{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 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "A:=a*x^5+b*x^2*y^2+c*x*y^3+d*y^4+e*x^4*y+f*x^3*y^2+g* x^2*y^3+h*x*y^4+j*y^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,4*&% \"aG\"\"\")%\"xG\"\"&F(F(*(%\"bGF()F*\"\"#F()%\"yGF/F(F(*(%\"cGF(F*F() F1\"\"$F(F(*&%\"dGF()F1\"\"%F(F(*(%\"eGF()F*F9F(F1F(F(*(%\"fGF()F*F5F( F0F(F(*(%\"gGF(F.F(F4F(F(*(%\"hGF(F*F(F8F(F(*&%\"jGF()F1F+F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polynomial [1]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%*(,$*(%\"xG\"\"\"%\"aG!\"\"%\"bGF(F*#\"\"$\"\"#F )F.F+!\"#*&F'F(-%'RootOfG6#,(*&%\"cGF(%#_ZGF(F(F+F(*&%\"dGF()F7F.F(F(F (,$*&F9F(%\"jGF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [ 4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A1:=eval(A,b=c^2/4/d) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,4*&%\"aG\"\"\")%\"xG\"\"&F (F(*,\"\"%!\"\"%\"cG\"\"#%\"dGF.F*F0%\"yGF0F(*(F/F(F*F()F2\"\"$F(F(*&F 1F()F2F-F(F(*(%\"eGF()F*F-F(F2F(F(*(%\"fGF()F*F5F()F2F0F(F(*(%\"gGF()F *F0F(F4F(F(*(%\"hGF(F*F(F7F(F(*&%\"jGF()F2F+F(F(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 14 "reevaluate [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%,$*&%\"dG\"\"\"%\"jG!\"\"F),&**\"\"#F)%\"xGF'%\"cGF'F&F)F)*.\"\") F)F0#F'F,**F-F',.**\"#;F'%\"eGF'F.F')F&\"\"%F'F'*(\"#KF'%\"aGF')F&\"\" &F'F)**F,F'%\"hGF')F.F8F'F&F'F)**F0F'%\"fGF')F.F,F')F&\"\"$F'F)**F8F'% \"gGF')F.FEF')F&F,F'F'*&F(F')F.F=F'F'F)F.F,F&F8#FEF,F3F,F.!\"%F&!\")F' ,$*,F5F',$*,F8F)F-F'F;F)F&F)F.F,F)FLF;F,F&F,F.FMF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "solve(16*e*c*d^4-32*a*d^5-2*h*c^4*d-8*f*c^2*d^3+4*g*c ^3*d^2+j*c^5,e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"#;!\"\",,** \"\"%\"\"\"%\"gGF*)%\"cG\"\"$F*)%\"dG\"\"#F*F&*(\"#KF*%\"aGF*)F0\"\"&F *F***F1F*%\"hGF*)F-F)F*F0F*F***\"\")F*%\"fGF*)F-F1F*)F0F.F*F**&%\"jGF* )F-F6F*F&F*F-F&F0!\"%F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " A2:=eval(A1,e=%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G,4*&%\"aG\" \"\")%\"xG\"\"&F(F(*,\"\"%!\"\"%\"cG\"\"#%\"dGF.F*F0%\"yGF0F(*(F/F(F*F ()F2\"\"$F(F(*&F1F()F2F-F(F(*.\"#;F.,,**F-F(%\"gGF()F/F5F()F1F0F(F.*( \"#KF(F'F()F1F+F(F(**F0F(%\"hGF()F/F-F(F1F(F(**\"\")F(%\"fGF()F/F0F()F 1F5F(F(*&%\"jGF()F/F+F(F.F(F/F.F1!\"%F*F-F2F(F(*(FGF()F*F5F()F2F0F(F(* (F " 0 "" {MPLTEXT 1 0 11 "factor(A2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#, $*,\"#;!\"\",&*&%\"cG\"\"\"%\"xGF*F**(\"\"#F*%\"yGF*%\"dGF*F*F*,<**F%F *%\"aGF*)F/\"\"%F*)F+F4F*F***)F+\"\"$F*%\"jGF*F.F*)F)F4F*F&*.F-F*F7F*F .F*%\"hGF*F/F*)F)F8F*F**.F4F*F7F*F.F*%\"gGF*)F/F-F*)F)F-F*F&*.\"\")F*F 7F*F.F*%\"fGF*)F/F8F*F)F*F**.F-F*)F+F-F*)F.F-F*F/F*F9F*F=F*F**.F4F*FGF *FHF*F@F*F