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makeWeylAlgebra -- Weyl algebra corresponding to a polynomial ring

Synopsis

Usage:

makeWeylAlgebra R

makeWA R
Inputs:
- R, a polynomial ring, the (commutative) polynomial ring
Optional inputs:
- SetVariables => a Boolean value, default value true, indicates whether the generators should be assigned to global variables
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 variable(s)

To skip naming the ring, use parentheses.

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

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

o3 : PolynomialRing, 3 differential variable(s)

Caveat

The polynomial ring R must be commutative.

See also

monoid(...,WeylAlgebra=>...) -- specify differential operators in the ring

Ways to use makeWeylAlgebra :

makeWeylAlgebra(PolynomialRing)

For the programmer

The object makeWeylAlgebra is a method function with options.

Menu

createDpairs -- pairs coordinate and derivation variables in a Weyl algebra
extractDiffsAlgebra -- underlying polynomial ring in the differentials of a Weyl algebra
extractVarsAlgebra -- underlying polynomial ring in the ordinary variables of a Weyl algebra