WeylAlgebra -- make a Weyl algebra

WeylAlgebra -- make a Weyl algebra

WeylAlgebra -- an option used when creating a polynomial ring to specify that a Weyl algebra is to be produced.

A Weyl algebra is an algebra in which some of the variables behave as derivatives with respect to the other variables.

i1 : R = ZZ/101[x,dx,y,dy,WeylAlgebra => {x=>dx, y=>dy}];

The list {x=>dx, y=>dy} indicates that the variable dx is to play the role of the derivative with respect to x, and that y is to play the role of the derivative with respect to y.

i2 : dx*x



o2 = x*dx + 1



o2 : R

i3 : dx*x^10



      10        9

o3 = x  dx + 10x



o3 : R

i4 : dx*y^10



         10

o4 = dx*y



o4 : R

Functions with optional argument named WeylAlgebra :

graphIdeal(..., WeylAlgebra) -- make a Weyl algebra

graphRing(..., WeylAlgebra) -- make a Weyl algebra

modifyRing(..., WeylAlgebra) -- make a Weyl algebra

symmetricAlgebra(..., WeylAlgebra) -- make a Weyl algebra

tensor(..., WeylAlgebra) -- make a Weyl algebra