LIB "tropicalNewton.lib";
ring r = (0,t),(p01,p02,p12,p03,p13,p23,p04,p14,p24,p34),dp;
number uniformizingParameter = t;
export(uniformizingParameter);
ideal I =
p23*p14-p13*p24+p12*p34,
p23*p04-p03*p24+p02*p34,
p13*p04-p03*p14+p01*p34,
p12*p04-p02*p14+p01*p24,
p12*p03-p02*p13+p01*p23;
system("--random",1337);
printlevel = 3;
matrix p = tropicalPointNewton(I);
==> maximal independent set: 1,1,1,0,1,1,0,0,1,1
==> substituting p01 with number of valuation 59
==> substituting p02 with number of valuation 14
==> substituting p12 with number of valuation 87
==> substituting p13 with number of valuation 16
==> substituting p23 with number of valuation 63
==> substituting p24 with number of valuation 90
==> substituting p34 with number of valuation 8
==> computing triangular decomposition (picking first factor)
==> starting analysis of Newton polygons
==> possible valuations for p14 (picking first): (968*t^104+1870*t^95+4136*t^\
   89+7990*t^80+1738*t^74+3960*t^73+7650*t^64+7426*t^59-5658*t^58-3936*t^56-\
   3198*t^55+7110*t^43-2760*t^42-1920*t^40-1560*t^39-2760*t^35-1920*t^33-156\
   0*t^32)/(29*t^22+71)
==> possible valuations for p04 (picking first): (-9889*t^175-14674*t^174-422\
   53*t^160-62698*t^159-13079*t^156-24211*t^153-35926*t^152-40455*t^144-6003\
   0*t^143-55883*t^141-103447*t^138-153502*t^137-32021*t^134-53505*t^125-990\
   45*t^122-146970*t^121-136817*t^119-130995*t^103+36300*t^102+70125*t^93+15\
   5100*t^87+299625*t^78+7744*t^75+68563*t^72+148500*t^71+14960*t^66+6545*t^\
   63+286875*t^62+33088*t^60+292951*t^57-212175*t^56-147600*t^54-119925*t^53\
   +63920*t^51+27965*t^48+13904*t^45+31680*t^44+6083*t^42+280485*t^41-103500\
   *t^40-72000*t^38-58500*t^37+61200*t^35-103500*t^33+26775*t^32-72000*t^31+\
   908*t^30-45264*t^29-5497*t^27-45387*t^26-13776*t^24-11193*t^23+56880*t^14\
   -22080*t^13+9525*t^11-22140*t^10-6720*t^8-5460*t^7-22080*t^6-15360*t^4-22\
   140*t^3-6720*t-5460)/(1189*t^86+580*t^70+2911*t^64+580*t^63+1420*t^48+142\
   0*t^41)
==> possible valuations for p03 (picking first): (-899*t^133-1334*t^132-1189*\
   t^114-2201*t^111-3266*t^110-2911*t^92+3300*t^60+6375*t^51+704*t^33+6233*t\
   ^30+1360*t^24+595*t^21+1264*t^3+553)/(82*t^80+40*t^64+40*t^57)
==> time used total: 0
==> computing independent set: 0
==> computing triangular decomposition: 0
==> analyzing newton polygons: 0
print(p);
==> -59,-14,-87,57,-16,-63,41,-32,-90,-8
intvec w = cccMatrixToPositiveIntvec(p);
print(w);
==> 32,
==> 77,
==> 4,
==> 148,
==> 75,
==> 28,
==> 132,
==> 59,
==> 1,
==> 83 
def s = switchRingsAndComputeInitialIdeal(I,w);
==> time used computing initial ideal: 0
kill uniformizingParameter;