{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 }}
{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 73 "A:=a*x^6+(x+y)^2*y^3+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,2*&%\"aG\"\"\")%\"xG\"\"'F(F(*&),&%\"yGF(F*F(\"
\"#F()F/\"\"$F(F(*(%\"gGF()F*\"\"&F(F/F(F(*(%\"hGF()F*\"\"%F()F/F0F(F(
*(%\"jGF()F*F2F(F1F(F(*(%\"kGF()F*F0F()F/F:F(F(*(%\"lGF(F*F()F/F6F(F(*
&%\"mGF()F/F+F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polyn
omial [1]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,
y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%,$*&\"\"\"F&%\"mG!\"\"F(,&*
&),0%\"gGF(%\"lGF(%\"aGF&%\"kGF&%\"jGF(%\"hGF&F'F&\"\"#F&)*&%\"xGF&F,F
(#\"\"$F3F&F&*(,0F-F&F.F&F/F(F0F(F1F&F2F(F'F(F&F6F&F,F(F&,$*&,$*&F6F&F
/F&F(#\"\"%F8F/F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=
0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(-g-l+a+k-j+h
+m,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.%\"gG\"\"\"%\"lGF%%\"aG!\"
\"%\"jGF%%\"hGF(%\"mGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "
A1:=eval(A,k=%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,2*&%\"aG\"
\"\")%\"xG\"\"'F(F(*&),&%\"yGF(F*F(\"\"#F()F/\"\"$F(F(*(%\"gGF()F*\"\"
&F(F/F(F(*(%\"hGF()F*\"\"%F()F/F0F(F(*(%\"jGF()F*F2F(F1F(F(*(,.F4F(%\"
lGF(F'!\"\"F=F(F8FB%\"mGFBF()F*F0F()F/F:F(F(*(FAF(F*F()F/F6F(F(*&FCF()
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 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"yG\"\"\"%\"xGF&F&,@*&%\"aGF&)F'
\"\"&F&F&*()F'\"\"%F&%\"gGF&F%F&F&*(F.F&F*F&F%F&!\"\"*()F'\"\"$F&%\"hG
F&)F%\"\"#F&F&*(F4F&F7F&F0F&F2*(F4F&F*F&F7F&F&*()F'F8F&%\"jGF&)F%F5F&F
&*(F6F&F<F&F>F&F2*(F<F&F>F&F0F&F&*(F<F&F>F&F*F&F2*(F'F&%\"mGF&)F%F/F&F
2*(%\"lGF&F'F&FDF&F&*&F>F&F'F&F&*$FDF&F&*&FCF&)F%F,F&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 }