Singular

LIB "tropical.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
ring r=0,(t,x,y,z),dp;
ideal i=-y2t4+x2,yt3+xz+y;
intvec w=2,-4,0,4;
displayTropicalLifting(tropicalLifting(i,w,3),"subst");
==> LP algorithm being used: "cddgmp".
==> Groebner basis Engine being used: "gfan".
==> 0
==> 0
==> 0
==> The procedure has created a list of lists. The jth entry of this list
==> contains a ring, an integer and an intvec.
==> In this ring lives an ideal representing the wanted lifting,
==> if the integer is N then in the parametrisation t has to be replaced by t\
   ^1/N,
==> and if the ith component of the intvec is w[i] then the ith component in \
   LIFT
==> should be multiplied by t^-w[i]/N in order to get the parametrisation.
==> 
==> Suppose your list has the name L, then you can access the 1st ring via:
==> 
==> def LIFTRing=L[1]; setring LIFTRing; LIFT;
==> 
==> The lifting of the point in the tropical variety lives in the ring
==> Q[[t^(1/2)]]
==> 
==> The lifting has the form:
==> x=(1)*t^(4/2)
==> y=(1)
==> z=(-1)*1/t^(4/2) + (-1)*t^(2/2)
==> 
==> Substituting the solution into the ideal gives:
==> i[1]=0
==> i[2]=0