{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 85 "A:=a*x^6+1*x^4*y-2*x^2*y^3+1 *y^5+g*x^5*y+h*x^4*y^2+j*x^3*y^3+k*x^2*y^4+l*x*y^5+m*y^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,6*&%\"aG\"\"\")%\"xG\"\"'F(F(*&)F*\"\"%F (%\"yGF(F(*(\"\"#F()F*F1F()F/\"\"$F(!\"\"*$)F/\"\"&F(F(*(%\"gGF()F*F8F (F/F(F(*(%\"hGF(F-F()F/F1F(F(*(%\"jGF()F*F4F(F3F(F(*(%\"kGF(F2F()F/F.F (F(*(%\"lGF(F*F(F7F(F(*&%\"mGF()F/F+F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polynomail [1]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#<&\"\"!,$*&\"\"\"F'%\"mG!\"\"F),&*(\"#;F),0%\"aGF'%\"gGF'%\"hGF'%\"l GF'%\"jGF'%\"kGF'F(F'\"\"#*&%\"xGF',0*&\"\"%F)F.F'F)*&F9F)F/F'F)*&F9F) F0F'F)*&F9F)F1F'F)*&F9F)F2F'F)*&F9F)F3F'F)*&F9F)F(F'F)F)#\"\"$F4F'F6F' ,&*(F,F),0F.F'F/F)F0F'F1F)F2F)F3F'F(F'F4*&F6F',0*&F9F)F.F'F'*&F9F)F/F' F)*&F9F)F0F'F'*&F9F)F1F'F)*&F9F)F2F'F)*&F9F)F3F'F'*&F9F)F(F'F'F)F@F'*( ,0*&F9F)F.F'F)*&F9F)F/F'F'*&F9F)F0F'F)*&F9F)F1F'F'*&F9F)F2F'F'*&F9F)F3 F'F)*&F9F)F(F'F)F'F6F'FFF)F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "n umerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "solve(-1/ 4*a-1/4*g-1/4*h-1/4*l-1/4*j-1/4*k-1/4*m,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.%\"aG!\"\"%\"gGF%%\"hGF%%\"lGF%%\"jGF%%\"mGF%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "A1:=eval(A,k=%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,6*&%\"aG\"\"\")%\"xG\"\"'F(F(*&)F*\" \"%F(%\"yGF(F(*(\"\"#F()F*F1F()F/\"\"$F(!\"\"*$)F/\"\"&F(F(*(%\"gGF()F *F8F(F/F(F(*(%\"hGF(F-F()F/F1F(F(*(%\"jGF()F*F4F(F3F(F(*(,.F'F5F:F5F=F 5%\"lGF5F@F5%\"mGF5F(F2F()F/F.F(F(*(FDF(F*F(F7F(F(*&FEF()F/F+F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(A1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&,&%\"yG!\"\"%\"xG\"\"\"F(,D*&%\"aGF()F'\"\"&F(F( *()F'\"\"%F(%\"gGF(F%F(F(*(F/F(F%F(F+F(F(*()F'\"\"$F(%\"hGF()F%\"\"#F( F(*&F%F(F4F(F(*(F4F(F1F(F7F(F(*(F4F(F7F(F+F(F(*()F'F8F(%\"jGF()F%F5F(F (*(F=F(F6F(F?F(F(*&F7F(F=F(F(*(F=F(F1F(F?F(F(*(F=F(F?F(F+F(F(*&F'F(F?F (F&*(F'F()F%F0F(%\"lGF(F&*(F'F(FFF(%\"mGF(F&*$FFF(F&*&)F%F-F(FIF(F&F( " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "polynomial factors [5]" }}}} {MARK "12" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }