loadPackage "Dmodules";
R=QQ[t,x,Dt,Dx,WeylAlgebra=>{t=>Dt,x=>Dx}];
II=AnnFs( t*(x-t) );
-- use I.ring;
-- J=sub(I,{s=>1/2});
-- It does not work. Why?
I=ideal(t*Dt + 2*t*Dx - x*Dx, - t*Dx + x*Dx - 1/2);
J=Fourier(I);
-- J is ideal(- t*Dt - 2*x*Dt + x*Dx, x*Dt - x*Dx - 3/2)
bFunction(J,{1,0});
-- s(s+2)
G=gbw(J,{-1,0,1,0});
--  ideal (t*Dt + x*Dx + 3, 2x*Dt - 2*x*Dx - 3, 2*t*x*Dx + 2*x^2*Dx + 3*t + 6*x)
Fourier(x*Dx+3);
Dintegration(I,{1,0})