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

Synopsis

Usage:

genToDistractionGen(f,thetaRing)
Inputs:
- f, a ring element, 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}, WeylAlgebra => {{x , dx }, {x , dx }, {x , dx }, {x , dx }}]
         1   4    1    4                                                   1    1     2    2     3    3     4    4

Ways to use `genToDistractionGens` :

"genToDistractionGens(RingElement,Ring)"

For the programmer

The object genToDistractionGens is a method function.

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

Synopsis

Description

Ways to use genToDistractionGens :

For the programmer

Ways to use `genToDistractionGens` :