{VERSION 6 0 "IBM INTEL NT" "6.0" }
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-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 0 115 "A:=y^2*(y-x)^2+l*x^6+m*x^4*
y+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*%\"xG!\"\"F)F*F**&%\"lGF*)F-\"\"'F*F**(%\"mGF*)F-\"
\"%F*F(F*F**(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F*)F(F:F*F**(%\"cGF*
F-F*)F(F6F*F**&%\"dGF*)F(\"\"&F*F**(%\"eGF*)F-FEF*F(F*F**(%\"fGF*F5F*F
'F*F**(%\"gGF*F9F*F>F*F**(%\"hGF*F=F*FAF*F**(%\"jGF*F-F*FDF*F**&%\"kGF
*)F(F2F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0
,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"
\")%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,&*&),,%\"cGF*%\"mGF*%\"bGF*F/F*%
\"aGF*F-F*)*&%\"xGF*,,F4!\"\"F5F<F6F<F/F<F7F<F<#\"\"$F-F*F*F:F**&)F:F-
F*-F%6#,(%\"lGF**&F5F*F,F*F**$F+F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "A1:=eval(A,a=-c-b-m-d);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#A1G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**&%\"lGF*)F-\"
\"'F*F**(%\"mGF*)F-\"\"%F*F(F*F**(,*%\"cGF.%\"bGF.F4F.%\"dGF.F*)F-\"\"
$F*F'F*F**(F:F*)F-F)F*)F(F=F*F**(F9F*F-F*)F(F6F*F**&F;F*)F(\"\"&F*F**(
%\"eGF*)F-FEF*F(F*F**(%\"fGF*F5F*F'F*F**(%\"gGF*F<F*F@F*F**(%\"hGF*F?F
*FBF*F**(%\"jGF*F-F*FDF*F**&%\"kGF*)F(F2F*F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,
F*F*F*F**&)%\"xGF-F*-F%6#,(%\"lGF**&%\"mGF*F,F*F**$F+F*F*F*,&F2F**&F1F
*-F%6#,4F9F**&,**&\"\"$F*F/F*F**&F-F*%\"cGF*F*%\"bGF*F8!\"\"F*F,F*F*F6
F*%\"hGF*%\"jGF*%\"fGF*%\"gGF*%\"eGF*F)F*F*F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 48 "discrim(_Z^2+(3*d+2*c+b-m)*_Z+l+h+j+f+g+e+k,_Z);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,D*&\"\"%\"\"\"%\"lGF&!\"\"*&F%F&%
\"jGF&F(*&F%F&%\"fGF&F(*&F%F&%\"gGF&F(*&F%F&%\"hGF&F(*&F%F&%\"eGF&F(*&
F%F&%\"kGF&F(*&\"\"*F&)%\"dG\"\"#F&F&*(\"#7F&F8F&%\"cGF&F&*(\"\"'F&F8F
&%\"bGF&F&*(F>F&F8F&%\"mGF&F(*&F%F&)F<F9F&F&*(F%F&F<F&F?F&F&*(F%F&F<F&
FAF&F(*$)F?F9F&F&*(F9F&F?F&FAF&F(*$)FAF9F&F&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 103 "A2:=eval(A1,j=1/4*(-4*l-4*f-4*g-4*h-4*e-4*k+9*d
^2+12*d*c+6*d*b-6*d*m+4*c^2+4*c*b-4*c*m+b^2-2*b*m+m^2));" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%#A2G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*
F**&%\"lGF*)F-\"\"'F*F**(%\"mGF*)F-\"\"%F*F(F*F**(,*%\"cGF.%\"bGF.F4F.
%\"dGF.F*)F-\"\"$F*F'F*F**(F:F*)F-F)F*)F(F=F*F**(F9F*F-F*)F(F6F*F**&F;
F*)F(\"\"&F*F**(%\"eGF*)F-FEF*F(F*F**(%\"fGF*F5F*F'F*F**(%\"gGF*F<F*F@
F*F**(%\"hGF*F?F*FBF*F**(,BF0F.FJF.FLF.FNF.FGF.%\"kGF.*(\"\"*F*F6F.F;F
)F**(F=F*F;F*F9F*F***F=F*F)F.F;F*F:F*F***F=F*F)F.F;F*F4F*F.*$)F9F)F*F*
*&F9F*F:F*F**&F9F*F4F*F.*&F6F.F:F)F**(F)F.F:F*F4F*F.*&F6F.F4F)F*F*F-F*
FDF*F**&FQF*)F(F2F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pu
iseux(A2,x=0,y,0,T);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG,$*(
\"\")!\"\",dp**\"#'*\"\"\"%\"dGF.%\"cGF.%\"mGF.F.**\"#aF.F/F.%\"bGF.F1
F.F.**\"#SF.F0F.F4F.F1F.F.**\"#sF.F/F.F0F.F4F.F**&\"#FF.)F/\"\"$F.F**&
\"#;F.)F0F<F.F**&F<F.)F4F<F.F**&\"\"&F.)F1F<F.F.*(F8F.)F/\"\"#F.F0F.F*
*(\"#XF.FFF.F4F.F**(\"#jF.FFF.F1F.F.*(\"#gF.F/F.)F0FGF.F**(\"#@F.F/F.)
F4FGF.F**(\"#LF.F/F.)F1FGF.F**(\"#GF.FNF.F4F.F**(\"#OF.FNF.F1F.F.*(F>F
.F0F.FQF.F**(\"#CF.F0F.FTF.F**(\"#6F.FQF.F1F.F.*(\"#8F.F4F.FTF.F**(\"#
[F.%\"eGF.F/F.F.*(\"#KF.F\\oF.F0F.F.*(F>F.F\\oF.F4F.F.*(F>F.F\\oF.F1F.
F**(FXF.%\"fGF.F/F.F.*(FenF.FboF.F0F.F.*(\"#7F.FboF.F4F.F.*(FeoF.FboF.
F1F.F**(FenF.%\"gGF.F/F.F.*(F)F.FhoF.F4F.F.*(F)F.FhoF.F1F.F**(F>F.FhoF
.F0F.F.*(FeoF.%\"hGF.F/F.F.*(F)F.F]pF.F0F.F.*(\"\"%F.F]pF.F4F.F.*(F`pF
.F]pF.F1F.F**(FMF.%\"lGF.F/F.F.*(F6F.FcpF.F0F.F.*(\"#?F.FcpF.F4F.F.*(F
fpF.FcpF.F1F.F**(FeoF.%\"kGF.F/F.F**(F)F.FipF.F0F.F**(F`pF.FipF.F4F.F*
*(F`pF.FipF.F1F.F.F.%\"TGFGF*/%\"yG,(*(\"$7&F*F+F<F]qFCF***\"$G\"F*F+F
G,**&F<F.F/F.F.*&FGF.F0F.F.F4F.F1F*F.F]qF`pF**&,dp**FeoF.F/F.F0F.F1F.F
**,F:F.F`pF*F/F.F4F.F1F.F***FCF.F0F.F4F.F1F.F***\"\"*F.F/F.F0F.F4F.F.*
(F:F.F)F*F/F<F.*&FGF.F?F.F.*(F<F.F)F*F4F<F.*(FCF.F)F*F1F<F**(F^rF.FFF.
F0F.F.**FIF.F)F*F/FGF4F.F.**FKF.F)F*F/FGF1F.F***\"#:F.FGF*F/F.F0FGF.**
FPF.F)F*F/F.F4FGF.**FSF.F)F*F/F.F1FGF.**\"\"(F.FGF*F0FGF4F.F.**F^rF.FG
F*F0FGF1F.F**(FGF.F0F.FQF.F.*(F<F.F0F.FTF.F.**FgnF.F)F*F4FGF1F.F***Fin
F.F)F*F4F.F1FGF.*(\"\"'F.F\\oF.F/F.F**(F`pF.F\\oF.F0F.F**(FGF.F\\oF.F4
F.F**(FGF.F\\oF.F1F.F.**F^rF.FGF*FboF.F/F.F**(F<F.FboF.F0F.F***F<F.FGF
*FboF.F4F.F***F<F.FGF*FboF.F1F.F.*(F<F.FhoF.F/F.F**&FhoF.F4F.F**&FhoF.
F1F.F.*(FGF.FhoF.F0F.F***F<F.FGF*F]pF.F/F.F**&F]pF.F0F.F**(FGF*F]pF.F4
F.F**(FGF*F]pF.F1F.F.**FgrF.FGF*FcpF.F/F.F**(FCF.FcpF.F0F.F***FCF.FGF*
FcpF.F4F.F***FCF.FGF*FcpF.F1F.F.**F<F.FGF*FipF.F/F.F.*&FipF.F0F.F.*(FG
F*FipF.F4F.F.*(FGF*FipF.F1F.F*F.)F]qFGF.F.7$/F&F]q/F_q-%'RootOfG6#,(*&
FipF.)%#_ZGFGF.F.*&F/F.FduF.F.F.F.7$F\\u/F_q*&FjtF.-F_u6#,(FcpF.*&F1F.
FduF.F.*$FcuF.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 338 "fact
or(96*d*c*m+54*d*b*m+40*c*b*m-72*d*c*b-27*d^3-16*c^3-3*b^3+5*m^3-72*d^
2*c-45*d^2*b+63*d^2*m-60*d*c^2-21*d*b^2-33*d*m^2-28*c^2*b+36*c^2*m-16*
c*b^2-24*c*m^2+11*b^2*m-13*b*m^2+48*e*d+32*e*c+16*e*b-16*e*m+36*f*d+24
*f*c+12*f*b-12*f*m+24*g*d+8*g*b-8*g*m+16*g*c+12*h*d+8*h*c+4*h*b-4*h*m+
60*l*d+40*l*c+20*l*b-20*l*m-12*k*d-8*k*c-4*k*b+4*k*m);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#*&,**&\"\"$\"\"\"%\"dGF'F'*&\"\"#F'%\"cGF'F'%\"bGF
'%\"mG!\"\"F',B*&F&F')F,F*F'F.*(\"#7F'F(F'F,F'F.*(\"#5F'F+F'F,F'F.*(\"
\")F'F,F'F-F'F'*&\"\"&F')F-F*F'F.*&F7F'%\"gGF'F'*&\"\"*F')F(F*F'F.*&\"
#;F'%\"eGF'F'*(\"#9F'F+F'F-F'F'*&\"#?F'%\"lGF'F'*&\"\"%F'%\"hGF'F'*&F3
F'%\"fGF'F'*&F7F')F+F*F'F.*&FIF'%\"kGF'F.*(\"#=F'F(F'F+F'F.*(FRF'F(F'F
-F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A3:=eval(A2,b=-(
3*d+2*c-m));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A3G,<*&)%\"yG\"\"#
\"\"\"),&F(F*%\"xG!\"\"F)F*F**&%\"lGF*)F-\"\"'F*F**(%\"mGF*)F-\"\"%F*F
(F*F**(,(%\"cGF**&F)F*%\"dGF*F**&F)F*F4F*F.F*)F-\"\"$F*F'F*F**(,(*&F>F
*F;F*F.*&F)F*F9F*F.F4F*F*)F-F)F*)F(F>F*F**(F9F*F-F*)F(F6F*F**&F;F*)F(
\"\"&F*F**(%\"eGF*)F-FIF*F(F*F**(%\"fGF*F5F*F'F*F**(%\"gGF*F=F*FDF*F**
(%\"hGF*FCF*FFF*F**(,BF0F.FNF.FPF.FRF.FKF.%\"kGF.*(\"\"*F*F6F.F;F)F**(
F>F*F;F*F9F*F***F>F*F)F.F;F*F@F*F***F>F*F)F.F;F*F4F*F.*$)F9F)F*F**&F9F
*F@F*F**&F9F*F4F*F.*&F6F.F@F)F**(F)F.F@F*F4F*F.*&F6F.F4F)F*F*F-F*FHF*F
**&FUF*)F(F2F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(
A3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&,&%\"yG!\"\"%\"xG\"\"\"F(,T*
()F'\"\"$F(%\"mGF(F%F(F(*(F'F()F%F,F(%\"cGF(F&*(F+F(%\"lGF()F%\"\"#F(F
(*()F'F4F(F-F(F3F(F&*()F'\"\"%F(F2F(F%F(F(*(F'F(%\"hGF()F%F9F(F(*$F/F(
F&*(F+F(%\"eGF(F3F(F(*(F'F(%\"gGF(F<F(F(*(F'F(F/F(%\"dGF(F&*(F+F(%\"fG
F(F3F(F(*(F8F(F?F(F%F(F(*(F6F(F0F(F3F(F(*(F6F(FAF(F/F(F(**F4F(F6F(FCF(
F3F(F(*(F6F(FEF(F/F(F(*(F6F(F?F(F/F(F(*(F6F(F2F(F/F(F(*(F'F(FEF(F<F(F(
*(F'F(F?F(F<F(F(*(F'F(F2F(F<F(F(*&F3F(F'F(F(*&)F%\"\"&F(%\"kGF(F&*&F2F
()F'FSF(F(*&F<F(FCF(F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
111 "A4:=eval(A2,g=-1/8*(-3*b^2-12*d*b-10*c*b+8*b*m-5*m^2-9*d^2+16*e+1
4*c*m+20*l+4*h+12*f-8*c^2-4*k-18*d*c+18*d*m));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%#A4G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**&%\"
lGF*)F-\"\"'F*F**(%\"mGF*)F-\"\"%F*F(F*F**(,*%\"cGF.%\"bGF.F4F.%\"dGF.
F*)F-\"\"$F*F'F*F**(F:F*)F-F)F*)F(F=F*F**(F9F*F-F*)F(F6F*F**&F;F*)F(\"
\"&F*F**(%\"eGF*)F-FEF*F(F*F**(%\"fGF*F5F*F'F*F**(,@*(F=F*\"\")F.F:F)F
***F=F*F)F.F;F*F:F*F***FEF*F6F.F9F*F:F*F**&F:F*F4F*F.*(FEF*FNF.F4F)F**
(\"\"*F*FNF.F;F)F**&F)F*FGF*F.**\"\"(F*F6F.F9F*F4F*F.*(FEF*F)F.F0F*F.*
&F)F.%\"hGF*F.*(F=F*F)F.FJF*F.*$)F9F)F*F**&F)F.%\"kGF*F***FTF*F6F.F;F*
F9F*F***FTF*F6F.F;F*F4F*F.F*F<F*F@F*F**(FZF*F?F*FBF*F**(,<FGF**(F=F*F)
F.F0F*F**&F)F.FJF*F**(F=F*F)F.FinF*F.*&F)F.FZF*F.**F=F*F6F.F9F*F4F*F**
(F6F.F9F*F:F*F.*(FTF*FNF.F;F)F***F=F*F6F.F;F*F9F*F***F=F*F6F.F;F*F4F*F
**&FNF.F:F)F.*(F)F.F:F*F4F*F**(F=F*FNF.F4F)F.F*F-F*FDF*F**&FinF*)F(F2F
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(%\"lGF(*&%\"mGF(%#_ZGF(F(*$)F0F'F(F(F(-F*6#,(*&%\"kGF(F2F(F(*&%\"dGF(
F0F(F(F(F(,(F&F(*&F%F(,**(\"\"$F(F'!\"\"F9F(F?%\"cGF?*&F'F?%\"bGF(F?*&
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F(FBF(F/F(F?**\"$?\"F(F-F(FBF(F/F(F?**\"#sF(F7F(F9F(FBF(F(**\"$G\"F(FK
F(F@F(FBF(F(**\"#[F(FNF(F@F(FBF(F(**FVF(F7F(F@F(F/F(F?**\"$S#F(F-F(F@F
(F/F(F?**FVF(%\"hGF(F9F(F@F(F?*&,2*(\"#;F(F@F(FBF(F?*(FinF(FBF(F/F(F?*
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" 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,$*(\"$c#\"\"\"),**&\"\"$F&%\"dGF&F&*&\"\"#F&%\"cGF&F&%\"bGF&%\"mG!\"
\"\"\"%F&,2*(F-F&F/F&F0F&F&*&\"\"&F&)F0F-F&F1*(F-F&F+F&F0F&F&*$)F+F-F&
F1*&F2F&%\"eGF&F&*&F2F&%\"kGF&F&*&\"#?F&%\"lGF&F&*(F-F&F.F&F0F&F&F&F1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "A7:=eval(A6,e=-1/4*(2*b
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