(F&F(F(*&)F/F+F()F-\"\"'F(F(*(%\"aGF()F-\"\"$F(F*F(F (*()F&F8F(F,F(%\"dGF(F(**F+F(F:F(F,F(F/F(F(*(%\"cGF(F-F(F%F(F(*&F;F()F &\"\"&F(F(**F6F(F/F()F-FAF(F&F(F(**F0F(F*F(F/F(F;F(F(*(F0F(F*F(F2F(F(* *F'!\"\"F-F'F&F+F6F+F(*,F+FGF-F8F&F8F;F(F6F(F(**F7F(F:F(F>F(F/F(F(**F, F(F%F(F/F(F;F(F(**F'FGF-F+F&F'F6F+FG*,F+FGF-F+F&F'F6F(F>F(F(**F'FGF-F+ F&F'F;F+F(*,F+FGF;F(F>F(F-F(F&FAF(*(F'FGF&F4F>F+F(*(F'FGF&F4F;F+F(**F+ FGF&F4F6F(F>F(FG*(F'FGF&F4F6F+F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A9,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%,,*&)%\"xG\"\"#\"\"\"%\"lGF)!\"\"**F(F+F'\"\"$%\"aGF)F*F)F)*&)F' \"\"%F),&*&#F)F(F)*&)F*F(F)%\"dGF)F)F+*&#F)F1F)*&)F.F(F)F*F)F)F+F)F)*& )F'\"\"&F),**(F(F+F*F-F.F)F+*(\"\")F+F.F-F*F)F)*(F(F+%\"cGF)F*F-F)*,F- F)F1F+F*F(F7F)F.F)F)F)F)*&)F'\"\"'F)-%'RootOfG6#,H*&\"$c#F))%#_ZGF(F)F )*&,,*(\"#KF))F.F1F)F*F)F)*(FNF))F7F(F))F*F-F)F)*(\"$7&F)F;F)FXF)F+**F ZF)FDF)FXF)F.F)F)**\"$%QF)F7F)F;F)F6F)F)F)FPF)F)*&)F.FBF)F6F)F)*(\"#kF ))F*FHF))F7F1F)F)**\"$g\"F))F*F1F)FWF)FUF)F)**\"$#>F))F*F>F))F7F-F)F;F )F)**\"#CF)F7F))F.FHF)FXF)F)**\"$G\"F))F*FBF)F.F)FDF)F+**FZF))F.F-F)F \\oF)FDF)F+**FTF)FDF)F`oF))F.F>F)F)**FNF))FDF(F)F\\oF)F;F)F)**FgnF)F7F )FcoF)FUF)F+*,FNF)FDF)F\\oF)FWF)F.F)F)*(F[oF)FjoF)F;F)F)*(FNF)F\\oF)FU F)F)*(FTF)FgoF)F`oF)F+*(F[oF)FjoF)F`pF)F)*,FgnF)F7F)F\\pF)FcoF)FDF)F)* *FNF)F;F)F\\oF)FWF)F+F)F)-FJ6#,(F1F)*&,**$F`pF)F)*$FWF)F)*(F(F)F.F)FDF )F+*$F;F)F)F)FOF)F)*(F1F)F7F)FPF)F)*&F'F)-FJ6#,&*$FOF)F)F)F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 311 "discrim(256*_Z^2+(32*a^4*l+ 256*d^2*l^3-512*a^2*l^3+512*c*l^3*a+384*d*a^2*l^2)*_Z+a^8*l^2+64*l^6*d ^4+160*l^4*d^2*a^4+192*l^5*d^3*a^2+24*d*a^6*l^3-128*l^8*a*c-512*a^3*l^ 6*c+32*c*l^4*a^5+256*c^2*l^6*a^2-384*d*l^5*a^4+256*c*l^6*d^2*a+64*l^8* a^2+256*l^6*a^4-32*a^6*l^4+64*l^8*c^2+384*d*a^3*l^5*c-256*a^2*l^6*d^2, _Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*(\"&Ob'\"\"\")%\"lG\"\")F&) %\"aG\"\"#F&!\"\"**\"'s58F&F'F&F+F&%\"cGF&F&*(F%F&)F0F,F&F'F&F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"&Ob'\"\"\")%\"lG\"\")F&),&%\"aGF&%\"cG!\"\"\" \"#F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A10:=eval(A9,a=c );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$A10G,<*()%\"yG\"\"#\"\"\",&F( F*%\"xG!\"\"F*,&F(F**&F)F*F,F*F-F*F***F)F*%\"lGF*)F,\"\"%F*F(F*F**(F)F -F1F)F,\"\"'F**(,**(\"#5F*\"\"*F-%\"bGF*F-*(F3F*\"\"$F-%\"cGF*F-*(\"#; F*F:F-%\"dGF*F-*(\"#F*F,F*)F(F3F*F**&FAF*)F(\"\"&F*F**(,&*(F)F-F7F*F1F*F**(F=F*F3F-F1F )F*F*)F,FLF*F(F*F**(,**(F)F-F1F*F;F*F**(\"\"(F*\"\")F-F1F)F**&FWF-F7F) F***F=F*F3F-F7F*F1F*F*F*F2F*F'F*F**(,.**FVF*FWF-F7F*F1F*F**(\"#:F*F@F- F1F)F**(F=F*F@F-F7F)F**(F3F-F;F*F7F*F***F=F*F3F-F1F*F;F*F**(F)F-F>F*F1 F*F*F*FDF*FGF*F**(,4*(F)F-F1F*FAF*F***F=F*FWF-F;F*F7F*F***FVF*FWF-F1F* F;F*F**(F3F-F7F*F>F*F**(FVF*\"#KF-F7F)F***FhnF*F@F-F7F*F1F*F***F=F*F3F -F>F*F1F*F**(\"#JF*FdoF-F1F)F**&FWF-F;F)F*F*FFF*FIF*F**(,8*(F3F-FAF*F7 F*F**(F=F*F@F-F;F)F**(FhnF*\"#kF-F7F)F***FhoF*FdoF-F7F*F1F*F***FVF*F@F -F;F*F7F*F***F=F*F3F-F1F*FAF*F**(\"#jF*F_pF-F1F)F***FhnF*F@F-F1F*F;F*F **(F3F-F>F*F;F*F***F=F*FWF-F7F*F>F*F***FVF*FWF-F>F*F1F*F*F*F,F*FKF*F** &,<*(FhoF*\"$G\"F-F7F)F***FdpF*F_pF-F7F*F1F*F**(FVF*FdoF-F;F)F***FhoF* FdoF-F1F*F;F*F***FhnF*FdoF-F;F*F7F*F***FVF*FWF-F1F*FAF*F***F=F*FWF-F>F *F;F*F***FVF*F@F-F7F*F>F*F***FhnF*F@F-F>F*F1F*F**(\"$F\"F*F\\qF-F1F)F* *(F3F-FAF*F;F*F***F=F*FWF-FAF*F7F*F**&FWF-F>F)F*F*)F(F5F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(A10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*(\"$C$!\"\",@*(\"#;\"\"\")%\"yG\"\"$F*%\"dGF*F& *(F-F*F+F*%\"cGF*F&*&\"#=F*)F,\"\"#F*F&*&%\"bGF*F+F*F&**\"#7F*)%\"xGF4 F*F,F*F0F*F&**F)F*F9F*F.F*F,F*F&*(F3F*F6F*F:F*F&**\"#5F*F,F*F6F*F9F*F& **F8F*F:F*F3F*F0F*F&**F)F*F:F*F3F*F.F*F&*(\"#OF*F,F*F:F*F**&%\"lGF*F+F *F**(F:F*F3F*FDF*F**(F,F*F9F*FDF*F**(F2F*)F:F-F*FDF*F*F*,@*(F4F*F+F*F. F*F&*(F-F*F+F*F0F*F**&F2F*F3F*F&F5F***\"\"'F*F9F*F,F*F0F*F&**\"\")F*F9 F*F.F*F,F*F&**F4F*F3F*F6F*F:F*F***\"\"&F*F,F*F6F*F9F*F&**F-F*F:F*F3F*F 0F*F&**\"\"%F*F:F*F3F*F.F*F&*(F2F*F,F*F:F*F*FCF&**F4F*F:F*F3F*FDF*F&** FVF*F,F*F9F*FDF*F&*(\"\"*F*FHF*FDF*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "27 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }