-- -*- M2-comint -*- hash: 1886230761

i1 : QQ[x,y,z];

i2 : sys = {y-x^2, z-x^3, (x+y+z-1)/x};

i3 : describe ring ideal sys

o3 = frac/QQ[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]\
         |                                                         {GRevLex => {3:1}  }                  |
         \                                                         {Position => Up    }                  /

i4 : convertedSys = toLaurentPolynomial(sys,w);

i5 : printWidth = 300;

i6 : toString convertedSys

o6 = {y-x^2, z-x^3, -w_0^(-1)+z*w_0^(-1)+y*w_0^(-1)+x*w_0^(-1), w_0-x}

i7 : ring ideal convertedSys

o7 = QQ {x..z, w }
                0

o7 : PolynomialRing

i8 : describe oo

o8 = QQ {x..z, w , Degrees => {4:1}, MonomialOrder => {Weights => {4:-1} }, DegreeRank => 1, Inverses => true, Global => false}
                0                                     {MonomialSize => 32}
                                                      {GroupRevLex => 4  }
                                                      {Position => Up    }

i9 : P = QQ[x,y,z];

i10 : f = (x*y + z^2*y) / y

       2
o10 = z  + x

o10 : frac P

i11 : liftable(f,P)

o11 = true

i12 : lift(f,P)

       2
o12 = z  + x

o12 : P

i13 : 
