{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 
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{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
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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 0 115 "A:=y^2*(y-x)^2+m*x^4*y+l*x^
6+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**(%\"mGF*)F-\"\"%F*F(F*F**&%\"lGF*)F
-\"\"'F*F**(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F*)F(F:F*F**(%\"cGF*F
-F*)F(F2F*F**&%\"dGF*)F(\"\"&F*F**(%\"eGF*)F-FEF*F(F*F**(%\"fGF*F1F*F'
F*F**(%\"gGF*F9F*F>F*F**(%\"hGF*F=F*FAF*F**(%\"jGF*F-F*FDF*F**&%\"kGF*
)F(F6F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,
y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\"
)%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,&*&),,%\"cGF*%\"mGF*%\"bGF*F/F*%\"a
GF*F-F*)*&%\"xGF*,,F4!\"\"F5F<F6F<F/F<F7F<F<#\"\"$F-F*F*F:F**&)F:F-F*-
F%6#,(%\"lGF**&F5F*F,F*F**$F+F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "A1:=eval(A,l=1/4*m^2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#A1G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"
\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F
*)F(F8F*F**(%\"cGF*F-F*)F(F2F*F**&%\"dGF*)F(\"\"&F*F**(%\"eGF*)F-FCF*F
(F*F**(%\"fGF*F1F*F'F*F**(%\"gGF*F7F*F<F*F**(%\"hGF*F;F*F?F*F**(%\"jGF
*F-F*FBF*F**&%\"kGF*)F(F4F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'Roo
tOfG6#,(*&%\"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<#\"\"
$F-F*F*F:F*,&*,\"\"%F<F5F>,(*&F-F*%\"eGF*F**&F7F*F5F*F<*$)F5F-F*F<F>FA
#F*F-*(F:F*F5F<FBF<#\"\"&F-F**(F-F<F:F-F5F*F<" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 29 "A2:=eval(A1,e=1/2*(a*m+m^2));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#A2G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%
\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(%\"aGF*)F-\"\"$F*F'F*F**(%
\"bGF*)F-F)F*)F(F8F*F**(%\"cGF*F-F*)F(F2F*F**&%\"dGF*)F(\"\"&F*F**(,&*
&#F*F)F**&F6F*F0F*F*F**&FGF**$)F0F)F*F*F*F*)F-FCF*F(F*F**(%\"fGF*F1F*F
'F*F**(%\"gGF*F7F*F<F*F**(%\"hGF*F;F*F?F*F**(%\"jGF*F-F*FBF*F**&%\"kGF
*)F(F4F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=
0,y,0);" }}{PARA 12 "" 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<#\"\"$F-F*F*F:F*,&*(F-F
<F:F-F5F*F<*&)F:F>F*-F%6#,,*&\"#;F*F+F*F**&,&*(\"\")F*F7F*F5F*F<*&FGF*
)F5F-F*F<F*F,F*F**(F-F*F6F*)F5F>F*F<*$)F5\"\"%F*F**(FRF*%\"fGF*FMF*F*F
*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "discrim(16*_Z^2+(-8*
a*m-16*m^2)*_Z-2*b*m^3+m^4+4*f*m^2,_Z);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,,*(\"$G\"\"\"\"%\"bGF&)%\"mG\"\"$F&F&*&\"$#>F&)F)\"\"%F&F&*(\"$
c#F&%\"fGF&)F)\"\"#F&!\"\"*(\"#kF&)%\"aGF3F&F2F&F&*(F0F&F8F&F(F&F&" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*(\"#k\"\"\")%\"mG\"\"#F&,,*&\"\"$F&F'F&F&*(F)F&
F(F&%\"bGF&F&*(\"\"%F&%\"aGF&F(F&F&*&F0F&%\"fGF&!\"\"*$)F1F)F&F&F&F&" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "A3:=eval(A2,f=1/4*(3*m^2+
2*m*b+4*a*m+a^2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A3G,<*&)%\"yG
\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F
-\"\"'F**(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F*)F(F8F*F**(%\"cGF*F-F
*)F(F2F*F**&%\"dGF*)F(\"\"&F*F**(,&*&#F*F)F**&F6F*F0F*F*F**&FGF**$)F0F
)F*F*F*F*)F-FCF*F(F*F**(,**&#F8F2F*FJF*F**&FGF**&F0F*F:F*F*F*FHF**&#F*
F2F**$)F6F)F*F*F*F*F1F*F'F*F**(%\"gGF*F7F*F<F*F**(%\"hGF*F;F*F?F*F**(%
\"jGF*F-F*FBF*F**&%\"kGF*)F(F4F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "puiseux(A3,x=0,y,0,T);" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%7$/%\"xG,$*&,,%\"cG\"\"\"
%\"mGF+%\"bGF+%\"dGF+%\"aGF+F+)%\"TG\"\"#F+!\"\"/%\"yG,&*&)F)F2F+)F1\"
\"$F+F+*&,,F*F3F,F3F-F3F.F3F/F3F+F0F+F+7$/F&,$**\"#;F3F,F:,0*(F:F+F/F+
F,F+F+*$)F/F2F+F+*&F2F+)F,F2F+F+*(F2F+F,F+F-F+F+*&F-F+F/F+F+*&F2F+%\"g
GF+F3*&F*F+F,F+F+F+F1F2F3/F5,(**\"&Ob'F3F,\"#7FB\"\"%F1\"\"(F+*,\"&%Q;
F3F,\"#5FBF:,&*&F2F+F,F+F+F/F+F+F1\"\"'F3**\"$7&F3F,FSFBF2F1FRF37$/F&F
1/F5-%'RootOfG6#,(*&%\"kGF+)%#_ZGF2F+F+*&F.F+F`oF+F+F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "A4:=eval(A3,g=1/2*(3*a*m+a^2+2*m^2+
2*m*b+b*a+c*m));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A4G,<*&)%\"yG\"
\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-
\"\"'F**(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F*)F(F8F*F**(%\"cGF*F-F*
)F(F2F*F**&%\"dGF*)F(\"\"&F*F**(,&*&#F*F)F**&F6F*F0F*F*F**&FGF**$)F0F)
F*F*F*F*)F-FCF*F(F*F**(,**&#F8F2F*FJF*F**&FGF**&F0F*F:F*F*F*FHF**&#F*F
2F**$)F6F)F*F*F*F*F1F*F'F*F**(,.**F8F*F)F.F6F*F0F*F**&F)F.F6F)F*FJF*FR
F**(F)F.F:F*F6F*F**(F)F.F>F*F0F*F*F*F7F*F<F*F**(%\"hGF*F;F*F?F*F**(%\"
jGF*F-F*FBF*F**&%\"kGF*)F(F4F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(A4,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,(*(
F-!\"\"%\"xGF-%\"mGF*F2*&)F3\"\"$F*,&*&#F*F-F**$)F4F-F*F*F**&#F*\"\"%F
**&%\"aGF*F4F*F*F*F*F**&)F3F?F*-F%6#,>*&\"#kF*F+F*F**&,**(\"#;F*%\"bGF
*F<F*F**(\"#'*F*FAF*F<F*F**(FLF*)FAF-F*F4F*F**&\"$7\"F*)F4F7F*F*F*F,F*
F**(F-F*F/F*)F4\"\"&F*F2*(\"\")F*FVF*FMF*F**&)FAF?F*F<F*F**(F?F*%\"cGF
*FVF*F2*(F?F*%\"hGF*)F4F?F*F**(\"#7F*)FAF7F*FTF*F**&\"#WF*)F4\"\"'F*F*
*(\"#wF*FVF*FAF*F**(\"#ZF*FQF*FjnF*F***FYF*FjnF*FMF*FAF*F***F-F*FTF*FM
F*FQF*F***F-F*FgnF*FAF*FjnF*F2F*F*,&*&),,FgnF*F4F*FMF*F/F*FAF*F-F*)*&F
3F*,,FgnF2F4F2FMF2F/F2FAF2F2#F7F-F*F*F3F*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 170 "discrim(64*_Z^2+(112*m^3+16*a^2*m+16*b*m^2+96*a*m^
2)*_Z-2*c*a*m^4+8*m^5*b+a^4*m^2-4*c*m^5+44*m^6+76*m^5*a+47*m^4*a^2+12*
m^3*a^3+8*m^4*b*a+4*h*m^4-2*d*m^5+2*m^3*b*a^2,_Z);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,6*(\"%C5\"\"\"%\"hGF&)%\"mG\"\"%F&!\"\"*&\"%!G\"F&)F
)\"\"'F&F&*(\"%[?F&)F)\"\"&F&%\"aGF&F&*(\"$o(F&)F4\"\"#F&F(F&F&**F%F&F
(F&%\"bGF&F4F&F&**\"$7&F&%\"cGF&F4F&F(F&F&*(F<F&%\"dGF&F2F&F&*(\"%O:F&
F2F&F:F&F&*(F%F&F=F&F2F&F&*(\"$c#F&)F:F8F&F(F&F&" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,$*(\"$c#\"\"\")%\"mG\"\"%F&,6*&\"\"&F&)F(\"\"#F&F&*(\"\")F&%\"aGF&F(
F&F&*(F.F&F(F&%\"dGF&F&*(\"\"'F&F(F&%\"bGF&F&*(F)F&%\"cGF&F(F&F&*&F)F&
%\"hGF&!\"\"*(F.F&F8F&F1F&F&*&\"\"$F&)F1F.F&F&*(F)F&F6F&F1F&F&*$)F6F.F
&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "A5:=eval(A4,h=1/
4*(5*m^2+6*m*b+8*a*m+4*c*m+2*m*d+2*a*c+b^2+3*a^2+4*b*a));" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#>%#A5G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F
*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(%\"aGF*)F-\"\"$F*F'F*
F**(%\"bGF*)F-F)F*)F(F8F*F**(%\"cGF*F-F*)F(F2F*F**&%\"dGF*)F(\"\"&F*F*
*(,&*&#F*F)F**&F6F*F0F*F*F**&FGF**$)F0F)F*F*F*F*)F-FCF*F(F*F**(,**&#F8
F2F*FJF*F**&FGF**&F0F*F:F*F*F*FHF**&#F*F2F**$)F6F)F*F*F*F*F1F*F'F*F**(
,.**F8F*F)F.F6F*F0F*F**&F)F.F6F)F*FJF*FRF**(F)F.F:F*F6F*F**(F)F.F>F*F0
F*F*F*F7F*F<F*F**(,4*(FCF*F2F.F0F)F***F8F*F)F.F0F*F:F*F**(F)F*F6F*F0F*
F**&F>F*F0F*F**(F)F.F0F*FAF*F**(F)F.F>F*F6F*F**&F2F.F:F)F**(F8F*F2F.F6
F)F**&F:F*F6F*F*F*F;F*F?F*F**(%\"jGF*F-F*FBF*F**&%\"kGF*)F(F4F*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A5,x=0,y,0);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"
\"#F*F**&%\"dGF*F,F*F*F*F*,&*&),,%\"cGF*%\"mGF*%\"bGF*F/F*%\"aGF*F-F*)
*&%\"xGF*,,F4!\"\"F5F<F6F<F/F<F7F<F<#\"\"$F-F*F*F:F*,***\"+C=ut5F<F5\"
#D,:*(F>F*F6F*F7F*F**(F>F*F4F*F5F*F**(F-F*F4F*F7F*F**&F4F*F6F*F**&F-F*
%\"jGF*F<*&F-F*)F7F-F*F**(\"\"&F*F7F*F5F*F**$)F6F-F*F**(\"\"%F*F5F*F6F
*F**&F>F*)F5F-F*F**(F-F*F5F*F/F*F**&F/F*F7F*F*FM,$**\"#kF*F:F*F5!\"&FC
F<F<#\"\"*F-F<**\"\")F<F5F*,**$FKF*F**(\"\"'F*F7F*F5F*F**&F5F*F6F*F**&
\"\"(F*FSF*F*F*F:FQF<**FQF<F5F*,&*&F-F*F5F*F*F7F*F*F:F>F**(F-F<F:F-F5F
*F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "factor(3*c*m-2*j+2*a
^2+5*a*m+c*b+3*b*a+3*m^2+b^2+4*m*b+d*a+2*a*c+2*m*d);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,:*(\"\"$\"\"\"%\"bGF&%\"aGF&F&*(F%F&%\"cGF&%\"mGF&F
&*(\"\"#F&F*F&F(F&F&*&F*F&F'F&F&*&F-F&%\"jGF&!\"\"*&F-F&)F(F-F&F&*(\"
\"&F&F(F&F+F&F&*$)F'F-F&F&*(\"\"%F&F+F&F'F&F&*&F%F&)F+F-F&F&*(F-F&F+F&
%\"dGF&F&*&F=F&F(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "A6
:=eval(A5,j=1/2*(3*c*m+2*a^2+5*a*m+c*b+3*b*a+3*m^2+b^2+4*m*b+d*a+2*a*c
+2*m*d));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A6G,<*&)%\"yG\"\"#\"\"
\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**
(%\"aGF*)F-\"\"$F*F'F*F**(%\"bGF*)F-F)F*)F(F8F*F**(%\"cGF*F-F*)F(F2F*F
**&%\"dGF*)F(\"\"&F*F**(,&*&#F*F)F**&F6F*F0F*F*F**&FGF**$)F0F)F*F*F*F*
)F-FCF*F(F*F**(,**&#F8F2F*FJF*F**&FGF**&F0F*F:F*F*F*FHF**&#F*F2F**$)F6
F)F*F*F*F*F1F*F'F*F**(,.**F8F*F)F.F6F*F0F*F**&F)F.F6F)F*FJF*FRF**(F)F.
F:F*F6F*F**(F)F.F>F*F0F*F*F*F7F*F<F*F**(,4*(FCF*F2F.F0F)F***F8F*F)F.F0
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F&)F(F0F&)F*F.F&F&*(%\"cGF&F(F&)F*F)F&F&*&%\"dGF&)F*\"\"&F&F&*&%\"kGF&
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{XPPMATH 20 "6#,>*(\"%'4%\"\"\"%\"kGF&)%\"mG\"\"'F&!\"\"**\"%#>)F&%\"a
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1 "" {XPPMATH 20 "6#,$*(\"%C5\"\"\")%\"mG\"\"'F&,>*&\"\"(F&)F(\"\"#F&F
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11 "" 1 "" {XPPMATH 20 "6#>%\"BG,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"
F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(,*%\"dGF.F0F.%\"cG
F.%\"bGF.F*)F-\"\"$F*F'F*F**(F9F*)F-F)F*)F(F;F*F**(F8F*F-F*)F(F2F*F**&
F7F*)F(\"\"&F*F**(%\"eGF*)F-FCF*F(F*F**(%\"fGF*F1F*F'F*F**(%\"gGF*F:F*
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{PARA 12 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"
\"#F*F**&%\"dGF*F,F*F*F*F*,&%\"xGF**&)F1F-F*-F%6#,4*&\"\"%F*F+F*F**&,*
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{MPLTEXT 1 0 69 "discrim(16*_Z^2+(8*m*d-8*m^2+8*m*b+8*c*m)*_Z+4*f*m^2-
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0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,$*(\"#k\"\"\")%\"mG\"\"#F&,4*(F)F&F(F&%\"dGF&!\"\"*(F)F&%\"cGF&
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"6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,&%
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(B3,x=0,y,0);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"
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b*c^2+32*m^4*b*c+d^4*m^2+b^4*m^2+c^4*m^2+4*d^3*m^2*b+4*d^3*m^2*c+6*d^2
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,$*(\"$c#\"\"\")%\"mG\"\"%F&,,*&F)F&%\"hGF&!\"\"*(F)
F&%\"dGF&%\"cGF&F&*&\"\"$F&)F/\"\"#F&F&*(F4F&F/F&%\"bGF&F&*$)F0F4F&F&F
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{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#B5G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"x
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{XPPMATH 20 "6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,
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50*d*m^7-140*c*m^7-510*d*b^2*m^5-84*d^4*m^3*b+380*d^3*m^4*b+60*d^2*b^3
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0*d^4*m^3*c+442*d^3*m^4*c-180*d^3*m^3*c^2-822*d^2*m^5*c+660*d^2*m^4*c^
2-804*d*c^2*m^5+15*d^4*c^2*m^2+15*d^2*b^4*m^2+15*d^2*c^4*m^2+6*d^5*m^2
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,$*(\"%C5\"\"\")%\"mG\"\"'F&,&*$)%\"dG\"\"#F&F&*&\"
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\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F
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F*)F(F;F*F**(F8F*F-F*)F(F2F*F**&F7F*)F(\"\"&F*F**(,(*(F)F.F8F*F0F*F.*(
F)F.F0F*F9F*F.*(F)F.F0F*F7F*F.F*)F-FCF*F(F*F**(,2*(F)F.F0F*F7F*F.*(F)F
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{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%!\"\",4*()%\"xG\"\"#\"\"\"%\"
dGF,%\"yGF,F&*(F*F,)F.F+F,F-F,F&*&)F.\"\"$F,F-F,F&*(F+F,F.F,F*F,F,*(F)
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%\"CG,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(
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F2\"\"$F+F'*$)F-FCF+F'*&\"#;F+)F6FCF+F'*(FGF+%\"jGF+F*F+F'*(F;F+FJF+F2
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F2F+F+*(F=F+FQF+F6F+F+*(FPF+FQF+F-F+F+*(F4F+%\"hGF+F*F+F'*(\"#OF+FVF+F
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F2F+F,F+F'*(\"#jF+F1F+F-F+F'*(FgnF+F-F+F5F+F'*(F.F+F6F+F9F+F'*(\"$W\"F
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(F8F+F2F+F-F+F'*(FPF+F6F+F-F+F'*&FjpF+F1F+F'*$F,F+F'*&FPF+FJF+F+*&FPF+
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F+*(F4F+F2F+F6F+F'*(FPF+F*F+F2F+F+FC,$**F=F+FapF+F*F'FesF'F'F\\sF'*(F.
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 305 "factor(9/4*b*m*d+6*c*m*d+c*
m*b-81/8*d^3-1/8*b^3-2*c^3+5*k*c+15/2*k*d+5/2*k*b+4*j*c+2*j*b+6*j*d+45
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%\"dGF+F+*&\"\"#F+%\"cGF+F+%\"bGF+F+,<*$)F0F.F+F&*(\"#7F+F,F+F0F+F&*(
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0 "" {MPLTEXT 1 0 75 "factor(2*c*m-9*d^2-4*c^2+4*h+4*k-12*d*c-6*d*b-4*
c*b+4*m*d+4*j+4*f+4*g-b^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,<*(\"
\"'\"\"\"%\"dGF&%\"bGF&!\"\"*(\"\"%F&%\"cGF&F(F&F)*&\"\"*F&)F'\"\"#F&F
)*$)F(F0F&F)*&F+F&%\"jGF&F&*&F+F&%\"fGF&F&*&F+F&)F,F0F&F)*&F+F&%\"hGF&
F&*&F+F&%\"kGF&F&*(F0F&F,F&%\"mGF&F&*&F+F&%\"gGF&F&*(\"#7F&F'F&F,F&F)*
(F+F&F>F&F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "C1:=eval
(C,j=-1/4*(2*c*m-9*d^2-4*c^2+4*h+4*k-12*d*c-6*d*b-4*c*b+4*m*d+4*f+4*g-
b^2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#C1G,<*&)%\"yG\"\"#\"\"\")
,&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(,*
%\"dGF.F0F.%\"cGF.%\"bGF.F*)F-\"\"$F*F'F*F**(F9F*)F-F)F*)F(F;F*F**(F8F
*F-F*)F(F2F*F**&F7F*)F(\"\"&F*F**(,(*(F)F.F8F*F0F*F.*(F)F.F0F*F9F*F.*(
F)F.F0F*F7F*F.F*)F-FCF*F(F*F**(%\"fGF*F1F*F'F*F**(%\"gGF*F:F*F>F*F**(%
\"hGF*F=F*F@F*F**(,:*(F)F.F8F*F0F*F.*(\"\"*F*F2F.F7F)F**$)F8F)F*F*FOF.
%\"kGF.*(F;F*F7F*F8F*F***F;F*F)F.F7F*F9F*F**&F8F*F9F*F**&F0F*F7F*F.FKF
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0 "" {MPLTEXT 1 0 20 "puiseux(C1,x=0,y,0);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#<%,(*(\"$7&!\"\",`o*(\"\"$\"\"\"%\"mGF+)%\"bG\"\"#F+F+*
(\"#RF+F,F+)%\"dGF/F+F+*(\"#?F+F,F+)%\"cGF/F+F+*(\"#5F+)F,F/F+F3F+F'**
\"#cF+F3F+F,F+F7F+F+**\"#;F+F7F+F,F+F.F+F+**\"#AF+F3F+F,F+F.F+F+*&\"#F
F+)F3F*F+F'*&F*F+)F.F*F+F'*&F>F+)F7F*F+F'*(\"#7F+%\"fGF+F,F+F'*(\"#OF+
FJF+F3F+F+*(\"#CF+FJF+F7F+F+*(FIF+FJF+F.F+F+*(\"\"%F+%\"hGF+F,F+F'*(FI
F+FRF+F3F+F+*(\"\")F+FRF+F7F+F+*(FQF+FRF+F.F+F+*(FQF+%\"kGF+F,F+F+*(FI
F+FXF+F3F+F'*(FUF+FXF+F7F+F'*(FQF+FXF+F.F+F'*(FUF+%\"gGF+F,F+F'*(FNF+F
gnF+F3F+F+*(F>F+FgnF+F7F+F+*(FUF+FgnF+F.F+F+*(F>F+F7F+F-F+F'*(\"#@F+F3
F+F-F+F'*(\"#XF+F2F+F.F+F'*(\"#GF+F.F+F6F+F'*(\"\"'F+F7F+F:F+F'*(\"#sF
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F/F3F+F+**\"\"(F+F3F+F,F+F7F+F'**F/F+F7F+F,F+F.F+F'*,\"#6F+FQF'F3F+F,F
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F,F+F+**F*F+F/F'FRF+F3F+F'*&FRF+F7F+F'*(F/F'FRF+F.F+F'*(F/F'FXF+F,F+F'
**F*F+F/F'FXF+F3F+F+*&FXF+F7F+F+*(F/F'FXF+F.F+F+*&FgnF+F,F+F+*(F*F+Fgn
F+F3F+F'*(F/F+FgnF+F7F+F'*&FgnF+F.F+F'*(F/F+F7F+F-F+F+**F]oF+FUF'F3F+F
.F/F+**F_oF+FUF'F3F/F.F+F+**FbpF+F/F'F.F+F7F/F+**F*F+FQF'F7F+F,F/F+*(F
[qF+F7F+F2F+F+**F[qF+F7F+F3F+F.F+F+**\"#:F+F/F'F7F/F3F+F+F'#F_pF/F'*,
\"$G\"F'F(F/,*F,F'*&F*F+F3F+F+*&F/F+F7F+F+F.F+F+FjoF/F[p!\"#F'FjoF+-%'
RootOfG6#,(*&FXF+)%#_ZGF/F+F+*&F3F+F`sF+F+F+F+,&*(F/F'FjoF/F,F+F'*&)Fj
oF*F+-F[s6#,,*&F>F+F_sF+F+*&,**(FUF+F,F+F3F+F+*&FUF+F:F+F'*(FUF+F,F+F.
F+F+*(FUF+F7F+F,F+F+F+F`sF+F+*(FQF+FJF+F:F+F+*(F/F+F.F+)F,F*F+F'*$)F,F
QF+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "discrim(16*_Z^
2+(8*m*d-8*m^2+8*m*b+8*c*m)*_Z+4*f*m^2-2*b*m^3+m^4,_Z);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,4*(\"$c#\"\"\"%\"fGF&)%\"mG\"\"#F&!\"\"*(\"#kF&
F(F&)%\"dGF*F&F&**\"$G\"F&F(F&F/F&%\"bGF&F&**F1F&F(F&F/F&%\"cGF&F&*(F1
F&)F)\"\"$F&F/F&F+*(F-F&F(F&)F2F*F&F&**F1F&F(F&F4F&F2F&F&*(F-F&F(F&)F4
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actor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"#k\"\"\")%\"mG\"\"#
F&,4*(F)F&F(F&%\"dGF&!\"\"*(F)F&%\"cGF&F(F&F-*&\"\"%F&%\"fGF&F-*$)F,F)
F&F&*(F)F&F,F&%\"bGF&F&*(F)F&F,F&F/F&F&*$)F6F)F&F&*(F)F&F/F&F6F&F&*$)F
/F)F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "C2:=eval(C1,
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"" {XPPMATH 20 "6#>%#C2G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(
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\"\"&F*F**(,(*(F)F.F8F*F0F*F.*(F)F.F0F*F9F*F.*(F)F.F0F*F7F*F.F*)F-FCF*
F(F*F**(,2*(F)F.F0F*F7F*F.*(F)F.F8F*F0F*F.*&F2F.F7F)F**(F)F.F7F*F9F*F*
*(F)F.F7F*F8F*F**&F2F.F9F)F**(F)F.F8F*F9F*F**&F2F.F8F)F*F*F1F*F'F*F**(
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F7F*F.FUF.F*F-F*FBF*F**&FgnF*)F(F4F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(C2,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,(*(
\"$7&!\"\",X*(\"#=F*%\"mGF*)F/F-F*F**(\"\"&F*F7F*)%\"cGF-F*F**(\"\"%F*
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F7F*FCF*F**&F6F*)F/\"\"$F*F3*&FEF*)F<FHF*F3*(F>F*%\"hGF*F7F*F3*(\"#7F*
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F/F*F**(\"#;F*FWF*F<F*F**(FPF*FWF*FCF*F**(F>F*F<F*)FCF-F*F3*(\"\"'F*F/
F*FhnF*F3*(FYF*F8F*FCF*F3*(\"#8F*FCF*F;F*F3*(\"#[F*F<F*F8F*F3**\"#OF*F
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FWF*F/F*F3*(F-F*FWF*F<F*F3*&FWF*FCF*F3*(F-F3F<F*FCF-F***FHF*F>F3F/F*FC
F-F**(FHF*F8F*FCF*F***F]oF*FPF3FCF*F<F-F**(FjnF*F<F*F8F*F**,FhoF*F-F3F
<F*F/F*FCF*F***FcoF*FPF3F<F-F/F*F*F3#F:F-F3*,\"$G\"F3F4F-,*F7F3*&FHF*F
/F*F**&F-F*F<F*F*FCF*F*FeoF-Ffo!\"#F3FeoF*,(*,FenF3F7FN,0*&F/F*FCF*F3*
&F-F*FWF*F**&F<F*FCF*F3*(F-F*F/F*F<F*F3*&F7F*F/F*F**$F;F*F3*$F8F*F3F>F
en#F*F-*(FeoF*F7!\"$F\\rF3#\"\"(F-F***F>F3F7F*,*F/F*FCF*F<F*F7F3F*FeoF
HF3*(F-F3FeoF-F7F*F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "fac
tor(-c^2+m*d-d^2+2*g-d*b-c*b-2*d*c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,0*&%\"dG\"\"\"%\"bGF&!\"\"*&\"\"#F&%\"gGF&F&*&%\"cGF&F'F&F(*(F*F&F%
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0 "" {MPLTEXT 1 0 49 "C3:=eval(C2,g=-1/2*(-c^2+m*d-d^2-d*b-c*b-2*d*c))
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F**(F)F.F7F*F9F*F**(F)F.F7F*F8F*F**&F2F.F9F)F**(F)F.F8F*F9F*F**&F2F.F8
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{MPLTEXT 1 0 20 "puiseux(C3,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<%-%'RootOfG6#,(*&%\"kG\"\"\")%#_ZG\"\"#F*F**&%\"dGF*F,F*F*F*F*,(*(
\"$7&!\"\",J*(F-F*%\"mGF*)F/F-F*F3*&F6F*)%\"cGF-F*F3**\"\"%F*F/F*F6F*F
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*F\\rF*F7F*F>F*F3**FirF*F\\rF*F7F*F:F*F3**F]sF*F\\rF*F/F*FQF*F3**\"#IF
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aqF*F**(FJF*F\\rF*FDF*F3*(\"#>F*FgrF*F9F*F*F*F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 525 "discrim(4*m^6+4*h*m^4-16*d*m^5+64*_Z^2-8*m^3*
d^3+17*m^4*d^2-6*m^3*b^3+13*m^4*b^2-8*c^3*m^3+19*c^2*m^4+4*d*b^3*m^2+4
*d*c^3*m^2+4*b^3*m^2*c+6*b^2*c^2*m^2+4*c^3*b*m^2+6*d^2*c^2*m^2-12*m^5*
b+(-48*b*m^2+32*m^3+16*m*b^2+32*c*m*d+32*c*m*b+32*b*m*d+16*m*c^2+16*m*
d^2-64*c*m^2-64*m^2*d)*_Z-16*c*m^5-44*m^3*d*b*c+30*m^4*d*b-24*m^3*d*c^
2+36*m^4*d*c-20*m^3*b^2*c-22*m^3*b*c^2+32*m^4*b*c+d^4*m^2+b^4*m^2+c^4*
m^2+4*d^3*m^2*b+4*d^3*m^2*c+6*d^2*m^2*b^2-22*m^3*d^2*b-24*m^3*d^2*c-20
*m^3*d*b^2+12*d^2*m^2*b*c+12*d*b^2*m^2*c+12*d*b*c^2*m^2,_Z);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,,*(\"%C5\"\"\"%\"hGF&)%\"mG\"\"%F&!\"\"**F%
F&F(F&%\"dGF&%\"cGF&F&*(\"$o(F&F(F&)F-\"\"#F&F&**\"$7&F&F(F&F-F&%\"bGF
&F&*(\"$c#F&F(F&)F.F2F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"$c#\"\"\")%\"m
G\"\"%F&,,*&F)F&%\"hGF&!\"\"*(F)F&%\"dGF&%\"cGF&F&*&\"\"$F&)F/\"\"#F&F
&*(F4F&F/F&%\"bGF&F&*$)F0F4F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "C4:=eval(C3,h=1/4*(3*d^2+c^2+2*d*b+4*d*c));" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%#C4G,<*&)%\"yG\"\"#\"\"\"),&F(F*%\"xG!\"\"
F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F)F-\"\"'F**(,*%\"dGF.F0F.%\"cG
F.%\"bGF.F*)F-\"\"$F*F'F*F**(F9F*)F-F)F*)F(F;F*F**(F8F*F-F*)F(F2F*F**&
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F&F3F&F,*(FbqF&F^oF&F0F&F,*(FAF&%\"hGF&F7F&F,*(F.F&%\"gGF&F7F&F,*(F?F&
FiqF&F(F&F,*(\"%C5F&FiqF&F3F&F,*(F.F&FiqF&F0F&F,*(FCF&FgqF&F(F&F,*(Fbo
F&FgqF&F3F&F,*(FAF&FgqF&F0F&F,**F=F&FgqF&F'F&F)F&F&**FboF&FgqF&F/F&F'F
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FboF&FgqF&F/F&F+F&F,**FbqF&FiqF&F'F&F)F&F&**F\\rF&FiqF&F/F&F'F&F&**Ffn
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iqF&F/F&F+F&F,*(\"&KG$F&F3F&F(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"#
k\"\"\"),*%\"mG!\"\"*&\"\"$F&%\"dGF&F&*&\"\"#F&%\"cGF&F&%\"bGF&F/F&,6*
(\"\")F&F-F&F1F&F**(F/F&F0F&F1F&F**&\"#LF&)F-F/F&F**&\"\"&F&)F0F/F&F**
&\"#CF&%\"jGF&F&*&\"\"%F&%\"gGF&F&*(F/F&F)F&F-F&F&*(\"#GF&F-F&F0F&F**&
\"#SF&%\"kGF&F&*&\"#7F&%\"hGF&F&F&F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "factor(-9*d*c-3*d*b+6*j-c*b-9*d^2-2*c^2+2*g+4*h+8*k+m
*d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,6*&\"\"#\"\"\"%\"gGF&F&*&\"\"
%F&%\"hGF&F&*&\"\")F&%\"kGF&F&*&F%F&)%\"cGF%F&!\"\"*(\"\"*F&%\"dGF&F0F
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F.%\"bGF.F*)F-\"\"$F*F'F*F**(F9F*)F-F)F*)F(F;F*F**(F8F*F-F*)F(F2F*F**&
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "discrim(16*_Z^2+(8*m*d-8*m^2+8*m*b
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\"#k\"\"\")%\"mG\"\"#F&,0*&\"#5F&)%\"dGF)F&F&*(\"\")F&F.F&%\"cGF&F&*&
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GF&*&\"\"$\"\"\"%\"dGF+F+*&\"\"#F+%\"cGF+F+%\"bGF+\"\"&,&*$)F,F.F+F+*&
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yG\"\"#\"\"\"),&F(F*%\"xG!\"\"F)F*F**(%\"mGF*)F-\"\"%F*F(F*F**(F2F.F0F
)F-\"\"'F**(,*%\"dGF.F0F.%\"cGF.%\"bGF.F*)F-\"\"$F*F'F*F**(F9F*)F-F)F*
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F.F0F*F9F*F.*(F)F.F0F*F7F*F.F*)F-FCF*F(F*F**(,2*(F)F.F0F*F7F*F.*(F)F.F
8F*F0F*F.*&F2F.F7F)F**(F)F.F7F*F9F*F**(F)F.F7F*F8F*F**&F2F.F9F)F**(F)F
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&#F;F2F**$)F7F)F*F*F**&#F*F2F**$)F8F)F*F*F**&#F*F)F**&F7F*F9F*F*F*FenF
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F,F.F,%\"bGF,F&*&F+F,F0F,F&*&)F*F3F,%\"mGF,F,*(F)F,F.F,%\"cGF,F&*(F*F,
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