Singular

LIB "finitediff.lib";
list D="Ut","Ux","Uy","U";
list V="t","x","y";
list P="a","b";
setinitials(V,D,P);////does not show the ring, since there is no output
basering;///does show the ring
==> //   characteristic : 0
==> //   13 parameter    : I T Px Py Cx Cy Sx Sy a b dt dx dy 
==> //   minpoly        : 0
==> //   number of vars : 8
==> //        block   1 : ordering c
==> //        block   2 : ordering lp
==> //                  : names    i t x y cx cy sx sy
==> // quotient ring from ideal
==> _[1]=cy^2+sy^2-1
==> _[2]=cx^2+sx^2-1
==> _[3]=i^2+1
poly f=t**3*cx**2-cy**2*dt+i**3*sx;
PartitionVar(f,1); ////i is the first variable
==> [1]:
==>    i^3*sx
==> [2]:
==>    t^3*cx^2+(-dt)*cy^2