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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 25 "restart: with(algcurves):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 2225 "`algcurves/lift_exp` := proc(v, f, x, y
)\nlocal i, ii, r, res, v7, vv7, v3, ext, a, j, n, np, ram, j3;\n    i
f v[5] = 1 then return \{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 erro
r \"degree estimate was wrong\" end if;\n    v7 := (ldegree(ii, x) - v
[2])/v3;\n    r := `algcurves/v_ext_m`(\n        `algcurves/g_factors`
(tcoeff(ii, x), y, v[4]), y);\n    for i in r do res := res union `alg
curves/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    end 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 wr
ong number of expansions\"\n    end if;\n    if v[5] = degree(tcoeff(i
i, x), y) then\n        if ldegree(ii, x) <> vv7 then error \"degree e
stimate was wrong\"\n        end if;\n        return res\n    end if;
\n    ii := collect(ii, y);\n    ii := add(`algcurves/normal_tcoeff`(c
oeff(ii, y, i), x)*y^i,\n        i = 0 .. degree(ii, y));\n    np := `
algcurves/Newtonpolygon`(ii, x, y);\n    if nops(np) = 2 and np[1][3] \+
= 0 then\n        error \"found wrong number of expansions\"\n    end \+
if;\n    for j in np do\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 := `algcurves/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, normal(subs(x = ram, v[3])), ext, i[2],\n            \+
        v[6]*i[4],\n                    (j[2] - j[1]*j[3] - a/degree(r
am, 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    r
es\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "A:=1*x^3*y
+3*x^2*y^2+3*x*y^3+1*y^4+x^5+g*x^4*y+h*x^3*y^2+j*x^2*y^3+k*x*y^4+l*y^5
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,6*&)%\"xG\"\"$\"\"\"%\"yGF
*F**(F)F*)F(\"\"#F*)F+F.F*F**(F)F*F(F*)F+F)F*F**$)F+\"\"%F*F**$)F(\"\"
&F*F**(%\"gGF*)F(F4F*F+F*F**(%\"hGF*F'F*F/F*F**(%\"jGF*F-F*F1F*F**(%\"
kGF*F(F*F3F*F**&%\"lGF*)F+F7F*F*" }}}{EXCHG {PARA 12 "" 1 "" {XPPMATH 
20 "6#74%'SiegelG%0WeierstrassformG%2algfun_series_solG%.differentials
G%&genusG%,homogeneousG%)homologyG%,implicitizeG%/integral_basisG%1is_
hyperellipticG%,j_invariantG%*monodromyG%0parametrizationG%-periodmatr
ixG%*plot_knotG%0plot_real_curveG%(puiseuxG%.singularitiesG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "puiseux(A,x=0,y,0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"!,$*&\"\"\"F'%\"lG!\"\"F),&*&,.%
\"gGF'%\"hGF)%\"kGF)%\"jGF'F(F'F'F)F),$*&%\"xGF'F,F'F)#\"\"%\"\"$F)F3F
)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "A1:=eval(A,h=g-k+j+l-1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G,6*&)%\"xG\"\"$\"\"\"%\"yG
F*F**(F)F*)F(\"\"#F*)F+F.F*F**(F)F*F(F*)F+F)F*F**$)F+\"\"%F*F**$)F(\"
\"&F*F**(%\"gGF*)F(F4F*F+F*F**(,,F9F*%\"kG!\"\"%\"jGF*%\"lGF*F*F>F*F'F
*F/F*F**(F?F*F-F*F1F*F**(F=F*F(F*F3F*F**&F@F*)F+F7F*F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(A1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yGF&F&,:*$)F%\"\"%F&F&*()F%\"\"$F&%\"
gGF&F'F&F&*&F-F&F'F&!\"\"*()F%\"\"#F&)F'F4F&%\"lGF&F&*(F3F&F5F&%\"jGF&
F&*&F'F&F3F&F&*(F3F&F5F&%\"kGF&F1*(F4F&F5F&F%F&F&*(F%F&)F'F.F&F6F&F1*(
F%F&F>F&F;F&F&*$F>F&F&*&)F'F+F&F6F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
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