Example

The canonical commutation relation can be implemented as

CCR

Needs["Yurie`Algebra`"]

algebraDefine["CCR"]

algebraDefault["CCR"]

<|"Generator"->{x,p},"Relation"->{x**p:>p**x+id}|>//algebraAdd["CCR"]

operatorPower[x,2]**operatorPower[p,2]//algS

Out[] = 2 id+4 p**x+p**p**x**x