next | previous | forward | backward | up | index | toc

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

## Synopsis

• Usage:
rationalFunctionAnnihilator f
rationalFunctionAnnihilator(g,f)
• Inputs:
• f, , polynomial
• g, , polynomial
• Outputs:
• an ideal, left ideal of the Weyl algebra

## Description

rationalFunctionAnnihilator f computes the annihilator ideal in the Weyl algebra of th, e rational function $1/f$.
rationalFunctionAnnihilator(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 variable(s) 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 = rationalFunctionAnnihilator (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 rationalFunctionAnnihilator :

• rationalFunctionAnnihilator(RingElement)
• rationalFunctionAnnihilator(RingElement,RingElement)

## For the programmer

The object rationalFunctionAnnihilator is .