Ddim -- dimension of a D-module

Synopsis

Usage:

Ddim M

Ddim I
Inputs:
- M, a module, over the Weyl algebra $D$
- I, an ideal, which represents the module $M=D/I$
Outputs:
- an integer, the dimension of $M$

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 $x_1,\dots,x_n$ 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 variable(s)

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

Ways to use Ddim:

Ddim(Ideal)
Ddim(Module)

For the programmer

The object Ddim is a method function.

Ddim -- dimension of a D-module

Synopsis

Description

See also

Ways to use Ddim:

For the programmer