# RatAnn -- annihilator of a rational function in Weyl algebra

## Synopsis

• Usage:
RatAnn f, RatAnn(g,f)
• Inputs:
• f, , polynomial
• g, , 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.