-- -*- M2-comint -*- {* hash: -775564198 *}

i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]

o1 = W

o1 : PolynomialRing

i2 : I = ideal (x*Dx+2*y*Dy-3, Dx^2-Dy) 

                                2
o2 = ideal (x*Dx + 2y*Dy - 3, Dx  - Dy)

o2 : Ideal of W

i3 : gbw(I, {1,3,3,-1})

                                2  2    2                                   
o3 = ideal (x*Dx + 2y*Dy - 3, 4y Dy  - x Dy + 2x*Dx - 2y*Dy, 2y*Dx*Dy + x*Dy
     ------------------------------------------------------------------------
              2
     - 2Dx, Dx  - Dy)

o3 : Ideal of W

i4 : gbw(I, {-1,-3,1,3})

                                  2
o4 = ideal (x*Dx + 2y*Dy - 3, - Dx  + Dy)

o4 : Ideal of W

i5 :