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Dmodules :: Ddim

Ddim -- dimension of a D-module

Synopsis

Description

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

See also

Ways to use Ddim :