# createDpairs(PolynomialRing) -- pairs up the variables in Weyl algebra

## Synopsis

• Function: createDpairs
• Usage:
createDpairs A
• Inputs:
• A, , the Weyl algebra
• Consequences:
• attaches to A a pair of keys to help distinguish the coordinate variables from the derivation variables.

## Description

Since the Weyl algebra has commutation rules, this routine attaches to the Weyl algebra two keys to organize the variables. The first key 'dpairVars' contains 3 lists: a list of the coordinate variables, a list of the derivative variables, and a list of the central variables. The second key 'dpairInds' also contains 3 lists of the corresponding indices to 'dpairVars'.
 i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing, 2 differential variables i2 : createDpairs W  i3 : W.dpairVars o3 = {{x, y}, {Dx, Dy}, {}} o3 : List i4 : W.dpairInds o4 = {{0, 1}, {2, 3}, {}} o4 : List