# genToDistractionGens -- the image in the thetaRing of a torus-fixed element in a Weyl algebra

## Synopsis

• Usage:
genToDistractionGen(f,thetaRing)
• Inputs:
• f, , in a Weyl algebra D of the form x^u Dx^v
• thetaRing, a ring, that is a stand in for the theta ring inside D
• Outputs:
• a list, in thetaRing that is the result of applying [SST, Lemma 2.3.1] to f.

## Description

This function rewrites a monomial $x^u \partial^v$ as a product $x^a p(\theta) \partial^b$, where $\theta_i = x_i \partial_i$ for $i = 1,\dots, n$. This is a step in a procedure for checking that D-ideal is torus-fixed, and is used in the isTorusFixed routine. Code Pre

 i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing i2 : W = makeWA R o2 = W o2 : PolynomialRing, 4 differential variables i3 : describe W o3 = QQ[x ..x , dx ..dx , Degrees => {8:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1, WeylAlgebra => {x => dx , x => dx , x => dx , x => dx }] 1 4 1 4 {GRevLex => {8:1} } 1 1 2 2 3 3 4 4 {Position => Up }

## Ways to use genToDistractionGens :

• "genToDistractionGens(RingElement,Ring)"

## For the programmer

The object genToDistractionGens is .