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, as there is  no output
basering;///does show the ring
==> // coefficients: QQ(I, T, Px, Py, Cx, Cy, Sx, Sy, a, b, dt, dx, dy)
==> // 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;
f;
==> i^3*sx+t^3*cx^2+(-dt)*cy^2
ComplexValue(f);
==> t^6*sx^4-2*t^6*sx^2+t^6+(-2*dt)*t^3*sx^2*sy^2+(2*dt)*t^3*sx^2+(2*dt)*t^3*\
   sy^2+(-2*dt)*t^3+sx^2+(dt^2)*sy^4+(-2*dt^2)*sy^2+(dt^2)