# Some test examples for the parametrization algorithm:
# genus0_f1 to genus0_f30 all have genus 0, and can all be handled by
# the algcurves package.

# from file: /home/hoeij/maple/IntBasis/vb_F8_winkler
F8:=-2*x1*x2^4*x3^4+x1^4*x2^5+12*x1^4*x2^3*x3^2+12*x1^2*x2^4*x3^3-x1^3*x2*x3^5+11
*x1^3*x2^2*x3^4-21*x1^3*x2^3*x3^3-4*x1^4*x2*x3^4+2*x1^4*x2^2*x3^3-6*x1^4*x2^4*
x3+x1^5*x3^4-3*x1^5*x2^2*x3^2+x1^5*x2^3*x3-3*x1*x2^5*x3^3-2*x1^2*x2^3*x3^4+x1^3
*x2^4*x3^2+x2^5*x3^4:
genus0_f1:=subs(x3=1,x2=y,x1=x,F8):

# from file: /home/hoeij/maple/IntBasis/vb_fraaie_kromme
genus0_f2:=
115605504*y^12-144506880*y^10+31610880*y^8+(26229504-29051904*x)*y^6+(-712320
*x+826980)*y^4+(1512-3276*x)*y^2+1-2*x+x^2:

# from file: /home/hoeij/maple/IntBasis/vb_graad8_ratpar
genus0_f3:=
3440*x^3*y+9792*x*y^3-1330*x^3*y^5-12968*x^3*y^2-2640*x^4*y^4+5300*x^2*y^6-
14858*x^2*y^5-9188*x^6*y+22012*x^2*y^4+8196*x^2*y^2-2861*x^6*y^2+10858*x^3*y^3-
20650*x^2*y^3+9146*x^5*y^2+16068*x^5*y-9792*x*y^6-1513*x^4*y^2-29376*x*y^4-
12236*x^4*y-7664*x^7+1916*x^4-7664*x^5+11496*x^6+1916*x^7*y+1916*x^8+19362*y^6-
12908*y^7+3227*y^4-12908*y^5+3227*y^8+29376*x*y^5:

genus0_f4:=25+1326*y*x+3740*x^3*y+3252*x^2*y+3582*y^3*x^2+4030*x^3*y^2+1476*x^2*y^4+
102*y^6*x+546*y^5*x+1590*y^4*x+244*x+184*y+518*y^2+720*y^3+854*x^2+1338*x^3+576*y^4
+1101*x^4+282*y^5+14*y^7+y^8+84*y^6+4770*y^2*x^2+2706*y^3*x+2646*y^2*x+18*x^7+
508*x^5+132*x^6+x^8+2264*x^4*y+2124*x^3*y^3+1716*x^4*y^2+738*y*x^5+354*y^2*x^5+
570*x^4*y^3+550*x^3*y^4+122*y*x^6+28*y^6*x^2+318*x^2*y^5+8*y^7*x+56*y^3*x^5+56*
y^5*x^3+70*y^4*x^4+28*y^2*x^6+8*y*x^7:

genus0_f5:=
-16*y^3-4-32*y-16*x+1/2*y^7-4*y^8-20*x^2*y^4+x*y^4+x^7+8*x^7*y-4*x^8-8*x^3*y-
x^3*y^5-5*x^4*y^2-8*x^4*y^3+32*x^5+12*x^5*y^2-24*x*y^5-2*x*y^7-6*x^2*y-80*x^2*y
^2:

genus0_f6:=
4*x*y^6+2*x^5*y^3-16*x^5*y-x^4*y^4-8*x^2*y^5+4*x^7-32*x^2*y^3-20*x*y^4-40*x^3
*y-16*x^3*y^4+6*x^2*y^4-4*x*y^7-12*x^2*y^2-4*x^5*y^2-20*x^4*y^2+x^8-32*x^4-8*y^
6+y^4+2*x*y^3+y^8:

genus0_f7:=
y^8-y^7+x*y^7+2*x^3*y^5+3*x*y^5-x*y^4+5*x^2*y^4+2*y^3+x^4*y^3-3*x^5*y^2+5*x^2
*y^2+5*x^4*y^2+y+x^3*y+3*x^2*y-x^7*y+x^8-x^7+1-2*x^5+x:

genus0_f8:=
x^7-6*x^2*y^4+x^3*y+3*x*y^5-3*x^3*y^2+3*x^2*y^3+2*x*y^3+3*x^4*y^3+3*y^5+y^7:

genus0_f9:=
y^7-3*x*y^5-3*y^5+6*x^2*y^4-3*x^4*y^3+2*x*y^3+3*x^2*y^3-3*x^3*y^2-x^3*y+x^7:

genus0_f10:=
y^7-3*x*y^5-3/2*y^5+3*x^2*y^4-1/2*x*y^3+3*x^2*y^3-3/2*x^4*y^3+3*x^3*y^2-x^3*y
-9/2*x^5*y+2*x^7:

genus0_f11:=
y^7-3*x*y^5-6*y^5+12*x^2*y^4+4*x*y^3+3*x^2*y^3-6*x^4*y^3-6*x^3*y^2-x^3*y+2*x^7:

# from file: /home/hoeij/maple/IntBasis/vb_hele_mooie_g0
genus0_f12:=8*y^3+10*x^2*y^4-6*x^5*y^2+2*x^8+8*x+x*y^7+4*x^3*y:

# from file: /home/hoeij/maple/IntBasis/vb_nieuwe_versie_doe
genus0_f13:=y^5+2*x*y^2+2*x*y^3+x^2*y-4*x^3*y+2*x^5:

genus0_f14:=
3610/907*x^2+14440/907*x+14440/907-4508/907*x^2*y-18032/907*x*y-16227/907*y+
5406/907*x^2*y^2+16218/907*x*y^2+10812/907*y^2-2703/907*x^2*y^3-12626/907*x*y^3
-13533/907*y^3+3610/907*x*y^4+3610/907*y^4+1805/907*y^5:

# from file: none
genus0_f15:=x^2+y^2+1:

# from file: /home/hoeij/maple/IntBasis/vb_rat_par_examples
F:=x3^5*x1*x2^4+x3^4*x1*x2^5+x3^5*x1^2*x2^3+x3^3*x1^5*x2^2-19*x3^3*x1^2*x2^5
-53*x3^3*x1^3*x2^4+x3^4*x1^5*x2+x1^5*x2^5+x3^5*x1^5+43*x3^4*x1^3*x2^3
+x3^3*x1^4*x2^3+12*x3^2*x1^4*x2^4+57*x3^2*x1^3*x2^5-19*x3^2*x1^5*x2^3
-36*x3*x1^4*x2^5+x3^5*x2^5+21*x3*x1^5*x2^4-15*x3^5*x1^3*x2^2:
genus0_f16:=subs(x1=x,x2=y,x3=1,F):

genus0_f17:=-y-y^2-2*y^3-y^5-x*y-x*y^3-2*x^2-2*x^2*y^2+x^3+x^4*y:

genus0_f18:=-89325/138014+413549/138014*y-185984/69007*y^2+1518117/552056*y^3-19259/69007*y^4+y^5-155466/69007*x+153719/69007*x*y-392407/138014*x*y^2+31903/138014*x*y^3
-66141/69007*x*y^4-314712/69007*x^2+165666/69007*x^2*y-392063/276028*x^2*y^2-
50807/138014*x^2*y^3-81846/69007*x^3-50807/138014*x^3*y+244125/138014*x^3*y^2-
688135/552056*x^4*y:

genus0_f19:=-y-4*y^2-y^2*x-5*y*x-2*x^2+3*x^2*y-6*y^3-2*y^4+x^3+3*x*y^4+6*y^5*x^2+4*x*y^7+12
*y^5*x+3*y^6+y^9+x^2*y^2+6*x^2*y^3+x*y^3-2*y^5+12*x*y^6+4*y^8+6*y^7+4*x^3*y^3+4
*y^2*x^3+12*y^4*x^2+x^4*y:

genus0_f20:=x^2*y^4-10*x^7*y+22*x^4*y^4+x^8+32*x^6*y^2-6*x^3*y^5+8*y^6*x^2-42*x^5*y^3-6*y
^7*x+y^8+480*y^4*x^6+32*x^8*y^2-640*y^5*x^5+480*y^6*x^4-192*y^7*x^3-192*y^3*x^7
+32*y^8*x^2:

genus0_f21:=y^8+4*y^6*x^2-8*y^5*x^3+6*y^4*x^4-16*y^3*x^5+20*y^2*x^6-8*y*x^7+x^8+4*y^7-60*
y^6*x+24*y^5*x^2+24*y^4*x^3+68*y^3*x^4-156*y^2*x^5+64*y*x^6-32*x^7+68*y^6+184*y
^5*x-116*y^4*x^2+176*y^3*x^3+796*y^2*x^4+408*y*x^5+404*x^6-608*y^5+512*y^4*x-
864*y^3*x^2-3872*y^2*x^3-5056*y*x^4-2656*x^5+1344*y^4-128*y^3*x+11136*y^2*x^2+
18432*y*x^3+10176*x^4-1344*y^3-11840*y^2*x-33152*y*x^2-22912*x^3+3648*y^2+29312
*y*x+29504*x^2-8704*y-20480*x+6400:

genus0_f22:=y^8+4*y^7*x+4*y*x^7+x^8-4*y^7-8*y^6*x+4*y^5*x^2+16*y^4*x^3+16*y^3*x^4+4*y^2*x
^5-8*y*x^6-4*x^7+6*y^6-24*y^4*x^2-48*y^3*x^3-24*y^2*x^4+6*x^6-4*y^5+8*y^4*x+36*
y^3*x^2+36*y^2*x^3+8*y*x^4-4*x^5+y^4-4*y^3*x-16*y^2*x^2-4*y*x^3+x^4:

genus0_f23:=-8+x^5*y+x^6+8*x^3*y^2+x*y^5+4*x*y+2*x^2*y^3-4*x^3*y-16*x*y^2-5*x*y^3+16*x*y^
4-6*x^2*y^2-9*x^2*y^4+x^3*y^3+12*x^2-6*x^4-4*y^6+12*y^2:

genus0_f24:=12222/13*y-22842/13*x^2+11421/13*x^4+11196/13*x^3*y-51/13*x^2*y^2-3477/26*x*y
^3-957/13*x^4*y^2-4611/13*x*y^2-168/13*x*y^5-12222/13*x^2*y+4611/26*x^3*y^2+89/
2*x^3*y^3-11196/13*x*y-2799/13*x^5*y+15228/13+3930/13*y^2+705/13*y^4-33/26*y^5-
3807/26*x^6+287/13*y^3+y^6+6111/26*x^4*y:

genus0_f25:=
-8+4*y+12*x^2-6*x^4+6*y^2-6*x*y^2+y^6+9*x^3*y^3+3*x^3*y^2-9*x^2*y^4+8*x^2*y^3
+7*y^5-3*x^2*y^2-15*x*y^4+6*y^4+2*y^3-9*x*y^3+x^6+x^4*y-4*x^2*y:

genus0_f26:=
y^6-6*y^5*x+12*y^4*x^2-15*y^3*x^3+75/4*y^2*x^4-25/2*x^6+y^5+9*y^4*x-53/2*y^3*
x^2+22*y*x^4-45/4*y^4+30*y^3*x-147/2*y^2*x^2+75*x^4+44*y^3-88*y*x^2+72*y^2-150*
x^2+88*y+100:

# from file: /home/hoeij/maple/IntBasis/vb_sqrfree
genus0_f27:=
147*x^3*y^4-37*x*y^4+80*x*y^5+268*x^2*y^5-29*x^5*y^2-34*x^2*y^3+26*x^5*y-117*
x^3*y^3-122*x^4*y^3+264*x^4*y^4+129*x^3*y^5-23*x^5*y^3-102*x^4*y^5+109*x^5*y^4-
5*x^3*y^2-53*x^5*y^5+x^5-11*y^5-10*x*y^9+61*x*y^8+21*x^2*y^8-86*x*y^7+32*x^2*y^
7+58*x^3*y^7-8*x*y^6-241*x^2*y^6-19*x^4*y^6-212*x^3*y^6+y^10-15*y^9+50*y^8-70*y
^7+45*y^6-46*x^2*y^4-20*x^4*y^2+5*x^4*y+5*x^6+10*x^7+10*x^8+5*x^9+x^10+x^6*y^4+
x^8*y^2-2*x^7*y^2-17*x^6*y^2+6*x^7*y^3+22*x^6*y^3+6*x^9*y+29*x^8*y+56*x^7*y+54*
x^6*y:

# from file: /home/hoeij/maple/IntBasis/vb_voorbeelden_nieuwe_versie
genus0_f28:=
-1-4*y+5*y^2-3*y^3-3*y^4-5*x*y-10*x*y^2+x^2-10*x^2*y+2*x^2*y^2+3*x^3+4*x^3*y+
5*x^4:


genus0_f29:=
36*x^2+9*y^2+36*x*y-34*x^3*y+3*x^4*y^2+12*y^3*x-7*x^2*y^2+3*y^4*x^2+x^6+6*y^4
+y^6-4*x^4:

genus0_f30:=
y^7+6*y^6+27/4*x*y^6+33/4*y^5+48*x^2*y^5-1/3*x*y^5+106*x*y^4-8/3*y^4+6*x^2*y^
4+10/3*x^3*y^4+31/9*x^2*y^3+128/3*y^3+16*x^3*y^3+19/2*x*y^3+6*x^4*y^3+27/4*x^3*
y^2+4/9*x^4*y^2-8/9*x*y^2+40*x^5*y^2+26*x^2*y^2+9/4*x^2*y-5/9*x^3*y+3*x^5*y+96*
x^4*y+16/9*x^6*y+9/2*x^4+54*x^3-8/3*x^6+x^7+22/9*x^5: