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Dmodules :: makeWeylAlgebra

makeWeylAlgebra -- Weyl algebra corresponding to a polynomial ring

Synopsis

Usage:

makeWeylAlgebra R

makeWA R
Inputs:
- R, a polynomial ring, the (commutative) polynomial ring
- SetVariables, a Boolean value, whether to set variables of the created algebra to be global
Optional inputs:
- SetVariables => ..., default value true
Outputs:
- a polynomial ring, the (non-commutative) Weyl algebra

Description

Given a polynomial ring R with variables x_1,..,x_n, this routine returns a Weyl algebra with variables x_1,..,x_n and dx_1,..,dx_n.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : D = makeWeylAlgebra R

o2 = D

o2 : PolynomialRing, 3 differential variables

To skip naming the ring, use parentheses.

i3 : makeWA(QQ[x,y,z])

o3 = QQ[x..z, dx, dy, dz]

o3 : PolynomialRing, 3 differential variables

Caveat

The polynomial ring R must be commutative.

See also

WeylAlgebra -- an optional argument

Ways to use `makeWeylAlgebra` :

"makeWeylAlgebra(PolynomialRing)"

For the programmer

The object makeWeylAlgebra is a method function with options.