{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 
2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 
2 2 1 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 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ma
ple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 
1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Output12" -1 
206 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 
0 0 0 0 2 0 2 0 2 2 -1 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 41 "`algcurves/lift_exp` := proc(v, f, x, y)\n" }{MPLTEXT 1 0 61 "
local i, ii, r, res, v7, vv7, v3, ext, a, j, n, np, ram, j3;\n" }
{MPLTEXT 1 0 40 "    if v[5] = 1 then return \{v\} end if;\n" }
{MPLTEXT 1 0 27 "    v3 := degree(v[3], x);\n" }{MPLTEXT 1 0 15 "    r
es := \{\};\n" }{MPLTEXT 1 0 26 "    r := v[1] + y*x^v[2];\n" }
{MPLTEXT 1 0 31 "    vv7 := v[7]*v3 + v[2] - 1;\n" }{MPLTEXT 1 0 23 " \+
   vv7 := vv7 + v[5];\n" }{MPLTEXT 1 0 73 "    ii := `algcurves/trunca
te_subs`(subs(x = v[3], f), x, y, r, vv7 + 1,\n" }{MPLTEXT 1 0 15 "   \+
     v[4]);\n" }{MPLTEXT 1 0 61 "    if ii = 0 then error \"degree est
imate was wrong\" end if;\n" }{MPLTEXT 1 0 38 "    v7 := (ldegree(ii, \+
x) - v[2])/v3;\n" }{MPLTEXT 1 0 30 "    r := `algcurves/v_ext_m`(\n" }
{MPLTEXT 1 0 59 "        `algcurves/g_factors`(tcoeff(ii, x), y, v[4])
, y);\n" }{MPLTEXT 1 0 58 "    for i in r do res := res union `algcurv
es/lift_exp`([\n" }{MPLTEXT 1 0 72 "        v[1] + x^v[2]*i[1], v[2] +
 1, v[3], [op(i[3]), op(v[4])], i[2],\n" }{MPLTEXT 1 0 62 "        v[6
]*i[4], v7, [op(v[8]), [op(1 .. 4, v)]]], f, x, y)\n" }{MPLTEXT 1 0 
12 "    end do;\n" }{MPLTEXT 1 0 60 "    if add(i[5]*i[6]*degree(i[3],
 x)/(v[6]*v3), i = res) <>\n" }{MPLTEXT 1 0 75 "    degree(tcoeff(ii, \+
x), y) then error \"found wrong number of expansions\"\n" }{MPLTEXT 1 
0 12 "    end if;\n" }{MPLTEXT 1 0 44 "    if v[5] = degree(tcoeff(ii,
 x), y) then\n" }{MPLTEXT 1 0 72 "        if ldegree(ii, x) <> vv7 the
n error \"degree estimate was wrong\"\n" }{MPLTEXT 1 0 16 "        end
 if;\n" }{MPLTEXT 1 0 19 "        return res\n" }{MPLTEXT 1 0 12 "    \+
end if;\n" }{MPLTEXT 1 0 26 "    ii := collect(ii, y);\n" }{MPLTEXT 1 
0 65 "    ii := add(`algcurves/normal_tcoeff`(coeff(ii, y, i), x)*y^i,
\n" }{MPLTEXT 1 0 33 "        i = 0 .. degree(ii, y));\n" }{MPLTEXT 1 
0 47 "    np := `algcurves/Newtonpolygon`(ii, x, y);\n" }{MPLTEXT 1 0 
42 "    if nops(np) = 2 and np[1][3] = 0 then\n" }{MPLTEXT 1 0 49 "   \+
     error \"found wrong number of expansions\"\n" }{MPLTEXT 1 0 12 " \+
   end if;\n" }{MPLTEXT 1 0 19 "    for j in np do\n" }{MPLTEXT 1 0 
54 "        if 2 < nops(j) and 0 < j[3] and j[3] < 1 then\n" }
{MPLTEXT 1 0 55 "            r := `algcurves/g_factors`(j[4], x, v[4])
;\n" }{MPLTEXT 1 0 44 "            r := `algcurves/v_ext_m`(r, x);\n" 
}{MPLTEXT 1 0 26 "            for i in r do\n" }{MPLTEXT 1 0 35 "     \+
           j3 := j[3] - v[2];\n" }{MPLTEXT 1 0 45 "                ext
 := [op(i[3]), op(v[4])];\n" }{MPLTEXT 1 0 51 "                n := mo
ds(1/numer(j3), denom(j3));\n" }{MPLTEXT 1 0 43 "                ram :
= i[1]^n*x^denom(j3);\n" }{MPLTEXT 1 0 51 "                a := v[2]*d
enom(j3) - numer(j[3]);\n" }{MPLTEXT 1 0 64 "                res := re
s union `algcurves/lift_exp`([collect(\n" }{MPLTEXT 1 0 40 "          \+
          subs(x = ram, v[1])\n" }{MPLTEXT 1 0 75 "                   \+
  + x^a*i[1]^((1 - n*numer(j3))/denom(j3)), x, normal),\n" }{MPLTEXT 
1 0 67 "                    a + 1, normal(subs(x = ram, v[3])), ext, i
[2],\n" }{MPLTEXT 1 0 31 "                    v[6]*i[4],\n" }{MPLTEXT 
1 0 75 "                    (j[2] - j[1]*j[3] - a/degree(ram, x))/degr
ee(v[3], x),\n" }{MPLTEXT 1 0 59 "                    [op(v[8]), [op(1
 .. 4, v)]]], f, x, y)\n" }{MPLTEXT 1 0 19 "            end do\n" }
{MPLTEXT 1 0 15 "        end if\n" }{MPLTEXT 1 0 12 "    end do;\n" }
{MPLTEXT 1 0 8 "    res\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "A:=a*x^4+b*x^2*y+c*x*y^2+d*y^3+e*x
^3*y+f*x^2*y^2+g*x*y^3+h*y^4+j*x^5+k*x^4*y+l*x^3*y^2+m*x^2*y^3+n*x*y^4
+p*y^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,>*&%\"aG\"\"\")%\"xG
\"\"%F(F(*(%\"bGF()%\"xG\"\"#F(%\"yGF(F(*(%\"cGF(%\"xGF()%\"yGF0F(F(*&
%\"dGF()%\"yG\"\"$F(F(*(%\"eGF()%\"xGF;F(%\"yGF(F(*(%\"fGF()%\"xGF0F()
%\"yGF0F(F(*(%\"gGF(%\"xGF()%\"yGF;F(F(*&%\"hGF()%\"yGF+F(F(*&%\"jGF()
%\"xG\"\"&F(F(*(%\"kGF()%\"xGF+F(%\"yGF(F(*(%\"lGF()%\"xGF;F()%\"yGF0F
(F(*(%\"mGF()%\"xGF0F()%\"yGF;F(F(*(%\"nGF(%\"xGF()%\"yGF+F(F(*&%\"pGF
()%\"yGFTF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polynomia
l [1]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"!-%'RootOfG6#,(*&%\"pG\"\"
\")%#_ZG\"\"#F+F+*&%\"hGF+F-F+F+%\"dGF+*&%\"xGF+-F&6#,(*&%\"dGF+)F-F.F
+F+*&%\"cGF+F-F+F+%\"bGF+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "di
scrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A1:=eval(A,b
=c^2/4/d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,>*&%\"aG\"\"\")%
\"xG\"\"%F(F(*,F+!\"\"%\"cG\"\"#%\"dGF-%\"xGF/%\"yGF(F(*(%\"cGF(%\"xGF
()%\"yGF/F(F(*&%\"dGF()%\"yG\"\"$F(F(*(%\"eGF()%\"xGF<F(%\"yGF(F(*(%\"
fGF()%\"xGF/F()%\"yGF/F(F(*(%\"gGF(%\"xGF()%\"yGF<F(F(*&%\"hGF()%\"yGF
+F(F(*&%\"jGF()%\"xG\"\"&F(F(*(%\"kGF()%\"xGF+F(%\"yGF(F(*(%\"lGF()%\"
xGF<F()%\"yGF/F(F(*(%\"mGF()%\"xGF/F()%\"yGF<F(F(*(%\"nGF(%\"xGF()%\"y
GF+F(F(*&%\"pGF()%\"yGFUF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "r
eevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 
"factor(A1);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#,$*(\"\"%!\"\",>**F%
\"\"\"%\"aGF))%\"xGF%F)%\"dGF)F)*()%\"cG\"\"#F))%\"xGF1F)%\"yGF)F)*,F%
F)%\"cGF)%\"xGF))%\"yGF1F)%\"dGF)F)*(F%F))%\"dGF1F))%\"yG\"\"$F)F)*,F%
F)%\"eGF))%\"xGF@F)%\"yGF)%\"dGF)F)*,F%F)%\"fGF))%\"xGF1F))%\"yGF1F)%
\"dGF)F)*,F%F)%\"gGF)%\"xGF))%\"yGF@F)%\"dGF)F)**F%F)%\"hGF))%\"yGF%F)
%\"dGF)F)**F%F)%\"jGF))%\"xG\"\"&F)%\"dGF)F)*,F%F)%\"kGF))%\"xGF%F)%\"
yGF)%\"dGF)F)*,F%F)%\"lGF))%\"xGF@F))%\"yGF1F)%\"dGF)F)*,F%F)%\"mGF))%
\"xGF1F))%\"yGF@F)%\"dGF)F)*,F%F)%\"nGF)%\"xGF))%\"yGF%F)%\"dGF)F)**F%
F)%\"pGF))%\"yGFgnF)%\"dGF)F)F)%\"dGF&F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#<%\"\"!-%'RootOfG6#,(*&%\"pG\"\"\")%#_ZG\"\"#F+F+*&%\"hGF+F-F+F+%\"
dGF+,&*,\"#k!\"\",,*(\"#;F+)%\"dG\"\"%F+%\"aGF+F5**F.F+%\"gGF+)%\"cG\"
\"$F+%\"dGF+F+**\"\")F+%\"eGF+%\"cGF+)%\"dGFAF+F+*&%\"hGF+)%\"cGF;F+F5
**F;F+%\"fGF+)%\"cGF.F+)%\"dGF.F+F5F.%\"cG!\"#%\"dG!\"),$*,FDF+%\"xGF+
,,*(F8F+)%\"dGF;F+%\"aGF+F5**F.F+%\"gGF+)%\"cGFAF+%\"dGF+F+**FDF+%\"eG
F+%\"cGF+)%\"dGFAF+F+*&%\"hGF+)%\"cGF;F+F5**F;F+%\"fGF+)%\"cGF.F+)%\"d
GF.F+F5F5%\"cGF+%\"dGF;F5#FAF.F+**F.F5%\"xGF+%\"cGF+%\"dGF5F5" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 57 "solve(-16*d^4*a+2*g*c^3*d+8*e*c*d^3-h*c^4
-4*f*c^2*d^2,e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\")!\"\",**(
\"#;\"\"\")%\"dG\"\"%F*%\"aGF*F***\"\"#F*%\"gGF*)%\"cG\"\"$F*%\"dGF*F&
*&%\"hGF*)%\"cGF-F*F***F-F*%\"fGF*)%\"cGF0F*)%\"dGF0F*F*F*%\"cGF&%\"dG
!\"$F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A2:=eval(A1,e=%);
" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#>%#A2G,>*&%\"aG\"\"\")%\"xG\"\"%F
(F(*,F+!\"\"%\"cG\"\"#%\"dGF-%\"xGF/%\"yGF(F(*(%\"cGF(%\"xGF()%\"yGF/F
(F(*&%\"dGF()%\"yG\"\"$F(F(*.\"\")F-,**(\"#;F()%\"dGF+F(%\"aGF(F(**F/F
(%\"gGF()%\"cGF<F(%\"dGF(F-*&%\"hGF()%\"cGF+F(F(**F+F(%\"fGF()%\"cGF/F
()%\"dGF/F(F(F(%\"cGF-%\"dG!\"$%\"xGF<%\"yGF(F(*(%\"fGF()%\"xGF/F()%\"
yGF/F(F(*(%\"gGF(%\"xGF()%\"yGF<F(F(*&%\"hGF()%\"yGF+F(F(*&%\"jGF()%\"
xG\"\"&F(F(*(%\"kGF()%\"xGF+F(%\"yGF(F(*(%\"lGF()%\"xGF<F()%\"yGF/F(F(
*(%\"mGF()%\"xGF/F()%\"yGF<F(F(*(%\"nGF(%\"xGF()%\"yGF+F(F(*&%\"pGF()%
\"yGFfoF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynom
ial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=0,y
,0);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#<%\"\"!-%'RootOfG6#,(*&%\"pG
\"\"\")%#_ZG\"\"#F+F+*&%\"hGF+F-F+F+%\"dGF+,&**F.!\"\"%\"xGF+%\"cGF+%
\"dGF4F4*&)%\"xGF.F+-F&6#,2**\"#;F+)%\"cGF.F+)%\"dG\"\"&F+)F-F.F+F+*&,
***F?F+%\"gGF+)%\"cG\"\"$F+)%\"dGFLF+F4**F?F+%\"fGF+)%\"cGF.F+)%\"dG\"
\"%F+F+**\"#7F+%\"hGF+)%\"cGFUF+)%\"dGF.F+F+*(\"#kF+)%\"dG\"\"'F+%\"aG
F+F4F+F-F+F+**\"#KF+%\"jGF+%\"cGF+)%\"dGFDF+F4**F.F+%\"nGF+)%\"cGFDF+%
\"dGF+F4**\"\")F+%\"lGF+)%\"cGFLF+)%\"dGFLF+F4**FUF+%\"mGF+)%\"cGFUF+)
%\"dGF.F+F+**F?F+%\"kGF+)%\"cGF.F+)%\"dGFUF+F+*&%\"pGF+)%\"cGF[oF+F+F+
F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "discrim(16*c^2*d^5*_Z^2+(-16*g*c^3
*d^3+16*f*c^2*d^4+12*h*c^4*d^2-64*d^6*a)*_Z-32*j*c*d^5-2*n*c^5*d-8*l*c
^3*d^3+4*m*c^4*d^2+16*k*c^2*d^4+p*c^6,_Z);" }}{PARA 206 "" 1 "" 
{XPPMATH 20 "6#,$*(\"#;\"\"\")%\"dG\"\"%F&,B**\"$G\"F&)%\"cG\"\"$F&)%
\"dG\"\"'F&%\"jGF&F&**F%F&)%\"cGF2F&)%\"dGF/F&%\"mGF&!\"\"**\"\")F&)%
\"cG\"\"(F&)%\"dG\"\"#F&%\"nGF&F&**\"#kF&)%\"cGF)F&)%\"dG\"\"&F&%\"kGF
&F:**F)F&)%\"cGF<F&%\"dGF&%\"pGF&F:**\"#KF&)%\"cGFJF&)%\"dGF)F&%\"lGF&
F&*,F,F&)%\"cGF/F&)%\"dGFJF&%\"gGF&%\"aGF&F&*,FRF&)%\"cGFJF&)%\"dGF/F&
%\"gGF&%\"fGF&F:**F%F&)%\"cGF2F&)%\"dGFBF&)%\"gGFBF&F&*,\"#CF&)%\"cGF?
F&%\"dGF&%\"gGF&%\"hGF&F:*,\"#'*F&)%\"cGF)F&)%\"dGF)F&%\"hGF&%\"aGF&F:
*,FhoF&)%\"cGF2F&)%\"dGFBF&%\"hGF&%\"fGF&F&*(\"\"*F&)%\"cGF<F&)%\"hGFB
F&F&*(\"$c#F&)%\"dGF<F&)%\"aGFBF&F&*,F,F&)%\"cGFBF&)%\"dGF2F&%\"aGF&%
\"fGF&F:**F%F&)%\"cGF)F&)%\"dGF)F&)%\"fGFBF&F&F&F&" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 226 "solve(128*c^3*d^6*j-16*c^6*d^3*m+8*c^7*d^2
*n-64*c^4*d^5*k-4*c^8*d*p+32*c^5*d^4*l+128*c^3*d^5*g*a-32*c^5*d^3*g*f+
16*c^6*d^2*g^2-24*c^7*d*g*h-96*c^4*d^4*h*a+24*c^6*d^2*h*f+9*c^8*h^2+25
6*d^8*a^2-128*c^2*d^6*a*f+16*c^4*d^4*f^2,k);" }}{PARA 206 "" 1 "" 
{XPPMATH 20 "6#,$**\"#k!\"\",@**\"$G\"\"\"\")%\"cG\"\"$F*)%\"dG\"\"'F*
%\"jGF*F***\"#;F*)%\"cGF0F*)%\"dGF-F*%\"mGF*F&**\"\")F*)%\"cG\"\"(F*)%
\"dG\"\"#F*%\"nGF*F**,\"#KF*)%\"cG\"\"&F*)%\"dGF-F*%\"gGF*%\"fGF*F&**
\"\"%F*)%\"cGF:F*%\"dGF*%\"pGF*F&**FCF*)%\"cGFFF*)%\"dGFLF*%\"lGF*F**,
F)F*)%\"cGF-F*)%\"dGFFF*%\"gGF*%\"aGF*F**,\"#CF*)%\"cGF0F*)%\"dGF@F*%
\"hGF*%\"fGF*F***F3F*)%\"cGF0F*)%\"dGF@F*)%\"gGF@F*F**,FinF*)%\"cGF=F*
%\"dGF*%\"gGF*%\"hGF*F&*,\"#'*F*)%\"cGFLF*)%\"dGFLF*%\"hGF*%\"aGF*F&**
F3F*)%\"cGFLF*)%\"dGFLF*)%\"fGF@F*F**(\"\"*F*)%\"cGF:F*)%\"hGF@F*F**(
\"$c#F*)%\"dGF:F*)%\"aGF@F*F**,F)F*)%\"cGF@F*)%\"dGF0F*%\"aGF*%\"fGF*F
&F*%\"cG!\"%%\"dG!\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
A3:=eval(A2,k=%);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#>%#A3G,>*&%\"aG
\"\"\")%\"xG\"\"%F(F(*,F+!\"\"%\"cG\"\"#%\"dGF-%\"xGF/%\"yGF(F(*(%\"cG
F(%\"xGF()%\"yGF/F(F(*&%\"dGF()%\"yG\"\"$F(F(*.\"\")F-,**(\"#;F()%\"dG
F+F(%\"aGF(F(**F/F(%\"gGF()%\"cGF<F(%\"dGF(F-*&%\"hGF()%\"cGF+F(F(**F+
F(%\"fGF()%\"cGF/F()%\"dGF/F(F(F(%\"cGF-%\"dG!\"$%\"xGF<%\"yGF(F(*(%\"
fGF()%\"xGF/F()%\"yGF/F(F(*(%\"gGF(%\"xGF()%\"yGF<F(F(*&%\"hGF()%\"yGF
+F(F(*&%\"jGF()%\"xG\"\"&F(F(*.\"#kF-,@**\"$G\"F()%\"cGF<F()%\"dG\"\"'
F(%\"jGF(F(**FAF()%\"cGF`pF()%\"dGF<F(%\"mGF(F-**F>F()%\"cG\"\"(F()%\"
dGF/F(%\"nGF(F(*,\"#KF()%\"cGFfoF()%\"dGF<F(%\"gGF(%\"fGF(F-**F+F()%\"
cGF>F(%\"dGF(%\"pGF(F-**F`qF()%\"cGFfoF()%\"dGF+F(%\"lGF(F(*,F[pF()%\"
cGF<F()%\"dGFfoF(%\"gGF(%\"aGF(F(*,\"#CF()%\"cGF`pF()%\"dGF/F(%\"hGF(%
\"fGF(F(**FAF()%\"cGF`pF()%\"dGF/F()%\"gGF/F(F(*,FjrF()%\"cGF[qF(%\"dG
F(%\"gGF(%\"hGF(F-*,\"#'*F()%\"cGF+F()%\"dGF+F(%\"hGF(%\"aGF(F-**FAF()
%\"cGF+F()%\"dGF+F()%\"fGF/F(F(*(\"\"*F()%\"cGF>F()%\"hGF/F(F(*(\"$c#F
()%\"dGF>F()%\"aGF/F(F(*,F[pF()%\"cGF/F()%\"dGF`pF(%\"aGF(%\"fGF(F-F(%
\"cG!\"%%\"dG!\"&%\"xGF+%\"yGF(F(*(%\"lGF()%\"xGF<F()%\"yGF/F(F(*(%\"m
GF()%\"xGF/F()%\"yGF<F(F(*(%\"nGF(%\"xGF()%\"yGF+F(F(*&%\"pGF()%\"yGFf
oF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [4
]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A3,x=0,y,0);" 
}}{PARA 206 "" 1 "" {XPPMATH 20 "6#<%\"\"!,(**\"\"#!\"\"%\"xG\"\"\"%\"
cGF*%\"dGF(F(*,\"\")F(%\"xGF',***\"\"%F*%\"gGF*)%\"cG\"\"$F*%\"dGF*F**
(F6F*%\"hGF*)%\"cGF2F*F(**F2F*%\"fGF*)%\"cGF'F*)%\"dGF'F*F(*(\"#;F*)%
\"dGF2F*%\"aGF*F*F*%\"cG!\"#%\"dG!\"$F**.\"$G\"F(FL#F*F'**%\"xGF*,fo**
\"#KF*)%\"cG\"\"*F*)%\"gGF6F*)%\"dGF6F*F(*,\"#kF*%\"fGF*)%\"cGF.F*)%\"
dGF2F*)%\"gGF'F*F**,FRF*)%\"fGF'F*)%\"cG\"\"(F*)%\"dG\"\"&F*%\"gGF*F(*
,\"#[F*)%\"fGF'F*)%\"cGF.F*)%\"dGF2F*%\"hGF*F**,\"$c#F*)%\"fGF'F*)%\"c
GF2F*)%\"dGF.F*%\"aGF*F**,\"%[?F*%\"fGF*)%\"dG\"#5F*)%\"aGF'F*)%\"cGF'
F*F(*,FenF*%\"lGF*)%\"cGF.F*)%\"dGFeoF*%\"gGF*F(*,FhoF*%\"lGF*)%\"cGFU
F*)%\"dGF2F*%\"hGF*F**,FenF*%\"lGF*)%\"cGFboF*)%\"dG\"\"'F*%\"fGF*F**,
FapF*%\"lGF*)%\"cGFeoF*)%\"dGF.F*%\"aGF*F(*,\"$W\"F*)%\"hGF'F*)%\"cGF.
F*)%\"dGF2F*%\"aGF*F(*,\"$o(F*%\"hGF*)%\"cGF2F*)%\"dGF.F*)%\"aGF'F*F(*
,FhoF*%\"nGF*)%\"cGF^qF*%\"gGF*)%\"dGF6F*F(*,FhoF*%\"nGF*)%\"cGFUF*)%
\"dGF2F*%\"fGF*F**,\"$#>F*%\"nGF*)%\"cGFboF*)%\"dGFgrF*%\"aGF*F(*,FapF
*)%\"cGFgrF*)%\"dGFboF*%\"jGF*%\"gGF*F**,FauF*)%\"cGFboF*)%\"dGFgrF*%
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GF*F(F(%\"cGFbo%\"dGF.#FeoF',fo**FRF*)%\"cGFUF*)%\"gGF6F*)%\"dGF6F*F(*
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F(*,FapF*)%\"cGFgrF*)%\"dGFboF*%\"jGF*%\"gGF*F**,FauF*)%\"cGFboF*)%\"d
GFgrF*%\"jGF*%\"hGF*F(*,FapF*)%\"cGFeoF*)%\"dGF.F*%\"jGF*%\"fGF*F(*,F^
wF*)%\"cGF6F*)%\"dGF^qF*%\"jGF*%\"aGF*F**,FenF*)%\"cGFUF*)%\"dGF2F*%\"
mGF*%\"gGF*F**,FenF*)%\"cGF.F*)%\"dGFeoF*%\"mGF*%\"fGF*F(*,FhoF*)%\"cG
F^qF*%\"mGF*%\"hGF*)%\"dGF6F*F(*,FapF*)%\"cGFgrF*)%\"dGFboF*%\"mGF*%\"
aGF*F**,FRF*)%\"cGF^qF*%\"pGF*%\"fGF*)%\"dGF6F*F(*,FLF*)%\"cGF.F*)%\"d
GFeoF*%\"pGF*%\"aGF*F**,F`zF*)%\"cGF6F*)%\"dGFUF*%\"gGF*)%\"aGF'F*F**.
FasF*%\"fGF*)%\"cGFUF*%\"gGF*%\"hGF*)%\"dGF6F*F(*.FapF*%\"fGF*)%\"cGFe
oF*)%\"dGFboF*%\"gGF*%\"aGF*F(*.FauF*%\"hGF*)%\"cGFboF*)%\"dGFeoF*%\"g
GF*%\"aGF*F**(Fa\\lF*)%\"hGF6F*)%\"cGFf\\lF*F**,Fh\\lF*%\"fGF*)%\"cGF^
qF*)%\"hGF'F*)%\"dGF'F*F**,Fa]lF*%\"hGF*)%\"cGF^qF*)%\"gGF'F*)%\"dGF'F
*F**,Fj]lF*)%\"hGF'F*)%\"cGF_^lF*%\"gGF*%\"dGF*F(*,Fc^lF*%\"nGF*)%\"cG
F_^lF*%\"hGF*)%\"dGF'F*F**(F[_lF*)%\"dGFf\\lF*)%\"aGF6F*F**,FRF*)%\"cG
F_^lF*%\"pGF*%\"gGF*)%\"dGF'F*F**,Fh_lF*)%\"cGFf\\lF*%\"pGF*%\"hGF*%\"
dGF*F(F6%\"cG!#@%\"dG!#CF*-%'RootOfG6#,(*&%\"pGF*)%#_ZGF'F*F**&%\"hGF*
FhamF*F*%\"dGF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "numerator =0 [
2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 614 "factor(-32*c^9*g^3*d
^3+64*f*c^8*d^4*g^2-32*f^2*c^7*d^5*g+48*f^2*c^8*d^4*h+256*f^2*c^4*d^8*
a-2048*f*d^10*a^2*c^2-64*l*c^8*d^5*g+48*l*c^9*d^4*h+64*l*c^7*d^6*f-256
*l*c^5*d^8*a-144*h^2*c^8*d^4*a-768*h*c^4*d^8*a^2-48*n*c^10*g*d^3+48*n*
c^9*d^4*f-192*n*c^7*d^6*a+256*c^6*d^7*j*g-192*c^7*d^6*j*h-256*c^5*d^8*
j*f+1024*c^3*d^10*j*a+64*c^9*d^4*m*g-64*c^8*d^5*m*f-48*c^10*m*h*d^3+25
6*c^6*d^7*m*a-32*c^10*p*f*d^3+128*c^8*d^5*p*a+1536*c^3*d^9*g*a^2-144*f
*c^9*g*h*d^3-256*f*c^5*d^7*g*a+192*h*c^7*d^5*g*a+27*h^3*c^12+72*f*c^10
*h^2*d^2+96*h*c^10*g^2*d^2-90*h^2*c^11*g*d+36*n*c^11*h*d^2+4096*d^12*a
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#*&,***\"\"%\"\"\"%\"gGF')%\"cG\"\"$F'%\"dGF'F'*(F+F'%\"hGF')%\"cGF&F'
!\"\"**F&F'%\"fGF')%\"cG\"\"#F')%\"dGF6F'F1*(\"#;F')%\"dGF&F'%\"aGF'F'
F',<*(\"$c#F')%\"dG\"\")F')%\"aGF6F'F'*,\"#kF')%\"cGF6F')%\"dG\"\"'F'%
\"aGF'%\"fGF'F1*,\"#KF')%\"cGF+F')%\"dG\"\"&F'%\"gGF'%\"aGF'F'**FGF')%
\"cGF+F')%\"dGFLF'%\"jGF'F'**F:F')%\"cGFUF')%\"dGF&F'%\"lGF'F1**F:F')%
\"cGFLF')%\"dGF+F'%\"mGF'F'*,FCF')%\"cGFUF')%\"dGF+F'%\"gGF'%\"fGF'F'*
*\"#7F')%\"cG\"\"(F')%\"dGF6F'%\"nGF'F1*,F\\pF')%\"cGFLF')%\"dGF6F'%\"
hGF'%\"fGF'F1**FCF')%\"cGFLF')%\"dGF6F')%\"gGF6F'F1*,\"#=F')%\"cGF_pF'
%\"dGF'%\"gGF'%\"hGF'F'**FCF')%\"cGFCF'%\"dGF'%\"pGF'F'*(\"\"*F')%\"cG
FCF')%\"hGF6F'F1F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "B case: sho
rt factor=0; A case: long factor=0 [7]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "solve(4*g*c^3*d-3*h*c^4-4*f*c^2*d^2+16*d^4*a,f);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"%!\"\",(**F%\"\"\"%\"gGF))%\"c
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GF()%\"yGF/F(F(*&%\"dGF()%\"yG\"\"$F(F(*.\"\")F-,(*(\"#KF()%\"dGF+F(%
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cGF-%\"dG!\"$%\"xGF<%\"yGF(F(*.F+F-,(**F+F(%\"gGF()%\"cGF<F(%\"dGF(F(*
(F<F(%\"hGF()%\"cGF+F(F-*(\"#;F()%\"dGF+F(%\"aGF(F(F(%\"cG!\"#%\"dGF^o
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(**FinF()%\"cGFipF()%\"dGF<F(%\"mGF(F-**F>F()%\"cG\"\"(F()%\"dGF/F(%\"
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GF(%\"hGF(F-*,\"#'*F()%\"cGF+F()%\"dGF+F(%\"hGF(%\"aGF(F-*$),(**F+F(%
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aGF(F(F/F(F(*(\"\"*F()%\"cGF>F()%\"hGF/F(F(*(\"$c#F()%\"dGF>F()%\"aGF/
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{PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG 
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cGF<F*)%\"yGF-F*)%\"dGF-F*%\"nGF*F&*.F5F*)%\"xGF-F*)%\"cGF<F*%\"yGF*)%
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F**,\"#KF*)%\"xGF-F*%\"yGF*)%\"dGFAF*%\"aGF*F**.F5F*%\"xGF*)%\"cGF<F*)
%\"yGF-F*)%\"dGF-F*%\"hGF*F&*.F5F*%\"xGF*)%\"cGF<F*)%\"yGF<F*)%\"dGF-F
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GF-F*)%\"yGF<F*)%\"dGF<F*%\"nGF*F**.FTF*%\"xGF*)%\"cGF-F*)%\"yGF-F*)%
\"dGF<F*%\"gGF*F***FTF*)%\"yGF-F*)%\"dGF5F*)%\"cGF-F*F**,FTF*)%\"cGF-F
*)%\"yGF<F*)%\"dGF<F*%\"hGF*F**,FTF*)%\"cGF-F*)%\"yGF5F*)%\"dGF<F*%\"p
GF*F*F*%\"cG!\"#%\"dG!\"%F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "po
lynomial factors, so case B complete [5]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 179 "solve(256*d^8*a^2-64*c^2*d^6*a*f+32*c^3*d^5*g*a+64*c
^3*d^6*j-16*c^5*d^4*l+16*c^6*d^3*m+8*c^5*d^3*g*f-12*c^7*d^2*n-12*c^6*d
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206 "" 1 "" {XPPMATH 20 "6#,$**\"#;!\"\",:*(\"$c#\"\"\")%\"dG\"\")F*)%
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{MPLTEXT 1 0 17 "A4:=eval(A3,l=%);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6
#>%#A4G,>*&%\"aG\"\"\")%\"xG\"\"%F(F(*,F+!\"\"%\"cG\"\"#%\"dGF-%\"xGF/
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F<%\"yGF(F(*(%\"fGF()%\"xGF/F()%\"yGF/F(F(*(%\"gGF(%\"xGF()%\"yGF<F(F(
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F<F()%\"dGF`pF(%\"jGF(F(*,F`qF()%\"cGF`pF()%\"dGF/F(%\"hGF(%\"fGF(F-**
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 1556 "discrim((2048*c^7*d^11*a*f+288*h^
2*c^13*d^5-8192*c^5*d^13*a^2+256*c^11*d^7*g^2+384*h*c^11*d^7*f-256*c^1
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1 "" {XPPMATH 20 "6#,$**\"%C5\"\"\")%\"cG\"#5F&)%\"dGF)F&,^t*,\"')o9\"
F&%\"gGF&)%\"dG\"#8F&)%\"aG\"\"$F&)%\"cGF5F&F&**\"#kF&)%\"dG\"\"%F&)%
\"cG\"#7F&)%\"gGF<F&F&*,F9F&)%\"dG\"\"'F&)%\"cGF)F&)%\"gG\"\"#F&)%\"fG
FJF&F&*,\"$G\"F&)%\"dG\"\"&F&)%\"cG\"#6F&)%\"gGF5F&%\"fGF&!\"\"*,\"&s'
GF&)%\"dGF?F&)%\"aGFJF&)%\"fGFJF&)%\"cGF<F&F&*,FNF&%\"hGF&)%\"cGF)F&)%
\"dGFEF&)%\"fGF5F&F&*,\"&?>)F&%\"hGF&)%\"dGF?F&)%\"aGF5F&)%\"cGF<F&FX*
,\"&CQ\"F&)%\"hGFJF&)%\"cG\"\")F&)%\"dGFdpF&)%\"aGFJF&F&*,\"$%QF&%\"nG
F&)%\"cGFTF&)%\"dGFEF&)%\"fGFJF&F&*,\"%WhF&%\"nGF&)%\"cG\"\"(F&)%\"dGF
)F&)%\"aGFJF&F&*,FjpF&%\"pGF&)%\"cGF?F&)%\"fGFJF&)%\"dGFQF&FX*,FcqF&%
\"pGF&)%\"cGFdpF&)%\"dG\"\"*F&)%\"aGFJF&FX*,\"%O:F&)%\"gGF5F&)%\"cGFjr
F&)%\"dGFgqF&%\"aGF&F&*,\"&/:#F&)%\"gGFJF&)%\"cGFEF&)%\"dGF)F&)%\"aGFJ
F&F&*,\"$c#F&%\"mGF&)%\"cGF?F&)%\"gGFJF&)%\"dGFQF&FX*,FatF&%\"mGF&)%\"
cGF)F&)%\"dGFgqF&)%\"fGFJF&FX*,\"%'4%F&%\"mGF&)%\"cGFEF&)%\"dGFTF&)%\"
aGFJF&FX*,\"%[?F&)%\"dGFdpF&)%\"cGFjrF&%\"jGF&)%\"gGFJF&F&*,\"%_6F&)%
\"dGFEF&)%\"cGFTF&%\"jGF&)%\"hGFJF&F&*,F[vF&)%\"dGF)F&)%\"cGFgqF&%\"jG
F&)%\"fGFJF&F&*,F[vF&)%\"dGF)F&)%\"cGFEF&%\"aGF&)%\"fGF5F&FX*.\"%sIF&)
%\"dGFgqF&)%\"cGF)F&%\"jGF&%\"gGF&%\"hGF&FX*.\"&#zLF&%\"hGF&)%\"cGFgqF
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%\"gGFJF&%\"aGF&FX*.\"$w&F&%\"hGF&)%\"cGFTF&%\"gGF&)%\"fGFJF&)%\"dGFQF
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cGFTF&%\"gGF&%\"aGF&)%\"dGFQF&F&*0\"%;#*F&%\"hGF&)%\"cGFjrF&)%\"dGFgqF
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F&%\"fGF&%\"aGF&F&*.\"%?^F&%\"gGF&)%\"cGFgqF&)%\"dGFjrF&)%\"fGFJF&%\"a
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)%\"gGFJF&)%\"cGFdpF&)%\"dGFdpF&%\"fGF&%\"aGF&FX*.\"$7&F&%\"mGF&)%\"cG
FTF&)%\"dGFEF&%\"gGF&%\"fGF&F&*.F[vF&%\"mGF&)%\"cGFjrF&)%\"dGFdpF&%\"g
GF&%\"aGF&FX*.FjpF&%\"mGF&)%\"cGF?F&%\"hGF&%\"fGF&)%\"dGFQF&FX*.F^sF&%
\"mGF&)%\"cGF)F&)%\"dGFgqF&%\"hGF&%\"aGF&F&*.F[vF&%\"mGF&)%\"cGFdpF&)%
\"dGFjrF&%\"fGF&%\"aGF&F&*.FbuF&)%\"dGFjrF&)%\"cGFdpF&%\"jGF&%\"gGF&%
\"fGF&FX*.\"&%Q;F&)%\"dGFTF&)%\"cGFEF&%\"jGF&%\"gGF&%\"aGF&F&*.F]xF&)%
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gqF&%\"jGF&%\"hGF&%\"aGF&FX*.F]flF&)%\"dGF?F&)%\"cGFQF&%\"jGF&%\"fGF&%
\"aGF&FX*(\"'3m>F&)%\"dG\"#;F&)%\"aGF<F&F&*(\"$N\"F&)%\"hGF<F&)%\"cGFb
hlF&F&*.FjyF&%\"pGF&)%\"cG\"#:F&%\"gGF&%\"hGF&)%\"dGFJF&F&*,\"$;%F&%\"
hGF&)%\"cGF2F&)%\"gGF5F&)%\"dGF5F&FX*,\"$c(F&)%\"hGFJF&)%\"cG\"#9F&)%
\"gGFJF&)%\"dGFJF&F&*,\"$S&F&)%\"hGF5F&)%\"cGF_ilF&%\"gGF&%\"dGF&FX*,
\"$K%F&)%\"hGF5F&)%\"cGFcjlF&%\"fGF&)%\"dGFJF&F&*,\"%G<F&)%\"hGF5F&)%
\"cGF?F&%\"aGF&)%\"dGF<F&FX*,Fa[mF&)%\"hGFJF&)%\"cGF?F&)%\"fGFJF&)%\"d
GF<F&F&*,FjpF&%\"nGF&)%\"cGF2F&)%\"gGFJF&)%\"dGF<F&F&*,\"$;#F&%\"nGF&)
%\"cGF_ilF&)%\"hGFJF&)%\"dGFJF&F&*,FjpF&%\"pGF&)%\"cGFcjlF&)%\"gGFJF&)
%\"dGF5F&FX*,Fd]mF&%\"pGF&)%\"cGFbhlF&)%\"hGFJF&%\"dGF&FX*,\"$W\"F&%\"
mGF&)%\"cGFcjlF&)%\"hGFJF&)%\"dGF5F&FX*,\"&oF$F&)%\"dGFcjlF&%\"jGF&)%
\"aGFJF&)%\"cGF5F&F&*,\"'s58F&)%\"dGFcjlF&)%\"aGF5F&%\"fGF&)%\"cGFJF&F
X*.\"$k)F&%\"hGF&)%\"cGF?F&)%\"gGFJF&%\"fGF&)%\"dGF<F&F&*.FdvF&)%\"hGF
JF&)%\"cGF2F&%\"gGF&%\"fGF&)%\"dGF5F&FX*.FjyF&%\"nGF&)%\"cGFcjlF&%\"gG
F&%\"hGF&)%\"dGF5F&FX*.FjyF&%\"nGF&)%\"cGF2F&%\"hGF&%\"fGF&)%\"dGF<F&F
&*.Fe]lF&%\"pGF&)%\"cGF2F&%\"gGF&%\"fGF&)%\"dGF<F&F&*.FjyF&%\"pGF&)%\"
cGFcjlF&%\"hGF&%\"fGF&)%\"dGF5F&FX*.FjpF&%\"mGF&)%\"cGF2F&%\"gGF&%\"hG
F&)%\"dGF<F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "facto
r(%);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#,$*,\"%C5\"\"\")%\"cG\"#5F&)
%\"dGF)F&),***\"\"%F&%\"gGF&)%\"cG\"\"$F&%\"dGF&F&*(F3F&%\"hGF&)%\"cGF
/F&!\"\"**F/F&%\"fGF&)%\"cG\"\"#F&)%\"dGF>F&F9*(\"#;F&)%\"dGF/F&%\"aGF
&F&F>F&,:*(\"$o(F&)%\"dG\"\")F&)%\"aGF>F&F&*,\"$G\"F&)%\"cGF>F&)%\"dG
\"\"'F&%\"aGF&%\"fGF&F9*,\"#kF&)%\"cGF3F&)%\"dG\"\"&F&%\"gGF&%\"aGF&F&
*,\"#KF&)%\"cGF/F&)%\"dGF/F&%\"hGF&%\"aGF&F9**FOF&)%\"cGF3F&)%\"dGFTF&
%\"jGF&F&**FBF&)%\"cGFTF&)%\"dGF3F&%\"mGF&F9**F/F&)%\"cGFTF&)%\"dGF>F&
)%\"gGF>F&F&**\"#CF&)%\"cG\"\"(F&)%\"dGF>F&%\"nGF&F&*,FKF&)%\"cGFTF&)%
\"dGF>F&%\"hGF&%\"fGF&F&**FfpF&)%\"cGFKF&%\"dGF&%\"pGF&F9*,\"#?F&)%\"c
GFipF&%\"dGF&%\"gGF&%\"hGF&F9*(\"#:F&)%\"cGFKF&)%\"hGF>F&F&F&F&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "The shorter factor is the same as \+
in case B, so it need not be considered again [7]." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 170 "solve(768*d^8*a^2-128*c^2*d^6*a*f+64*c^3*d
^5*g*a-32*c^4*d^4*h*a+128*c^3*d^6*j-16*c^6*d^3*m+4*c^6*d^2*g^2+24*c^7*
d^2*n+8*c^6*d^2*h*f-24*c^8*d*p-20*c^7*d*g*h+15*c^8*h^2,j);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$**\"$G\"!\"\",8*(\"$o(\"\"\")%\"dG\"\")F*)
%\"aG\"\"#F*F**,F%F*)%\"cGF0F*)%\"dG\"\"'F*%\"aGF*%\"fGF*F&*,\"#kF*)%
\"cG\"\"$F*)%\"dG\"\"&F*%\"gGF*%\"aGF*F**,\"#KF*)%\"cG\"\"%F*)%\"dGFGF
*%\"hGF*%\"aGF*F&*,F-F*)%\"cGF6F*)%\"dGF0F*%\"hGF*%\"fGF*F***\"#;F*)%
\"cGF6F*)%\"dGF=F*%\"mGF*F&**FGF*)%\"cGF6F*)%\"dGF0F*)%\"gGF0F*F***\"#
CF*)%\"cG\"\"(F*)%\"dGF0F*%\"nGF*F***F\\oF*)%\"cGF-F*%\"dGF*%\"pGF*F&*
,\"#?F*)%\"cGF_oF*%\"dGF*%\"gGF*%\"hGF*F&*(\"#:F*)%\"cGF-F*)%\"hGF0F*F
*F*%\"cG!\"$%\"dG!\"'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
A5:=eval(A4,j=%);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#>%#A5G,>*&%\"aG
\"\"\")%\"xG\"\"%F(F(*,F+!\"\"%\"cG\"\"#%\"dGF-%\"xGF/%\"yGF(F(*(%\"cG
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hGF+)%\"dGFAF+F4*.F\\jlF+%\"pGF+)%\"cGFNF+)%\"gGF.F+%\"fGF+)%\"dGF]qF+
F4*.FifnF+%\"pGF+)%\"cGFapF+)%\"hGF.F+%\"fGF+)%\"dGFAF+F4*.FcgnF+%\"pG
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\"cGFapF+%\"fGF+)%\"hGF=F+)%\"dGF.F+F+*,FadmF+)%\"dGFNF+)%\"fGF.F+)%\"
aGFAF+)%\"cGF=F+F+*,F\\boF+)%\"cGFNF+%\"hGF+)%\"gGF=F+)%\"dGF=F+F+*,Fe
boF+)%\"cGFapF+)%\"hGFAF+)%\"gGF.F+)%\"dGF.F+F+*,F_coF+)%\"cGFbvF+)%\"
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{PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 2513 "factor(-1080*p*c^20*h^3*d+65536*m*d^15*a^3*c^6
-432*m*c^18*h^3*d^3+567*c^20*h^5-9216*c^16*n*f*g*h*d^5-2048*c^16*n*g^3
*d^5+11520*p*c^17*g*h*f*d^4+2560*p*c^17*g^3*d^4-16384*d^14*f^3*a^2*c^6
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*g*d^5-589824*d^16*h*a^4*c^4+180224*d^14*a^3*g^2*c^6+4096*d^11*c^9*g^3
*a^2-3072*d^8*c^12*g^4*a+41472*d^8*c^12*h^3*a^2+1024*m*c^15*g^3*d^6-10
24*m*c^12*d^9*f^3-131072*d^14*n*a^3*c^7+2048*n*c^13*d^8*f^3+512*h*c^12
*d^8*f^4+163840*p*c^8*d^13*a^3-2560*p*c^14*d^7*f^3-768*d^7*c^13*f^2*g^
3+256*d^8*c^12*f^3*g^2+24576*d^12*c^8*a^3*h^2+768*c^14*f*g^4*d^6+2496*
c^14*f^3*h^2*d^6-3072*d^10*c^10*f^2*g^2*a+18432*m*c^12*d^9*h*f*a-46080
*p*c^15*h*g*a*d^6-18432*m*c^13*d^8*g*h*a-3072*d^7*c^13*f^3*g*h+46080*p
*c^14*d^7*h*a*f-61440*p*c^13*d^8*g*a*f-92160*p*c^12*d^9*h*a^2-122880*p
*c^10*d^11*f*a^2+30720*p*c^12*d^9*f^2*a+7680*p*c^15*f^2*g*d^6+30720*p*
c^14*d^7*g^2*a+6144*d^9*c^11*f*g^3*a+55296*d^10*c^10*f*h^2*a^2+69120*d
^7*c^13*f*h^2*g*a-25344*d^8*c^12*f^2*h^2*a-12288*d^12*c^8*f^2*h*a^2+30
720*d^9*c^11*f^2*h*g*a-6144*d^10*c^10*f^3*h*a-24576*d^11*c^9*f*a^2*g*h
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*a*f-92160*d^9*c^11*h^2*g*a^2-45504*c^14*h^2*g^2*a*d^6+6720*c^14*f^2*g
^2*h*d^6-196608*d^13*a^3*g*h*c^7-3072*m*c^14*d^7*g^2*f+3072*m*c^13*d^8
*g*f^2+49152*m*c^9*d^12*g*a^2+6912*m*c^14*d^7*h^2*a-2304*m*c^14*d^7*h*
f^2-36864*m*c^10*d^11*h*a^2+12288*m*c^10*d^11*f^2*a-49152*m*c^8*d^13*f
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*f*g*a-6144*d^7*c^14*n*f^2*g+6144*c^15*n*f*g^2*d^6+4608*c^15*n*f^2*h*d
^6-24576*d^10*c^11*n*f^2*a+98304*d^12*c^9*n*f*a^2-13824*c^15*n*h^2*a*d
^6+73728*d^10*c^11*n*h*a^2-98304*d^11*c^10*n*g*a^2+49152*d^9*c^12*n*f*
g*a+36864*d^7*c^14*n*h*g*a+122880*d^10*c^11*p*g*a^2-24576*n*c^13*d^8*g
^2*a-36864*n*c^13*d^8*h*f*a+4608*m*c^15*g*h*f*d^6-36864*d^12*c^8*f*g^2
*a^2+12288*m*c^12*d^9*g^2*a-9792*c^15*f^2*g*h^2*d^5+12528*c^16*f*g^2*h
^2*d^4+1728*m*c^17*g*h^2*d^4+4320*p*c^19*g*h^2*d^2-5760*p*c^18*g^2*h*d
^3-7680*p*c^16*g^2*f*d^5-4320*p*c^18*h^2*f*d^3-5760*p*c^16*f^2*h*d^5+1
7280*p*c^16*a*h^2*d^5-6272*c^15*f*g^3*h*d^5-9504*c^17*f*h^3*g*d^3-3932
16*d^15*a^3*g*f*c^5-1728*m*c^16*h^2*f*d^5+262144*d^14*h*a^3*f*c^6+3456
*c^17*n*f*h^2*d^4+4608*c^17*n*h*g^2*d^4-3456*c^18*n*h^2*g*d^3+786432*d
^17*a^4*g*c^3-786432*d^18*a^4*f*c^2+3888*c^16*f^2*h^3*d^4+2484*c^18*f*
h^4*d^2+196608*d^16*f^2*a^3*c^4+2112*c^16*h*g^4*d^4+5724*c^18*h^3*g^2*
d^2-5232*c^17*h^2*g^3*d^3-2916*c^19*h^4*g*d-9072*c^16*h^4*a*d^4-2304*m
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\"%\"gGF()%\"cG\"\"$F(%\"dGF(F(*(F,F(%\"hGF()%\"cGF'F(!\"\"**F'F(%\"fG
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%\"dG\"\")F()%\"aGF7F(F(**F;F()%\"cG\"\"'F()%\"dGF,F(%\"mGF(F(**\"#KF(
)%\"cG\"\"(F()%\"dGF7F(%\"nGF(F2*,FDF()%\"cGFJF()%\"dGF7F(%\"hGF(%\"fG
F(F2**F'F()%\"cGFJF()%\"dGF7F()%\"gGF7F(F2**\"#SF()%\"cGFDF(%\"dGF(%\"
pGF(F(*,\"#CF()%\"cGFRF(%\"dGF(%\"gGF(%\"hGF(F(*(\"#@F()%\"cGFDF()%\"h
GF7F(F2F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "As previously, the s
horter factor is the same as in case B and need not be considered agai
n [7]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "solve(256*d^8*a^
2+16*c^6*d^3*m-32*c^7*d^2*n-8*c^6*d^2*h*f-4*c^6*d^2*g^2+40*c^8*d*p+24*
c^7*d*g*h-21*c^8*h^2,m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"#;!
\"\",0*(\"$c#\"\"\")%\"dG\"\")F*)%\"aG\"\"#F*F***\"#SF*)%\"cGF-F*%\"dG
F*%\"pGF*F***\"#KF*)%\"cG\"\"(F*)%\"dGF0F*%\"nGF*F&*,F-F*)%\"cG\"\"'F*
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%\"xGF()%\"yGF/F(F(*&%\"dGF()%\"yG\"\"$F(F(*.\"\")F-,**(\"#;F()%\"dGF+
F(%\"aGF(F(**F/F(%\"gGF()%\"cGF<F(%\"dGF(F-*&%\"hGF()%\"cGF+F(F(**F+F(
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\"\"'F(%\"aGF(%\"fGF(F-*,\"#kF()%\"cGF<F()%\"dG\"\"&F(%\"gGF(%\"aGF(F(
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pGF(F(**F>F()%\"cG\"\"(F()%\"dGF/F(%\"nGF(F-*,F+F()%\"cGF\\rF(%\"dGF(%
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F-*.FdpF-,8*(\"%O:F()%\"dGF>F()%\"aGF/F(F-*,FdpF()%\"cGF<F()%\"dGFipF(
%\"gGF(%\"aGF(F(*,F]qF()%\"cGF+F()%\"dGF+F(%\"hGF(%\"aGF(F-*,F>F()%\"c
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qF()%\"cGF\\rF()%\"dGF/F(%\"nGF(F(**F+F()%\"cGF`pF()%\"dGF/F()%\"gGF/F
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F/F(F(**FAF()%\"cGF+F()%\"dGF+F()%\"fGF/F(F(*,FAF()%\"cGFipF()%\"dGF<F
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gGF/F(F-*,F>F()%\"cGF\\rF(%\"dGF(%\"gGF(%\"hGF(F-*(\"#:F()%\"cGF>F()%
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x%\"xGF<%\"yGF/F(*.FAF-,0*(\"$c#F()%\"dGF>F()%\"aGF/F(F(**FgyF()%\"cGF
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`pF()%\"dGF/F(%\"hGF(%\"fGF(F-**F+F()%\"cGF`pF()%\"dGF/F()%\"gGF/F(F-*
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()%\"yGFipF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate poly
nomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A6,x=
0,y,0);" }}{PARA 206 "" 1 "" {XPPMATH 20 "6#<%\"\"!-%'RootOfG6#,(*&%\"
pG\"\"\")%#_ZG\"\"#F+F+*&%\"hGF+F-F+F+%\"dGF+,***F.!\"\"%\"xGF+%\"cGF+
%\"dGF4F4*,\"\")F4%\"xGF.,***\"\"%F+%\"gGF+)%\"cG\"\"$F+%\"dGF+F+*(FAF
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=F+%\"aGF+F+F+%\"cG!\"#%\"dG!\"$F+*,\"#KF4%\"xGFA,2*,\"#7F+)%\"cG\"\"'
F+)%\"dGF.F+%\"hGF+%\"fGF+F4**F9F+)%\"cGFhnF+)%\"dGF.F+)%\"gGF.F+F4*(
\"\"*F+)%\"cGF9F+)%\"hGF.F+F4*(\"$c#F+)%\"dGF9F+)%\"aGF.F+F+*,\"#=F+)%
\"cG\"\"(F+%\"dGF+%\"gGF+%\"hGF+F+*,FWF+)%\"cGFAF+)%\"dG\"\"&F+%\"gGF+
%\"aGF+F+*,\"#kF+)%\"cGF.F+)%\"dGFhnF+%\"aGF+%\"fGF+F4*,F9F+)%\"cGF]qF
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.\"&oF$F+)%\"dG\"#9F+)%\"cG\"#5F+)%\"aGF.F+)%\"fGFAF+%\"hGF+F4*.\"'3m>
F+)%\"dGF\\sF+)%\"cGF_sF+)%\"aGF.F+)%\"fGF.F+)%\"gGF.F+F4*.\"';KRF+)%
\"dGF\\sF+)%\"cGF_sF+)%\"aGFAF+%\"fGF+)%\"hGF.F+F+*.\"'s58F+)%\"dG\"#:
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0*f^3*c^18*h^3*a*d^10-737280*f^2*c^16*d^12*h^3*a^2+1474560*f*c^17*d^11
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GF()%\"cG\"\"$F(%\"dGF(F(*(F,F(%\"hGF()%\"cGF'F(!\"\"**F'F(%\"fGF()%\"
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{MPLTEXT 1 0 39 "solve(256*d^8*a^2+4*c^8*d*p-c^8*h^2,p);" }}{PARA 11 "
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F(%\"aGF(F-F(%\"cGFV%\"dG!\"'%\"xGFipF-*.FdpF-,4*(\"%SQF()%\"dGF>F()%
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%\"cGF>F()%\"hGF/F(F-*,F+F()%\"cGF]tF(%\"dGF(%\"gGF(%\"hGF(F(**F+F()%
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%\"aGF*%\"yGF*%\"xGF*F***\"\")F*)%\"dG\"\"$F*%\"yGF*)%\"cG\"\"%F*F&**F
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GF>F*F&*,F>F*%\"gGF*%\"dGF*)%\"cGF-F*)%\"xGF>F*F**.F:F*%\"gGF*)%\"dGF>
F*)%\"cGF:F*%\"yGF*%\"xGF*F&F*,:*,\"#;F*)%\"dGF6F*)%\"cGF6F*%\"aGF*)%
\"xGF6F*F**.F)F*)%\"dGF-F*%\"cGF*%\"aGF*)%\"yGF>F*%\"xGF*F**.FCF*)%\"d
GF:F*)%\"cGF>F*%\"aGF*%\"yGF*)%\"xGF>F*F**,F:F*)%\"dGF>F*)%\"cGF-F*%\"
yGF*%\"xGF*F***F3F*)%\"dGF6F*)%\"cGF:F*)%\"yGF>F*F**.F:F*)%\"dGF>F*)%
\"cGF:F*%\"yGF*)%\"xGF>F*%\"fGF*F***F%F*%\"aGF*)%\"yGF6F*)%\"dGFYF*F**
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\"gGF*%\"dGF*)%\"cGF-F*%\"yGF*)%\"xGF>F*F&*.F:F*%\"gGF*)%\"dGF>F*)%\"c
GF:F*)%\"yGF>F*%\"xGF*F*F*%\"dG!\"&%\"cG!\")F&" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 22 "polynomial factors [5]" }}}}{MARK "0 0 0" 0 }
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