{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 97 "A:=y^4+2*y^2*x^3+x^6+d*x^5*y +e*x^4*y^2+f*x^3*y^3+g*x^2*y^4+h*x*y^5+j*y^6+a*x^2*y^3+b*x*y^4+c*y^5; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,:*$)%\"yG\"\"%\"\"\"F**(\" \"#F*)F(F,F*)%\"xG\"\"$F*F**$)F/\"\"'F*F**(%\"dGF*)F/\"\"&F*F(F*F**(% \"eGF*)F/F)F*F-F*F**(%\"fGF*F.F*)F(F0F*F**(%\"gGF*)F/F,F*F'F*F**(%\"hG F*F/F*)F(F7F*F**&%\"jGF*)F(F3F*F**(%\"aGF*F@F*F=F*F**(%\"bGF*F/F*F'F*F **&%\"cGF*FCF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polyno mial [1]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y ,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,(*&%\"jG\"\"\") %#_ZG\"\"#F*F**&%\"cGF*F,F*F*F*F*,&*(\"$c#!\"\",&%\"dGF3%\"aGF*\"\"%,$ *(\"#;F*%\"xGF*F4!\"#F3#\"\"(F7F**(\"#kF3F4\"\"$F8#FAF-F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "A1:=eval(A,d=a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,:*$)%\"yG\"\"%\"\"\"F**(\"\"#F*)F(F,F*)%\"xG\"\"$F*F**$)F /\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(%\"eGF*)F/F)F*F-F*F**(%\"fGF*F.F* )F(F0F*F**(%\"gGF*)F/F,F*F'F*F**(%\"hGF*F/F*)F(F7F*F**&%\"jGF*)F(F3F*F **(F5F*F@F*F=F*F**(%\"bGF*F/F*F'F*F**&%\"cGF*FCF*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#<$-%'RootOfG6#,(*&%\"jG\"\"\")%#_ZG\"\"#F*F**&%\"cGF*F, F*F*F*F*,&*$),$%\"xG!\"\"#\"\"$F-F*F**&)F4F-F*-F%6#,**&\"\"%F*F+F*F*% \"eGF**(F-F*%\"aGF*F,F*F*%\"bGF5F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "exp and((2*a)^2-4*4*(e-b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"%\" \"\")%\"aG\"\"#F&F&*&\"#;F&%\"eGF&!\"\"*&F+F&%\"bGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A2:=eval(A1,e=1/16*(4*a^2+16*b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G,:*$)%\"yG\"\"%\"\"\"F**(\"\"# F*)F(F,F*)%\"xG\"\"$F*F**$)F/\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(,&*&F )!\"\"F5F,F*%\"bGF*F*)F/F)F*F-F*F**(%\"fGF*F.F*)F(F0F*F**(%\"gGF*)F/F, F*F'F*F**(%\"hGF*F/F*)F(F7F*F**&%\"jGF*)F(F3F*F**(F5F*FCF*F@F*F**(F " 0 "" {MPLTEXT 1 0 20 "pu iseux(A2,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,(*(\"&oF$!\" \",(*&%\"bG\"\"\"%\"aGF+F+*&\"\"#F+%\"fGF+F'*&F.F+%\"cGF+F+\"\"&,$*(\" #kF+%\"xGF+F(!\"#F'#\"\"*\"\"%F'*(F:F'F,F+F6F.F'*(\"$7&F'F(\"\"$F3#F>F .F'-%'RootOfG6#,(*&%\"jGF+)%#_ZGF.F+F+*&F1F+FGF+F+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A3:=eval(A2,f=1/2*(b*a+2*c));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#A3G,:*$)%\"yG\"\"%\"\"\"F**(\"\"#F*)F(F,F*)%\"xG\" \"$F*F**$)F/\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(,&*&F)!\"\"F5F,F*%\"bG F*F*)F/F)F*F-F*F**(,&*(F,F;F " 0 "" {MPLTEXT 1 0 20 "pu iseux(A3,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,(*$),$%\"xG! \"\"#\"\"$\"\"#\"\"\"F-*(\"\"%F)%\"aGF-F(F,F)*&)F'#\"\"&F,F--%'RootOfG 6#,.*&\"%C5F-)%#_ZGF,F-F-*&,&*&\"$7&F-%\"bGF-F)*&\"#kF-)F0F,F-F)F-F " 0 "" {MPLTEXT 1 0 69 "expand((-512*b-64*a^2)^2-4*1024*(16*b*a^2-128*c*a+256*g+a^4))/ 262144;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"bG\"\"#\"\"\"F(*(F' F(%\"cGF(%\"aGF(F(*&\"\"%F(%\"gGF(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A4:=eval(A3,g=1/4*(b^2+2*c*a));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A4G,:*$)%\"yG\"\"%\"\"\"F**(\"\"#F*)F(F,F*)%\"xG\"\" $F*F**$)F/\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(,&*&F)!\"\"F5F,F*%\"bGF* F*)F/F)F*F-F*F**(,&*(F,F;F " 0 "" {MPLTEXT 1 0 20 "puiseux(A4,x=0,y,0);" }{TEXT -1 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,(*&%\"jG\"\"\")%#_ZG\"\"#F*F**&% \"cGF*F,F*F*F*F*,**(\"'W@E!\"\",&*&F-F*%\"hGF*F3*&F/F*%\"bGF*F*\"\"',$ *(\"#kF*%\"xGF*F4!\"#F3#\"#6\"\"%F***\"(w&[5F3F4\"\"&,&*$)%\"aGF-F*F** &\"\")F*F8F*F*F*F:#FDF-F3*(FAF3FHF*F=F-F3*(\"$7&F3F4\"\"$F:#FOF-F3" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A5:=eval(A4,h=1/2*c*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A5G,:*$)%\"yG\"\"%\"\"\"F**(\"\"#F*)F(F,F*)%\"xG \"\"$F*F**$)F/\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(,&*&F)!\"\"F5F,F*%\" bGF*F*)F/F)F*F-F*F**(,&*(F,F;F " 0 "" {MPLTEXT 1 0 20 "puiseux(A5,x=0,y,0);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,(*&%\"jG\"\"\")%#_ZG\"\"#F*F**&% \"cGF*F,F*F*F*F*,**$),$%\"xG!\"\"#\"\"$F-F*F**(\"\"%F5%\"aGF*F4F-F5*&) F3#\"\"&F-F*,&*&\"#KF5F:F-F**&F9F5%\"bGF*F*F*F**&)F4F7F*-F%6#,,*&\"#kF *F+F*F**&,&*&FAF*F/F*F**(\"#;F*FCF*F:F*F*F*F,F*F***F9F*F/F*FCF*F:F*F** &FOF*F)F*F**&)FCF-F*)F:F-F*F*F*F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "expand ((32*c+16*b*a)^2-4*64*(4*c*b*a+16*j+b^2*a^2))/1024;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*$)%\"cG\"\"#\"\"\"F(*&\"\"%F(%\"jGF(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A6:=eval(A5,j=1/4*c^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A6G,:*$)%\"yG\"\"%\"\"\"F**(\"\"#F* )F(F,F*)%\"xG\"\"$F*F**$)F/\"\"'F*F**(%\"aGF*)F/\"\"&F*F(F*F**(,&*&F)! \"\"F5F,F*%\"bGF*F*)F/F)F*F-F*F**(,&*(F,F;F " 0 "" {MPLTEXT 1 0 11 "factor(A6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%!\"\",,*&\"\"#\"\"\")%\"xG\"\"$F*F**(%\"y GF*)F,F)F*%\"aGF*F**()F/F)F*F,F*%\"bGF*F**&)F/F-F*%\"cGF*F**&F)F*F3F*F *F)F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "polynomial factors [5]" }}}}{MARK "33 0 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }