stafford(Ideal) -- computes 2 generators for a given ideal in the Weyl algebra

A theorem of Stafford says that every ideal in the Weyl algebra can be generated by 2 elements. This routine is the implementation of the effective version of this theorem following the constructive proof in A.Leykin, `Algorithmic proofs of two theorems of Stafford', Journal of Symbolic Computation, 38(6):1535-1550, 2004.

The current implementation provides a weaker result: the 2 generators produced are guaranteed to generate only the extension of the ideal I in the Weyl algebra with rational-function coefficients.

i1 : R = QQ[x_1..x_4,D_1..D_4, WeylAlgebra=>(apply(4,i->x_(i+1)=>D_(i+1)))] 

o1 = R

o1 : PolynomialRing

i2 : stafford ideal (D_1,D_2,D_3,D_4)

                 4        2        3
o2 = ideal (D , x x D  + x x D  + x D  + x D  + D )
             1   1 4 4    1 3 3    1 4    1 3    2

o2 : Ideal of QQ[x , x , x , x , D , D , D , D ]
                  1   2   3   4   1   2   3   4