RatAnn -- annihilator of a rational function in Weyl algebra

Synopsis

Usage:
RatAnn f, RatAnn(g,f)
Inputs:
- f, a ring element, polynomial
- g, a ring element, polynomial
Outputs:
- an ideal, left ideal of the Weyl algebra

Description

RatAnn f computes the annihilator ideal in the Weyl algebra of the rational function 1/f
RatAnn(g,f) computes the annihilator ideal in the Weyl algebra of the rational function g/f

i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx, y=>Dy}]

o1 = W

o1 : PolynomialRing

i2 : f = x^2-y^3

        3    2
o2 = - y  + x

o2 : W

i3 : g = 2*x*y

o3 = 2x*y

o3 : W

i4 : I = RatAnn (g,f)

                                3  2    2  2     2           2  2          3
o4 = ideal (3x*Dx + 2y*Dy + 1, y Dy  - x Dy  + 6y Dy + 6y, 9y Dx Dy - 4y*Dy 
     ------------------------------------------------------------------------
             2      2    3  2     2  2
     + 27y*Dx  + 2Dy , 9y Dx  - 4y Dy  + 10y*Dy - 10)

o4 : Ideal of W

Caveat

The inputs f and g should be elements of a Weyl algebra, and not elements of a commutative polynomial ring. However, f and g should only use the commutative variables.

Ways to use `RatAnn` :

RatAnn(RingElement)
RatAnn(RingElement,RingElement)

RatAnn -- annihilator of a rational function in Weyl algebra

Synopsis

Description

Caveat

See also

Ways to use RatAnn :

Ways to use `RatAnn` :