monoid[x,dx,y,dy, WeylAlgebra => {x => dx, y => dy}]
monoid[x,dx,y,dy,h, WeylAlgebra => {x => dx, y => dy, h}]
The WeylAlgebra option may be used to provide a list of variables and their corresponding differential operators in a Weyl algebra. For instance, an option of the form x => dx specifies that dx plays the role of the derivative with respect to x in the resulting Weyl algebra.
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Note that only when the monoid is used to create a polynomial ring the Weyl algebra variables take effect. There are multiple acceptable ways to populate this option, but the differential variable always has to come to the right of the corresponding algebra variable.
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The package Dmodules contains further methods for creating and manipulating Weyl algebras.
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Lastly, if a single variable is provided at the end, it is used as a homogenizing variable.
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This option may also be used when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.