The dimension of $M$ is equal to the dimension of the associated graded module with respect to the Bernstein filtration. If $D$ is the Weyl algebra over ℂ with generators $x_1,\dots,x_n$ and $\partial_1,\dots,\partial_n$, then the Bernstein filtration corresponds to the weight vector $(1,...,1,1,...,1)$.
i1 : makeWA(QQ[x,y]) o1 = QQ[x..y, dx, dy] o1 : PolynomialRing, 2 differential variables |
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 QQ[x..y, dx, dy]
|
i3 : Ddim I o3 = 2 |
The object Ddim is a method function.