{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 
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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 0 174 "A1:=a*y^2*x+0*x^4+0*x^2*y+y
^2+2*x^3*y+v*y^3+c*x^2*y^2+d*x*y^3+e*y^4+0*x^5+g*x^4*y+h*x^3*y^2+j*x^2
*y^3+k*x*y^4+l*y^5+1*x^6+n*x^5*y+p*x^4*y^2+q*x^3*y^3+r*x^2*y^4+s*x*y^5
+t*y^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,H*(%\"aG\"\"\")%\"yG
\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(%\"c
GF()F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&%\"eGF()F*\"\"%F(F(*(%\"gGF()F,F<
F(F*F(F(*(%\"hGF(F/F(F)F(F(*(%\"jGF(F6F(F3F(F(*(%\"kGF(F,F(F;F(F(*&%\"
lGF()F*\"\"&F(F(*$)F,\"\"'F(F(*(%\"nGF()F,FIF(F*F(F(*(%\"pGF(F?F(F)F(F
(*(%\"qGF(F/F(F3F(F(*(%\"rGF(F6F(F;F(F(*(%\"sGF(F,F(FHF(F(*&%\"tGF()F*
FLF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "define polynomial [1]" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A1,x=0,y,0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,,*&%\"tG\"\"\")%#_ZG\"
\"%F*F**&%\"lGF*)F,\"\"$F*F**&%\"vGF*F,F*F**&%\"eGF*)F,\"\"#F*F*F*F*,&
*&),&%\"gG!\"\"%\"aGF*F-F*)*&%\"xGF*,&F<F*F>F=F=#\"\"(F7F*F**(F;F1FAF1
FB!\"$F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A2:=eval(A1,g=a);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#A2G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*
$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(%\"cGF()F,F+F(F)F(F(*
(%\"dGF(F,F(F3F(F(*&%\"eGF()F*\"\"%F(F(*(F'F()F,F<F(F*F(F(*(%\"hGF(F/F
(F)F(F(*(%\"jGF(F6F(F3F(F(*(%\"kGF(F,F(F;F(F(*&%\"lGF()F*\"\"&F(F(*$)F
,\"\"'F(F(*(%\"nGF()F,FHF(F*F(F(*(%\"pGF(F>F(F)F(F(*(%\"qGF(F/F(F3F(F(
*(%\"rGF(F6F(F;F(F(*(%\"sGF(F,F(FGF(F(*&%\"tGF()F*FKF(F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A2,x=0,y,0);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,,*&%\"tG\"\"\")%#_ZG\"\"%F*F**&%
\"lGF*)F,\"\"$F*F**&%\"vGF*F,F*F**&%\"eGF*)F,\"\"#F*F*F*F*,&*$)%\"xGF1
F*!\"\"*&)F;F-F*-F%6#,**&%\"aGF*F,F*F<%\"nGF<*$F6F*F*%\"cGF*F*F*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 25 "A3:=eval(A2,c=1/4*a^2+n);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#A3G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*(
F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F()
F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&%\"eGF()F*F7F(F(*(F'F()F,F7F(F*F(F(*(
%\"hGF(F/F(F)F(F(*(%\"jGF(F:F(F3F(F(*(%\"kGF(F,F(F?F(F(*&%\"lGF()F*\"
\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FKF(F*F(F(*(%\"pGF(FAF(F)F(F(*(%\"qGF(F/
F(F3F(F(*(%\"rGF(F:F(F?F(F(*(%\"sGF(F,F(FJF(F(*&%\"tGF()F*FNF(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "revaluate polynomial [3]" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A3,x=0,y,0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,(*(\"#K!\"\",(*&%\"nG\"\"\"%\"aGF+F
+*&\"\"#F+%\"hGF+F'*&F.F+%\"vGF+F+\"\"&*&%\"xGF+,(*(F.F'F*F+F,F+F+F/F'
F1F+F'#\"\"*F.F+*,F&F'F,F+F(\"\"%F4F:F5!\"%F+**\"\")F'F(\"\"$F4F>F5!\"
$F'-%'RootOfG6#,,*&%\"tGF+)%#_ZGF:F+F+*&%\"lGF+)FGF>F+F+*&F1F+FGF+F+*&
%\"eGF+)FGF.F+F+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator
=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "A4:=eval(A3,h=1/2
*n*a+v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A4G,H*(%\"aG\"\"\")%\"y
G\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*
&\"\"%!\"\"F'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&%\"eGF()F*
F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(%\"jGF(
F:F(F3F(F(*(%\"kGF(F,F(F?F(F(*&%\"lGF()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F(
)F,FLF(F*F(F(*(%\"pGF(FAF(F)F(F(*(%\"qGF(F/F(F3F(F(*(%\"rGF(F:F(F?F(F(
*(%\"sGF(F,F(FKF(F(*&%\"tGF()F*FOF(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(A4,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#<$,(*$)%\"xG\"\"$\"\"\"!\"\"*(\"\"#F*%\"aGF)F'\"\"%F)*&)F'\"\"&F)-%
'RootOfG6#,0*&\"#;F))%#_ZGF,F)F)*&,&*&F7F)%\"nGF)F**&\"\")F))F-F,F)F)F
)F9F)F)*(F.F)F=F)F@F)F**(F?F)%\"vGF)F-F)F)*&F7F)%\"pGF)F)*$)F-F.F)F)*&
F7F)%\"dGF)F*F)F)-F36#,,*&%\"tGF))F9F.F)F)*&%\"lGF))F9F(F)F)*&FCF)F9F)
F)*&%\"eGF)F8F)F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=
0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "expand((-16*n+8*a^
2)^2-4*16*(-4*n*a^2+8*v*a+16*p+a^4-16*d));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,**&\"$c#\"\"\")%\"nG\"\"#F&F&*(\"$7&F&%\"vGF&%\"aGF&!
\"\"*&\"%C5F&%\"pGF&F.*&F0F&%\"dGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "A5:=eval(A4,p=1/1024*(256*n^2-512*v*a+1024*d));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A5G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"x
GF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F
'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&%\"eGF()F*F7F(F(*(F'F(
)F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(%\"jGF(F:F(F3F(F(*(
%\"kGF(F,F(F?F(F(*&%\"lGF()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FLF(F*F(F
(*(,(*&F7F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FAF(F)F(F(*(%\"qGF(F/F(F3F(F(*(
%\"rGF(F:F(F?F(F(*(%\"sGF(F,F(FKF(F(*&%\"tGF()F*FOF(F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "puiseux(A5,x=0,y,0);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#<$,**(\"%'4%!\"\",**&%\"vG\"\"\")%\"aG\"\"#F+F+*
(F.F+F*F+%\"nGF+F'*(F.F+%\"dGF+F-F+F'*&\"\"%F+%\"jGF+F+\"\"'*&%\"xGF+,
**(F4F'F*F+F-F.F+*(F.F'F*F+F0F+F'*(F.F'F2F+F-F+F'F5F+F'#\"#6F.F+*,F&F'
F(\"\"&,&*$F,F+F+*&F.F+F0F+F'F+F8F@F9!\"&F'*,\"$7&F'F-F+F(F4F8F4F9!\"%
F+**\"#kF'F(\"\"$F8FJF9!\"$F'-%'RootOfG6#,,*&%\"tGF+)%#_ZGF4F+F+*&%\"l
GF+)FSFJF+F+*&F*F+FSF+F+*&%\"eGF+)FSF.F+F+F+F+" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "A6:=eval(A5,j=-(1/4*v*a^2-1/2*v*n-1/2*d*a));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A6G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"x
GF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F
'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&%\"eGF()F*F7F(F(*(F'F(
)F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(,(*(F7F8F2F(F'F+F8*
(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:F(F3F(F(*(%\"kGF(F,F(F?F(F(*&%\"lGF
()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FOF(F*F(F(*(,(*&F7F8F9F+F(*(F+F8F2
F(F'F(F8F<F(F(FAF(F)F(F(*(%\"qGF(F/F(F3F(F(*(%\"rGF(F:F(F?F(F(*(%\"sGF
(F,F(FNF(F(*&%\"tGF()F*FRF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "
reevlauate the polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "puiseux(A6,x=0,y,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,**$)%
\"xG\"\"$\"\"\"!\"\"*(\"\"#F*%\"aGF)F'\"\"%F)*&)F'\"\"&F),&*&F.F*F-F,F
**&F,F*%\"nGF)F)F)F)*&)F'\"\"'F)-%'RootOfG6#,6*&\"#kF))%#_ZGF,F)F)*&,(
*&\"#;F))F-F(F)F**(F>F)F5F)F-F)F)*&F>F)%\"vGF)F)F)F@F)F)*(\"#KF)%\"dGF
)F5F)F)*(\"\")F))F-F.F)F5F)F**(FDF))F-F,F))F5F,F)F)*(FMF)FHF)FEF)F**$)
F-F8F)F)*&F>F)%\"eGF)F)**FDF)FHF)F5F)F-F)F)*&F>F)%\"qGF)F*F)F)-F:6#,,*
&%\"tGF))F@F.F)F)*&%\"lGF))F@F(F)F)*&FHF)F@F)F)*&FVF)F?F)F)F)F)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 95 "expand((64*n*a+64*v-16*a^3)^2-4*64*(32*n*d-8
*a^4*n+16*a^2*n^2-64*q+a^6-8*v*a^3+16*v*n*a+64*e));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,,**\"%'4%\"\"\"%\"vGF&%\"nGF&%\"aGF&F&*&F%F&)F'\"\"#
F&F&*(\"%#>)F&%\"dGF&F(F&!\"\"*&\"&%Q;F&%\"eGF&F0*&F2F&%\"qGF&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "A7:=eval(A6,e=1/16384*(4096*
v*n*a+4096*v^2-8192*n*d+16384*q));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
>%#A7G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F
(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"
dGF(F,F(F3F(F(*&,***F7F8F2F(F9F(F'F(F(*&F7F8F2F+F(*(F+F8F<F(F9F(F8%\"q
GF(F()F*F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*
(,(*(F7F8F2F(F'F+F8*(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:F(F3F(F(*(%\"kG
F(F,F(FCF(F(*&%\"lGF()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FSF(F*F(F(*(,(
*&F7F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF(F)F(F(*(FBF(F/F(F3F(F(*(%\"rGF(F
:F(FCF(F(*(%\"sGF(F,F(FRF(F(*&%\"tGF()F*FVF(F(" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 26 "reevaluate  polynomial [3]" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 22 "(puiseux(A7,x=0,y,0));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#<$-%'RootOfG6#,,\"\"%\"\"\"*(F(F)%\"tGF))%#_ZGF(F)F)*(F
(F)%\"lGF))F-\"\"$F)F)*&,**$)%\"vG\"\"#F)F)*(F6F)%\"nGF)%\"aGF)F)*&F(F
)%\"qGF)F)*(F7F)%\"dGF)F9F)!\"\"F))F-F7F)F)*(F(F)F6F)F-F)F),,*(\"(_r4#
F?,.*(F(F)F<F)F:F)F?*(F6F))F:F7F)F9F)F?*(F7F)F5F)F:F)F)*(F(F)F>F)F6F)F
?*&\"\")F)%\"kGF)F)**F7F)F>F)F9F)F:F)F)\"\"(*&%\"xGF),.*(F7F?F<F)F:F)F
)**FLF?F6F)F:F7F9F)F)*(F(F?F6F7F:F)F?*(F7F?F>F)F6F)F)FMF?**F(F?F>F)F9F
)F:F)F?F?#\"#8F7F?*,FDF?FE\"\"',(*$)F:F1F)F?*(F(F)F9F)F:F)F)*&F(F)F6F)
F)F)FQFenFR!\"'F?*,\"'s58F?FE\"\"&,&*$FHF)F)*&F7F)F9F)F?F)FQF^oFR!\"&F
)*,\"%#>)F?F:F)FEF(FQF(FR!\"%F)**\"$7&F?FEF1FQF1FR!\"$F)" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 57 "A8:=eval(A7,k=1/8*(v*a^2*n-2*d*n*a-2*v^2*a+4*d*v
+4*q*a));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A8G,H*(%\"aG\"\"\")%\"
yG\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&
*&\"\"%!\"\"F'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&,***F7F8F
2F(F9F(F'F(F(*&F7F8F2F+F(*(F+F8F<F(F9F(F8%\"qGF(F()F*F7F(F(*(F'F()F,F7
F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(,(*(F7F8F2F(F'F+F8*(F+F8
F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:F(F3F(F(*(,,**\"\")F8F2F(F'F+F9F(F(**F7F
8F<F(F9F(F'F(F8*(F7F8F2F+F'F(F8*(F+F8F<F(F2F(F(*(F+F8FBF(F'F(F(F(F,F(F
CF(F(*&%\"lGF()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FYF(F*F(F(*(,(*&F7F8F
9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF(F)F(F(*(FBF(F/F(F3F(F(*(%\"rGF(F:F(FCF(
F(*(%\"sGF(F,F(FXF(F(*&%\"tGF()F*FfnF(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(A8,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<$-%'RootOfG6#,,\"\"%\"\"\"*(F(F)%\"tGF))%#_ZGF(F)F)*(F(F)%\"lGF))F
-\"\"$F)F)*&,**$)%\"vG\"\"#F)F)*(F6F)%\"nGF)%\"aGF)F)*&F(F)%\"qGF)F)*(
F7F)%\"dGF)F9F)!\"\"F))F-F7F)F)*(F(F)F6F)F-F)F),,*$)%\"xGF1F)F?*(F7F?F
:F)FEF(F)*&)FE\"\"&F),&*&F(F?F:F7F?*&F7F?F9F)F)F)F)*&)FE\"\"'F),(*&#F)
\"\")F)*$)F:F1F)F)F)*&#F)F7F)F6F)F?*&#F)F7F)*&F9F)F:F)F)F?F)F)*&)FE\"
\"(F)-F%6#,D*&\"$c#F)F@F)F)*&,,*(\"$7&F)F6F)F:F)F?*&\"#KF))F:F(F)F)*&F
\\oF)F>F)F)*&\"$G\"F))F9F7F)F)*(\"$#>F)F9F))F:F7F)F?F)F-F)F)*(\"#WF)Fc
oF)FgoF)F)*(FboF))F:FIF)F6F)F?*(\"#7F))F:FOF)F9F)F?*(\"$S#F)FjoF)F5F)F
)**\"$g\"F)F6F)FgoF)F:F)F?*&F\\oF)%\"rGF)F)**FioF)FUF)F6F)F9F)F)*$)F:F
SF)F)*(\"#[F)FjoF))F9F1F)F?**FioF)F>F)F6F)F:F)F?**\"#'*F)F>F)F9F)FjoF)
F?*(FfoF)F>F)FgoF)F)*(FfoF)F<F)F9F)F?*&\"#;F))F9F(F)F)*(FdqF)F>F)FcoF)
F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "discrim=0 [4]" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 200 "expand((32*a^4-512*v*a+256*
d-192*n*a^2+128*n^2)^2-4*256*(192*a^3*v*n-96*d*n*a^2-192*d*v*a+16*d*a^
4-48*a^2*n^3-12*a^6*n-32*a^5*v+44*a^4*n^2+a^8+128*d*n^2-160*v*n^2*a+24
0*a^2*v^2+16*n^4+256*r-128*q*n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
0*(\"&%Q;\"\"\")%\"aG\"\"#F&)%\"vGF)F&F&**\"&oF$F&F+F&)%\"nGF)F&F(F&F&
**\"&Ob'F&%\"dGF&F+F&F(F&!\"\"*(F1F&F2F&F.F&F3*(\"'s58F&%\"qGF&F/F&F&*
&F1F&)F2F)F&F&*&\"'W@EF&%\"rGF&F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 99 "A9:=eval(A8,r=1/262144*(65536*d^2-65536*d*v*a+32768*v
*n^2*a+16384*a^2*v^2-65536*d*n^2+131072*q*n));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%#A9G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*(F+
F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F()F,
F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&,***F7F8F2F(F9F(F'F(F(*&F7F8F2F+F(*(F+F
8F<F(F9F(F8%\"qGF(F()F*F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2
F(F(F/F(F)F(F(*(,(*(F7F8F2F(F'F+F8*(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:
F(F3F(F(*(,,**\"\")F8F2F(F'F+F9F(F(**F7F8F<F(F9F(F'F(F8*(F7F8F2F+F'F(F
8*(F+F8F<F(F2F(F(*(F+F8FBF(F'F(F(F(F,F(FCF(F(*&%\"lGF()F*\"\"&F(F(*$)F
,\"\"'F(F(*(F9F()F,FYF(F*F(F(*(,(*&F7F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF
(F)F(F(*(FBF(F/F(F3F(F(*(,.*&F7F8F<F+F(**F7F8F<F(F2F(F'F(F8**FQF8F2F(F
9F+F'F(F(*(\"#;F8F'F+F2F+F(*(F7F8F<F(F9F+F8*(F+F8FBF(F9F(F(F(F:F(FCF(F
(*(%\"sGF(F,F(FXF(F(*&%\"tGF()F*FfnF(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "puiseux(A9,x=0,y,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<$-%'RootOfG6#,,\"\"%\"\"\"*(F(F)%\"tGF))%#_ZGF(F)F)*(F(F)%\"lGF))F
-\"\"$F)F)*&,**$)%\"vG\"\"#F)F)*(F6F)%\"nGF)%\"aGF)F)*&F(F)%\"qGF)F)*(
F7F)%\"dGF)F9F)!\"\"F))F-F7F)F)*(F(F)F6F)F-F)F),.*(\");sx;F?,**(F5F)F:
F)F9F)F)**F7F)F>F)F6F)F9F)F?*(F(F)F<F)F6F)F)*&\"\")F)F/F)F?FJ*&%\"xGF)
,***FJF?F6F7F:F)F9F)F?**F(F?F>F)F6F)F9F)F)*(F7F?F<F)F6F)F?F/F)F?#\"#:F
7F)*,\")KWbLF?FE\"\"(,,*(\"\"'F)F9F))F:F7F)F)*$)F:F(F)F?*&F(F))F9F7F)F
?*&FJF)F>F)F?*(\"#;F)F6F)F:F)F)F)FLFUFM!\"(F?*,\"(_r4#F?FEFX,(*$)F:F1F
)F?*(F(F)F9F)F:F)F)*&F(F)F6F)F)F)FLFXFM!\"'F?*,\"'s58F?FE\"\"&,&*$FYF)
F)*&F7F)F9F)F?F)FLFfoFM!\"&F)*,\"%#>)F?F:F)FEF(FLF(FM!\"%F)**\"$7&F?FE
F1FLF1FM!\"$F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "numerator=0 [2]
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "A10:=eval(A9,l=-(-1/8*v
^2*a*n+1/4*d*v*n-1/2*q*v));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$A10G
,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F(*&%
\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dGF(F,
F(F3F(F(*&,***F7F8F2F(F9F(F'F(F(*&F7F8F2F+F(*(F+F8F<F(F9F(F8%\"qGF(F()
F*F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(,(*(F
7F8F2F(F'F+F8*(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:F(F3F(F(*(,,**\"\")F8
F2F(F'F+F9F(F(**F7F8F<F(F9F(F'F(F8*(F7F8F2F+F'F(F8*(F+F8F<F(F2F(F(*(F+
F8FBF(F'F(F(F(F,F(FCF(F(*&,(**FQF8F2F+F'F(F9F(F(**F7F8F<F(F2F(F9F(F8*(
F+F8FBF(F2F(F(F()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FfnF(F*F(F(*(,(*&F7
F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF(F)F(F(*(FBF(F/F(F3F(F(*(,.*&F7F8F<F+
F(**F7F8F<F(F2F(F'F(F8**FQF8F2F(F9F+F'F(F(*(\"#;F8F'F+F2F+F(*(F7F8F<F(
F9F+F8*(F+F8FBF(F9F(F(F(F:F(FCF(F(*(%\"sGF(F,F(FenF(F(*&%\"tGF()F*FinF
(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "puiseux(A10,x=0,y,0);" 
}}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,,\"\")\"\"\"*(F(F)%\"
tGF))%#_ZG\"\"%F)F)*&,(*()%\"vG\"\"#F)%\"aGF)%\"nGF)F)**F4F)%\"dGF)F3F
)F6F)!\"\"*(F.F)%\"qGF)F3F)F)F))F-\"\"$F)F)*&,**&F4F)F2F)F)*(F.F)F8F)F
6F)F9**F4F)F3F)F6F)F5F)F)*&F(F)F;F)F)F))F-F4F)F)*(F(F)F3F)F-F)F),.*$)%
\"xGF=F)F9*(F4F9F5F)FIF.F)*&)FI\"\"&F),&*&F.F9F5F4F9*&F4F9F6F)F)F)F)*&
)FI\"\"'F),(*&#F)F(F)*$)F5F=F)F)F)*&#F)F4F)F3F)F9*&#F)F4F)*&F6F)F5F)F)
F9F)F)*&)FI\"\"(F),,*&\"#;F9F5F.F9*&F3F)F5F)F)*&F.F9F6F4F9*&F4F9F8F)F9
**F=F)F(F9F6F)F5F4F)F)F)*&)FIF(F)-F%6#,R*&\"%C5F)FDF)F)*&,.*(\"%O:F)F3
F)F6F)F9*(\"$7&F)F6F)FXF)F)*(\"$o(F)F5F))F6F4F)F9*(\"%/BF)F3F))F5F4F)F
)*(F\\pF)F8F)F5F)F9*&\"#kF))F5FMF)F9F)F-F)F)*(\"$#>F))F5F.F))F6F=F)F9*
,\"%39F)F6F)F8F)F3F)F5F)F)**\"%[7F)FXF)F3F)FapF)F9**\"%G<F)FXF)F8F)F3F
)F9**\"$%QF)F[qF)F8F)F6F)F9**\"$w&F)FdpF)F8F)FapF)F)**\"$C'F)FhpF)F3F)
F6F)F)**FfqF)F3F)F\\qF)F5F)F)**\"%#z\"F)F6F)FdpF)F2F)F9*(\"#sF))F5FjnF
)F3F)F9*(F]oF))F5F(F)F6F)F9*(\"%'H\"F)F[qF)F2F)F)*(\"#))F))F5FSF)FapF)
F)*(\"$c#F)F6F))F8F4F)F9*(\"#[F)FerF)F8F)F)*(\"$W\"F)FdpF))F6F.F)F)*(F
fqF)FdpF)FhrF)F)*(F^pF)F;F)F8F)F)*(FfqF)FapF)F2F)F)*$)F5\"#5F)F)**FgrF
)F;F)F3F)F5F)F9*&FhoF)%\"sGF)F9F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 13 "discrim=0 [4]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "ex
pand((512*a^3*n+2304*v*a^2-64*a^5-1536*d*a-1536*v*n-768*a*n^2)^2-4*102
4*(48*a^6*d-192*a^4*n^3-16*a^8*n-72*a^7*v+88*a^6*n^2+1296*a^4*v^2+144*
a^2*n^4-256*n*d^2-1024*s-384*a^4*d*n+512*q*d+624*a^5*v*n-1248*a^3*v*n^
2+576*a^2*d*n^2+576*a^2*d^2-256*q*v*a+1408*n*d*v*a+576*n^2*v^2-1792*n*
a^2*v^2+576*v*n^3*a+a^10-1728*a^3*d*v));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,.*,\"(w&[5\"\"\"%\"nGF&%\"dGF&%\"vGF&%\"aGF&!\"\"**\"'W@EF&F'F&
)F*\"\"#F&)F)F/F&F&*(F%F&F'F&)F(F/F&F&**F%F&%\"qGF&F)F&F*F&F&*(\"(_r4#
F&F4F&F(F&F+*&\"(/V>%F&%\"sGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 103 "A11:=eval(A10,s=-1/4194304*(1048576*n*d^2-2097152*q*
d+262144*n*a^2*v^2-1048576*n*d*v*a+1048576*q*v*a));" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%$A11G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*
(F+F()F,\"\"$F(F*F(F(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F(
)F,F+F(F)F(F(*(%\"dGF(F,F(F3F(F(*&,***F7F8F2F(F9F(F'F(F(*&F7F8F2F+F(*(
F+F8F<F(F9F(F8%\"qGF(F()F*F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F
(F2F(F(F/F(F)F(F(*(,(*(F7F8F2F(F'F+F8*(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F
(F:F(F3F(F(*(,,**\"\")F8F2F(F'F+F9F(F(**F7F8F<F(F9F(F'F(F8*(F7F8F2F+F'
F(F8*(F+F8F<F(F2F(F(*(F+F8FBF(F'F(F(F(F,F(FCF(F(*&,(**FQF8F2F+F'F(F9F(
F(**F7F8F<F(F2F(F9F(F8*(F+F8FBF(F2F(F(F()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9
F()F,FfnF(F*F(F(*(,(*&F7F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF(F)F(F(*(FBF(
F/F(F3F(F(*(,.*&F7F8F<F+F(**F7F8F<F(F2F(F'F(F8**FQF8F2F(F9F+F'F(F(*(\"
#;F8F'F+F2F+F(*(F7F8F<F(F9F+F8*(F+F8FBF(F9F(F(F(F:F(FCF(F(*(,,*(F7F8F9
F(F<F+F8*(F+F8FBF(F<F(F(**FgoF8F9F(F'F+F2F+F8*,F7F8F9F(F<F(F2F(F'F(F(*
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0 "" 0 "" {TEXT -1 25 "reevaluate polynomial [3]" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 21 "puiseux(A11,x=0,y,0);" }{TEXT -1 0 "" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#<$-%'RootOfG6#,,\"\")\"\"\"*(F(F)%\"tG
F))%#_ZG\"\"%F)F)*&,(*()%\"vG\"\"#F)%\"aGF)%\"nGF)F)**F4F)%\"dGF)F3F)F
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)F9**F4F)F3F)F6F)F5F)F)*&F(F)F;F)F)F))F-F4F)F)*(F(F)F3F)F-F)F),0*$)%\"
xGF=F)F9*(F4F9F5F)FIF.F)*&)FI\"\"&F),&*&F.F9F5F4F9*&F4F9F6F)F)F)F)*&)F
I\"\"'F),(*&#F)F(F)*$)F5F=F)F)F)*&#F)F4F)F3F)F9*&#F)F4F)*&F6F)F5F)F)F9
F)F)*&)FI\"\"(F),,*&\"#;F9F5F.F9*&F3F)F5F)F)*&F.F9F6F4F9*&F4F9F8F)F9**
F=F)F(F9F6F)F5F4F)F)F)*&)FIF(F),.*&\"#KF9F5FMF)*(F.F9F6F)F5F=F9**F=F)F
(F9F5F)F6F4F)**\"\"*F)F(F9F3F)F5F4F9**F=F)F.F9F3F)F6F)F)**F=F)F.F9F8F)
F5F)F)F)F)*&)FIFjoF)-F%6#,dp**\"%sIF)F8F)F2F))F5F4F)F)*,\"&[[\"F)F8F)F
3F)F6F)FXF)F)*,\"%7pF)F8F)F3F))F6F4F)F5F)F9*,\"%!o(F)F;F)F3F)F6F)F5F)F
9**\"%orF))F3F=F)F5F)F6F)F)**\"&;S\"F)F2F)FdpF)FipF)F)**\"%[?F)F8F)F2F
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)FdpF)F9**FcpF)F;F)F8F)F6F)F)**\"%7`F))F5FMF)F3F)FipF)F9**\"%WhF)F[rF)
F8F)F3F)F9**\"%C5F))F5FSF)F8F)F6F)F9**\"%WHF))F5F.F)F8F)FipF)F)**\"%/:
F))F5FjnF)F3F)F6F)F)**\"%+kF)FXF)F3F))F6F=F)F)**\"%/BF)FdpF)F8F)FirF)F
9**\"%#z\"F)F3F))F6F.F)F5F)F9*(FbqF)F;F)F2F)F9*(\"$o(F)FipF)FfqF)F)*(
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[\"F))F5F(F)FipF)F)*(\"$'\\F)F`rF)FirF)F9*(\"#'*F)F]tF)F8F)F)*(\"$O(F)
FcrF)F^sF)F)*(F[sF)FcrF)FfqF)F)*(\"$7&F)FirF)F2F)F9*(FdqF)FXF)F^qF)F9*
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> " 0 "" {MPLTEXT 1 0 640 "expand((-4096*q-1024*n^3+3072*a^2*n^2+4096*
v^2+128*a^6-4096*n*d+14336*v*n*a-8192*v*a^3+6144*d*a^2-1280*a^4*n)^2-4
*4096*(768*n^2*d^2+64*n^6+4096*t-1536*q*a^2*n^2+640*q*a^4*n-64*q*a^6+5
12*q*n^3+1024*v^4+512*d*n^4-4096*a^3*v^3+3072*d*v^2*a^2-2304*a^2*d*n^3
-512*n^3*v^2+1504*a^7*v*n-5312*a^5*v*n^2+2944*a^4*d*n^2-1792*v*n^4*a+a
^12+6400*a^3*v*n^3-1024*a^6*d*n-6144*a^5*d*v+96*a^8*d-496*a^6*n^3-20*a
^10*n-128*a^9*v+148*a^8*n^2+4160*a^6*v^2+736*a^4*n^4+2304*a^4*d^2-384*
a^2*n^5+7168*v^3*a*n-3072*q*d*a^2-3072*n*d^2*a^2+3072*q*d*n-6912*d*v*n
^2*a-7680*q*v*n*a+14848*d*v*n*a^3-2048*d*v^2*n-14976*v^2*a^4*n+14016*v
^2*a^2*n^2-2048*q*v^2+4096*q*v*a^3));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,0*,\"(/V>%\"\"\"%\"dGF&%\"vGF&)%\"nG\"\"#F&%\"aGF&!\"\"*,\"(3')Q)F
&%\"qGF&F(F&F*F&F,F&F&**\"(w&[5F&)F(F+F&)F,F+F&F)F&F&**\");sx;F&F0F&F'
F&F*F&F-*(F%F&F)F&)F'F+F&F&*&F6F&)F0F+F&F&*&\")k)3r'F&%\"tGF&F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "A12:=eval(A11,t=1/67108864*
(4194304*n^2*d^2+16777216*q^2-16777216*q*d*n-4194304*d*v*n^2*a+8388608
*q*v*n*a+1048576*v^2*a^2*n^2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$
A12G,H*(%\"aG\"\"\")%\"yG\"\"#F(%\"xGF(F(*$F)F(F(*(F+F()F,\"\"$F(F*F(F
(*&%\"vGF()F*F0F(F(*(,&*&\"\"%!\"\"F'F+F(%\"nGF(F()F,F+F(F)F(F(*(%\"dG
F(F,F(F3F(F(*&,***F7F8F2F(F9F(F'F(F(*&F7F8F2F+F(*(F+F8F<F(F9F(F8%\"qGF
(F()F*F7F(F(*(F'F()F,F7F(F*F(F(*(,&*(F+F8F9F(F'F(F(F2F(F(F/F(F)F(F(*(,
(*(F7F8F2F(F'F+F8*(F+F8F2F(F9F(F(*(F+F8F<F(F'F(F(F(F:F(F3F(F(*(,,**\"
\")F8F2F(F'F+F9F(F(**F7F8F<F(F9F(F'F(F8*(F7F8F2F+F'F(F8*(F+F8F<F(F2F(F
(*(F+F8FBF(F'F(F(F(F,F(FCF(F(*&,(**FQF8F2F+F'F(F9F(F(**F7F8F<F(F2F(F9F
(F8*(F+F8FBF(F2F(F(F()F*\"\"&F(F(*$)F,\"\"'F(F(*(F9F()F,FfnF(F*F(F(*(,
(*&F7F8F9F+F(*(F+F8F2F(F'F(F8F<F(F(FEF(F)F(F(*(FBF(F/F(F3F(F(*(,.*&F7F
8F<F+F(**F7F8F<F(F2F(F'F(F8**FQF8F2F(F9F+F'F(F(*(\"#;F8F'F+F2F+F(*(F7F
8F<F(F9F+F8*(F+F8FBF(F9F(F(F(F:F(FCF(F(*(,,*(F7F8F9F(F<F+F8*(F+F8FBF(F
<F(F(**FgoF8F9F(F'F+F2F+F8*,F7F8F9F(F<F(F2F(F'F(F(**F7F8FBF(F2F(F'F(F8
F(F,F(FenF(F(*&,.*(FgoF8F9F+F<F+F(*&F7F8FBF+F(**F7F8FBF(F<F(F9F(F8*,Fg
oF8F<F(F2F(F9F+F'F(F8*,FQF8FBF(F2F(F9F(F'F(F(**\"#kF8F2F+F'F+F9F+F(F()
F*FinF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "reevaluate polynomia
l [3]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(A12);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#k!\"\",6**\"\"%\"\"\"%\"yGF*)%
\"xG\"\"#F*%\"nGF*F&*,F.F*F-F*)F+F.F*%\"vGF*%\"aGF*F***)F+\"\"$F*F2F*F
3F*F/F*F&**F)F*F-F*F1F*%\"dGF*F&**F.F*F5F*F8F*F/F*F***F)F*F+F*F-F*F3F*
F&*&\"\")F*F+F*F&*(F)F*F1F*F2F*F&*&F<F*)F-F6F*F&*(F)F*%\"qGF*F5F*F&F.F
*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "polynomial factors [5]" }}}}
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