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 x1,…,xn and ∂1,…,∂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 |