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 : makeWA(QQ[x,y])

o1 = QQ[x..y, dx, dy]

o1 : PolynomialRing, 2 differential variables

i2 : f = x^2-y^3

        3    2
o2 = - y  + x

o2 : QQ[x..y, dx, dy]

i3 : g = 2*x*y

o3 = 2x*y

o3 : QQ[x..y, dx, dy]

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 QQ[x..y, dx, dy]

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)"

For the programmer

The object RatAnn is a method function.